Hilbert space

Named after German mathematician David Hilbert (1862–1943).

named-after

(functional analysis) A generalized Euclidean space in which mathematical functions take the place of points; crucial to the understanding of quantum mechanics and other applications.


vector space

A vector space is a set of vectors which can be linearly combined.

Each vector space has a basis and dimension.

scalar multiplication
scalar multiplication

(algebra, geometry, topology) A set of elements called vectors, together with some field and operations called addition (mapping two vectors to a vector) and scalar multiplication (mapping a vector and an element in the field to a vector), satisfying a list of constraints; equivalently, a module over a field.


atomic orbital

The physical region or space where an electron can be calculated to be present, as defined by the particular mathematical form of the orbital.


cone

From Middle English cone (“corner, angle”) and conoun (“cone”), from Medieval Latin cōnus, cōnon (“cone, wedge, peak”), from Ancient Greek κῶνος (kônos, “cone, spinning top, pine cone”). Reinforced by Middle French cone, from the same Graeco-Latin source.

der

surface of revolution
surface of revolution

(geometry) A surface of revolution formed by rotating a segment of a line around another line that intersects the first line.

(geometry) A solid of revolution formed by rotating a triangle around one of its altitudes.


wavefunction

The interpretation of the wavefunction was one of the thorny issues facing the early pioneers of quantum theory.

2011, Brian Cox, Jeff Forshaw, The Quantum World, Allen Lane, published 2011, page 41:

(physics) A mathematical function that describes the propagation of the quantum mechanical wave associated with a particle (or system of particles), related to the probability of finding the particle in a particular region of space.


oblong

From Middle English oblong, oblonge, borrowed from Latin oblongus.

Jessamy looked round her in a puzzled way, but there was nothing to see but the pale oblong of what looked like a star-pierced sky behind the bars of the nursery window.

1967, Barbara Sleigh, Jessamy, Sevenoaks, Kent: Bloomsbury, published 1993, →ISBN, page 88:

A rectangle with length and width that are different.

An ellipse with minor and major axes that are different.


oblong

en-verb

oblong (third-person singular simple present oblongs, present participle oblonging, simple past and past participle oblonged)

oblongs (present singular third-person)
oblonging (participle present)
oblonged (participle past)
oblonged (past)

[…]; by John Denmans hom lot on the north sid the front by a salt crek the reare to the comon which hom lot with all the upland oblonging to it conteining to about fourtie acers more or lese with about one acer & half of salt medo liing before the said house[…]

1670, John Bull, signed sealed and delivered in the psents of Antony Waters [/] Rachell (X) Waters; republished as “Town Minutes”, in Town Minutes of Newtown: 1656-1688 (Transcriptions of Early Town Records of New York; […]), volume 1, New York, N.Y.: The Historical Records Survey, 1940 June, pages 181–182:

That the Gilbert tract, according to his opinion and the law, ought to have been oblonged up the creek. That by oblonging it across the creek, it afforded Elijah Robertson, who superintended the surveying, an opportunity of laying a warrant not located there, for himself, and thereby takes 5,000 acres.

1818, John Haywood, “Childress versus Holland. Whyte, Judge, delivered the opinion of himself and Judge Roane.”, in Reports of Cases Argued and Adjudged in the Court of Errors and Appeals of the State of Tennessee, from the Year 1816 to 1817, volume III, Knoxville, Tenn.: […] Heiskell & Brown, page 276:

To extend so as to form an oblong shape.

A. Why, by dropping them off of cars or dropping them off of trucks or some way it would oblong them .

1928, New York Supreme Court, page 2149:

His silhouette: broad shoulders, big legs, a square face oblonged by a crest of thick hair and almost lantern jaw.

2006, Nancy Zafris, Lucky Strike, page 165:

And there were suddenly berries where there had been none before, bright red and bright blue, all with a careless water drop oblonging their form.

2008, Gary D. Schmidt, Trouble, New York, N.Y.: Clarion Books, →ISBN, page 287:

[…] the venue (a private country club nestled in the woods outside Cincinnati, with a dance hall whose ceilings went straight to the moon), to the ice cubes (truly cubed, not oblonged or crushed, and king-sized cubes for the bourbon rocks),


corner

→ German: Corner

→ Japanese: コーナー (kōnā)

From Middle English corner, from Anglo-Norman cornere (compare Old French cornier, corniere (“corner”)), from Old French corne (“corner, angle”, literally “a horn, projecting point”), from Vulgar Latin *corna (“horn”), from Latin cornua, plural of cornū (“projecting point, end, horn”). The sense of "angle, corner" in Old French is not found in Latin or other Romance languages. It was possibly calqued from Frankish *hurnijā (“corner, angle”), which is similar to, and derived from *hurn, the Frankish word for "horn". Displaced native cognate Middle English hirn, herne, from Old English hyrne, from Proto-Germanic *hurnijǭ (“little horn, hook, angle, corner”), whence modern English hirn (“nook, corner”), itself related to horn.

nurkka

business: interest that is sufficient for price manipulation

Herbert bruised his shin on the corner of the coffee table.

The point where two converging lines meet; an angle, either external or internal.

The projection into space of an angle in a solid object.

връх

projection into space of an angular solid

The pitch was just off the corner, low and outside.

(heading) Relating to the playing field.

(baseball) One of the four vertices of the strike zone.


corner

en-verb

corner (third-person singular simple present corners, present participle cornering, simple past and past participle cornered)

corners (present singular third-person)
cornering (participle present)
cornered (participle past)
cornered (past)

The cat had cornered a cricket between the sofa and the television stand.

In Juazeiro do Norte, demonstrators cornered the mayor inside a bank for hours and called for his impeachment, while thousands of others protested teachers’ salaries.

2013 June 18, Simon Romero, “Protests Widen as Brazilians Chide Leaders”, in New York Times, retrieved 2013-06-21:

(transitive) To drive (someone or something) into a corner or other confined space.

As the stock car driver cornered the last turn, he lost control and spun out.

(automotive, transitive) To turn a corner or drive around a curve.


chiral

From Ancient Greek χείρ (kheír, “hand”) + -al.

suf

In the close vicinity of a chiral nanostructure, the circular dichroism of a biomolecule could be greatly enhanced, due to the interaction with the local superchiral fields.

2016, S. Hamed Shams Mousavi, Sajanlal R. Panikkanvalappil, Mostafa A. El-Sayed, Ali A. Eftekhar, Ali Adibi, “Large Enhancement of Circular Dichroism Using an Embossed Chiral Metamaterial”, in arXiv:

(geometry, physical chemistry) that exhibits chirality; as in the left-handed and right-handed versions of a helix, or a molecule with L- and D- stereoisomers.


excess

en-noun

excess (countable and uncountable, plural excesses)

From Middle English exces (“excess, ecstasy”), from Old French exces, from Latin excessus (“a going out, loss of self-possession”), from excedere, excessum (“to go out, go beyond”). See exceed.

der

(geometry) Spherical excess, the amount by which the sum of the three angles of a spherical triangle exceeds two right angles. The spherical excess is proportional to the area of the triangle.


oval

From Late Latin ovalis, from ovum; cognate with French and Italian ovale, Dutch ovaal. From 1570.

An elongated round shape resembling an egg or ellipse.

A thing having such a shape, such as an arena.

(mathematics) In a projective plane, a set of points such that no three are collinear and there is a unique tangent line at each point.

(Australia) A sports field, typically but not exclusively oval in shape.


oval

en-adj

oval (comparative more oval, superlative most oval)

more oval (comparative)
most oval (superlative)


construct

en-verb

construct (third-person singular simple present constructs, present participle constructing, simple past and past participle constructed)

constructs (present singular third-person)
constructing (participle present)
constructed (participle past)
constructed (past)

Borrowed from Latin cōnstrūctus, from cōnstruō (“to heap together”), from com- (“together”) + struō (“I heap up, pile”). Doublet of construe.

Construct a circle that touches each vertex of the given triangle.

(transitive, geometry) To draw (a geometric figure) by following precise specifications and using geometric tools and techniques.


great circle route

en-noun

great circle route (plural great circle routes)

A route, taken by intercontinental aircraft for instance, which is the shortest distance between two destinations on the surface of the Earth; an arc of a great circle.


exponential growth

exponential growth (usually uncountable, plural exponential growths)

(by extension, proscribed) Very rapid growth.


great circle

(geometry) A circle defined as the intersection of the surface of a sphere and a plane which passes through the centre of the sphere.


contour line

(geography) A line on a map through points of equal elevation, often height above sea level.


hypergeometric distribution

hypergeometric distribution (plural hypergeometric distributions)

The hypergeometric distribution differs from the binomial distribution in that the random sample of n items is selected from a finite population of N items. With the hypergeometric distribution, there is no replacement. If N is large in respect to n (N>10n), the binomial distribution is a good approximation to the hypergeometric distribution.

2002, Bryan Dodson, Dennis Nolan, Reliability Engineering Handbook, QA Publishing, page 57:

2013, Alexandr A. Borovkov, unspecified translator, Probability Theory, [2009, Alexandr A. Borovkov, Teoriya Veroyatnostei, Knizhnyi dom Librokom, 5th Edition], Springer, page 1,
Sampling without replacement from a large population is considered, and convergence of the emerging hypergeometric distributions to the binomial one is formally proved.

Knowing that the asymptotic form approaches that of a hypergeometric distribution is not all that helpful since this is a complicated function.[…]To demonstrate analytically what the figure suggests graphically, it is better to work directly with the probability function (2.1.7) than with a moment generating function or a characteristic function, neither of which is easily calculable or useful in the case of a hypergeometric distribution.

2014, Mark P. Silverman, A Certain Uncertainty: Nature's Random Ways, Cambridge University Press, page 99:

probability distribution
probability distribution

(probability theory, statistics) A discrete probability distribution that describes the probability of k "successes" in a sequence of n draws without replacement from a finite population.


isopleth

From iso- + Ancient Greek πλῆθος (plêthos, “a great number”).

der

A line drawn on a map through all points having the same value of some measurable quantity.

isopleet

line through all points having the same value


spacetime

en-noun

spacetime (countable and uncountable, plural spacetimes)

From space + time, as a calque of German Raumzeit, introduced in this sense by Hermann Minkowski. First appears in print c. 1893 in the Philosophical Review.

An event is a point in spacetime, specified by the coordinates x, y, z, and t.

(uncountable, physics) The four-dimensional continuum of the three spatial dimensions plus time.


exponential

There were two deaths on Monday, four on Tuesday, and eight on Wednesday. The rate of increase seems exponential.

... Students apply the definition of slope to various representations of growth functions to discover differences between exponential and constant rate of growth.

2013, Yvelyne Germain-McCarthy, Bringing the NCTM Standards to Life: Best Practices, High School, page 101:

(mathematics) Characterised by a rate of change that is proportional to the value of the varying quantity, or, equivalently, by a doubling or halving over successive fixed intervals of time or other parameter, described as exponential growth or exponential decay.


sextant

(geometry) One sixth of a circle or disc; a sector with an angle of 60°.


effective

en-adj

effective (comparative more effective, superlative most effective)

more effective (comparative)
most effective (superlative)

From French effectif, from Latin effectīvus (“productive; effective”), from efficiō (“I make; I bring about”).

der

(geometry, of a cycle or divisor) Having no negative coefficients.


brachistochrone

From Ancient Greek βράχιστος (brákhistos, “shortest”) + χρόνος (khrónos, “time”). The term was coined by Johann Bernoulli.

quote-book

2012, Liberzon, Daniel, Calculus of Variations and Optimal Control Theory: A Concise Introduction, Princeton University Press, →ISBN, page 30:

Let A and B be two fixed points. Then the time it takes a particle to slide under the influence of gravity along some path joining A and B depends on the choice of the path (curve), and hence is a functional. The curve such that the particle takes the least time to go from A to B is called the brachistochrone.

1963, Gelfand, I.M. and S.V. Fomin, Calculus of Variations, Prentice-Hall, Inc., page 3:

(mathematics) A cycloid; the curve of fastest descent between two points.


uniform

en-adj

uniform (comparative more uniform, superlative most uniform)

more uniform (comparative)
most uniform (superlative)

Borrowed from Middle French uniforme, from Latin uniformis.

(geometry) (of a polyhedron) That is isogonal and whose faces are regular polygons; (of an n-dimensional (n>3) polytope) that is isogonal and whose bounding (n-1)-dimensional facets are uniform polytopes.


zone

→ Korean: 존 (jon)

→ Punjabi: ਜ਼ੋਨ (zon)

From Latin zōna, from Ancient Greek ζώνη (zṓnē, “girdle, belt”).

der

1835, Charles Davies, David Brewster (editors and translators), Adrien-Marie Legendre, Elements of Geometry and Trigonometry, [1794, Eléments de géométrie], page 293,
To find the surface of a spherical zone.
Rule.—Multiply the altitude of the zone by the circumference of a great circle of the sphere, and the product will be the surface (Book VIII. Prop. X. Sch. 1).

A zone of a sphere is the curved surface of a frustum.[…]Determine, correct to 3 significant figures (a) the volume of the frustum of the sphere, (b) the radius of the sphere and (c) the area of the zone formed.

2014, John Bird, Engineering Mathematics, page 183:

(geometry) The curved surface of a frustum of a sphere, the portion of surface of a sphere delimited by parallel planes.

(geometry, loosely, perhaps by meronymy) A frustum of a sphere.


catenary

From Late Latin catenaria, in turn from Latin catēna (“chain”). Attested since 1788.

/ˈkætəˌnɛɹi/

(geometry) The curve described by a flexible chain or a rope if it is supported at each end and is acted upon by no other forces than a uniform gravitational force due to its own weight and variations involving additional and non-uniform forces. It is described by the hyperbolic cosine function.

(engineering) Any physical cable, rope, chain, or other weight-supporting structure taking such geometric shape, as a suspension cable for a bridge or a power-transmission line or an arch for a bridge or roof.

(nautical) The curve of an anchor cable from the seabed to the vessel; it should be horizontal at the anchor so as to bury the flukes.

The result was catenary being torn down several hundred feet at a time.

1958, The Railway Review: An Intelligent Survey of Transit News and Trends:

The colour-lights showed up much better than the semaphores which, in spite of their approach warning boards, are not readily visible at any distance between the supports for the catenaries.

1962 April, P. W. B. Semmens, “The Netherlands Railways today”, in Modern Railways, page 241:

The electric overhead was catenary, using 0000 contact wire, and the new railway employed the latest in electric block signal systems.

1977, Paul Castelhun Trimble, Interurban Railways of the Bay Area, page 119:

In addition the catenary itself is divided into 1-2 km sections (corresponding to mechanical sections or tension lengths) with motorized remotely controlled sectioning off-load isolators such that only one train is likely to be immobilized at any one time as a result of an incident associated with the catenary system.

1995, The Channel Tunnel: Transport systems, →ISBN, page 22:

Overhead construction was catenary rather than a single wire to allow the use of pantographs instead of trolley poles so that speeds could be higher.

2009, Jan Young, Studebaker and the Railroads, volume 2, page 47:

(transport) A cable, the segments of which between supports take a catenary geometric shape, supporting in turn an overhead conductor that provides trains, trams or trolley buses with electricity, or the combination of the conductor, the cable, and supports.


anti

Conversion of the prefix anti- to an adjective.

On one occasion, franchise supporters accused antis of dumping lemons, wet sponges, rolls of ticker tape, bags of water, and garbage pails on innocent suffrage supporters parading outside the anti-suffrage offices.

2002, Thomas Jablonsky, “Female Opposition: The Anti-Suffrage Campaign”, in Jean H. Baker, editor, Votes for Women: The Struggle for Suffrage Revisited (Viewpoints on American culture), Oxford University Press, →ISBN, page 121:

Antis jumped on this announcement, calling it vote buying and indicative of the hypocrisy of prohibitionists who talked incessantly in the first election about the immorality of the antis' vote-buying efforts.

2012, H. Paul Thompson, Jr., A Most Stirring and Significant Episode: Religion and the Rise and Fall of Prohibition in Black Atlanta, 1865–1887, page 222:

A person opposed to a concept or principle.


inclination

en-noun

inclination (countable and uncountable, plural inclinations)

From Middle English inclinacioun, inclinacyon, from Old French inclination and Latin inclīnātiō.
Morphologically incline + -ation

The astronomer calculated the inclination of the equator or ecliptic of Earth and the orbital planes of each visible heavenly body.

Artillery must take account of a weapon's precise inclination.

(geometry) The angle of intersection of a reference plane


cyclic

en-adj

cyclic (comparative more cyclic, superlative most cyclic)

more cyclic (comparative)
most cyclic (superlative)

From Ancient Greek κυκλικός (kuklikós). Possibly from cycle + -ic.

(geometry, of a polygon) Able to be inscribed in a circle.


incircle

To construct the incircle of ΔABC, we need the center of the circle and a pass-through point.

2003, Clark Kimberling, Geometry in Action: A Discovery Approach Using the Geometer's Sketchpad, page 16:

Having constructed K, the incircle of the quadrilateral can be easily constructed since it is tangent to BA and BC.

2005, István Reiman, International Mathematical Olympiad: 1959-1975, page 51:

For example, in Figure 4.2a only two edges of the polygon are tangent to the incircle. The other four edges do not even touch the incircle, but their extensions, shown by dotted lines, are tangent to the incircle.

2012, Tom M. Apostol, Mamikon A. Mnatsakanian, New Horizons in Geometry, Mathematical Association of America, page 106:

(geometry) A circle within a polygon, especially a triangle, that is tangent to each side.

вписана окръжност

the circle within a polygon that is tangent to each side


ecliptic

So named because an eclipse can occur only when the Moon lies on this plane.
Borrowed from Latin ecliptica.

(geometry) A great circle drawn on a terrestrial globe, used for illustrating and solving astronomical problems.


orthodrome

Coordinate term: rhumb line (loxodrome)

(geometry) A great circle, or part of one.


insist

en-verb

insist (third-person singular simple present insists, present participle insisting, simple past and past participle insisted)

insists (present singular third-person)
insisting (participle present)
insisted (participle past)
insisted (past)

Partly from Middle French insister, from Latin īnsistere; and partly from a back-formation from insistence.

Angles likewise which insist on the Diameter, are all Right Angles.

1709, Venturus Mandey, Synopsis Mathematica Universalis:

(obsolete, chiefly geometry) To stand (on); to rest (upon); to lean (upon).


spindle

From Middle English spyndel, spindle, spyndylle, from Old English spindle, spindel, alteration of earlier spinel, spinil, spinl (“spindle”), from Proto-West Germanic *spinnilu (“spindle”), equivalent to spin + -le. Cognate with Scots spindil, spinnell (“spindle”), Dutch spindel ("spindle"; < Middle Dutch spille, spinle), German Spindel (“spindle”), Danish spindel (“spindle”), Swedish spindel (“spindle”).

gloss

(geometry) A solid generated by the revolution of a curved line about its base or double ordinate or chord.


deficiency

en-noun

deficiency (countable and uncountable, plural deficiencies)

From deficient + -cy. Compare Latin dēficientia.

(geometry) The amount by which the number of double points on a curve is short of the maximum for curves of the same degree.

(geometry) The codimension of a linear system in the corresponding complete linear system.


octagonal

(geometry) Shaped like an octagon, in having eight sides and eight angles.


petal

From Ancient Greek πέταλον (pétalon), from πέταλος (pétalos, “broad, flat”), from Proto-Hellenic *pétalos, from Proto-Indo-European *peth₂- (“to spread out”), whence Latin pandō and Proto-Germanic *faþmaz (“embrace”) (English fathom).

der

(geometry) A lobe of a rose (geometric shape).


apothem

From Ancient Greek ἀπόθεμα (apóthema, “deposit”), from ἀπό (apó, “off, away”) + θέμα (théma, “that which is laid down”).

uder

(geometry) The perpendicular distance from the center of a circle to a chord of the same circle.

apoteema

(geometry) The distance from the center of a regular polygon perpendicular to one of its sides (a special case of the above).

апотема

the distance from the center of a polygon to a side


hull

From Middle English holle, hoole (“hull, hold of a ship, ship”), of uncertain origin. Possibly a variant and special use of Etymology 1 above, conformed to hull. Alternatively, a variant of Middle English hole, hoole, holle (“hiding place, lair, den, shelter, compartment”, literally “hole, hollow”), related to Middle Dutch and Dutch hol (“hole, ship's cargo hold”). More at hole.

The orthogonal convex hull of an orthogonal polygon is the smallest orthogonally convex polygon that encloses the original polygon.

holomorphically convex hull; affine hull; injective hull

(mathematics, geometry, of a set A) The smallest set that possesses a particular property (such as convexity) and contains every point of A; slightly more formally, the intersection of all sets which possess the specified property and of which A is a subset.


concurrent

en-adj

concurrent (comparative more concurrent, superlative most concurrent)

more concurrent (comparative)
most concurrent (superlative)

/kəŋˈkʌɹənt/

/kɒŋˈkʌɹənt/

/kəŋˈkɝɹənt/

From Middle English concurrent, from Old French concurrent, from Latin concurrēns, present active participle of concurrō (“happen at the same time”), from con- (“with”) + currō (“run”).


Möbius strip

August Ferdinand Möbius
Johann Benedict Listing
Möbius strip

Named after August Ferdinand Möbius (1790–1868), one of two German mathematicians—the other being Johann Benedict Listing (1808–1882)—who independently discovered the strip at the same time (1858).

Like a mind moving on a Möbius strip of events, one's consciousness goes over the same territory again and again without ever becoming aware of the nature of awareness.

1981, William Irwin Thompson, The Time Falling Bodies Take to Light: Mythology, Sexuality and the Origins of Culture, page 8:

1991, Theoni Pappas, More Joy of Mathematics, Wide World Publishing, page 117,
B. F. Goodrich Co. has a patent for a Möbius strip conveyor belt. It lasts longer since the wear and tear is spread uniformly over the entire surface.

A geometrical model of electron (positron) structure is presented based upon an object of two linked loops obtained by cutting a Möbius strip asymmetrically.

1992, Speculations in Science and Technology, Volume 15, Elsevier Sequoia, page 221:

Proust's novel grew and deepened into over 3,000 pages of everything and nothing: a Möbius strip of profundity twisting into mundanity, mundanity twisting into profundity.

2013 November 16, Patrick McGuinness, “Who's afraid of Marcel Proust?”, in The Daily Telegraph (Review), page R20:

(topology) A one-sided surface formed by identifying two opposite edges of a square in opposite senses;

A one-sided surface formed by identifying two opposite edges of a square in opposite senses;
a narrow strip given a half twist and joined at the ends, forming a three-dimensional embedding of said surface.


orientation

en-noun

orientation (countable and uncountable, plural orientations)

/ˌɔɹiɛnˈteɪʃən/

From French orientation. By surface analysis, orient + -ation.

mathematical analysis
mathematical analysis

differential geometry
differential geometry

(mathematical analysis, differential geometry, countable) The choice of which ordered bases are "positively" oriented and which are "negatively" oriented on a real vector space.

(analytic geometry, topology, countable) The designation of a parametrised curve as "positively" or "negatively" oriented; the analogous description of a surface or hypersurface.


solid angle

(geometry) The three-dimensional analog of an angle, equivalent to the area of that portion of the surface of a unit sphere that it subtends.


lemniscate

From Latin lēmniscātus (“decorated with ribbons”).

uder

lemniscate of Bernoulli
lemniscate of Bernoulli

(mathematics) The lemniscate of Bernoulli

lemniscaat

mathematics: figure-of-eight closed curve


waveform

independent variable
independent variable

(mathematics) The shape of a wave function represented by a graph showing some dependent variable as function of an independent variable.


semicircular

In the shape of half of a circle or a semicircle.


semicircle

(soccer) An arc whose center is the penalty spot, extending from the top of the penalty area.


obround

(geometry) A plane shape consisting of two semicircles connected by parallel lines tangent to their endpoints.


curvilinear

From curve + -i- + linear, compare curve, linear.

In early art rectilinear decoration marks an advance on curvilinear, which, in the long ages before pottery was thought of, would naturally be associated with the fibrous baskets that served as vessels.

1907, Ronald M. Burrows, The Discoveries In Crete, page 52:


geodesic

(geometry) The shortest curve between two points on a specific surface.

geodèsica

mathematics: the shortest line between two points on a specific surface

(spherical geometry) A segment of a great circle.


intercept

Borrowed from Latin interceptum, past participle of intercipiō.

the y intercept ― point at which a line crosses the y-axis

Because the horizontal-axis intercept occurs when y=0 and the vertical-axis intercept occurs when x=0, we can find the intercepts algebraically.

2012, Alice Kaseberg, Greg Cripe, Peter Wildman, Introductory Algebra: Everyday Explorations, page 278:

(algebraic geometry) The coordinate of the point at which a curve intersects an axis.


projection

en-noun

projection (countable and uncountable, plural projections)

/pɹəˈd͡ʒɛkʃən/

From either the Middle French projection or its etymon, the Classical Latin prōiectiō (stem: prōiectiōn-), from prōiciō, equivalent to project + -ion. Compare the Modern French projection, the German Projektion, and the Italian proiezione.

(geometry) An image of an object on a surface of fewer dimensions.

проекция

geometry: image of an object on a surface of fewer dimensions


umbilicus

umbilicus (plural umbilici or umbilicuses)

Borrowed from Latin umbilīcus (“navel”).

(geometry, obsolete) One of the foci of an ellipse or other curve.

A sphere may be osculatory to the surface in every direction at an umbilicus.

(geometry) A point of a surface at which the curvatures of the normal sections are all equal to each other.


groin

From earlier grine, from Middle English grinde, grynde, from Old English grynde (“abyss”) (perhaps also "depression, hollow"), probably related to Proto-Germanic *grunduz; see ground. Later altered under the influence of loin.

(geometry) The surface formed by two such vaults.


hypersphere

To prove that the hypersphere is a manifold we wish to divide it into polyhedral solids.

2014, Donald W. Blackett, Elementary Topology: A Combinatorial and Algebraic Approach, Academic Press, →ISBN, page 198:

(geometry) The set of all points in a given hyperspace that are at a given distance from a given point; a generalization of a sphere in four or more dimensions.

гиперсфера

the points of a hyperspace at the same distance from a given point


chiliahedron

chiliahedron (plural chiliahedra or chiliahedrons)

chiliahedra (plural)
chiliahedrons (plural)

(geometry) A polyhedron bounded by one thousand plane surfaces.


hyperspace

hyperspace (countable and uncountable, plural hyperspaces)

(mathematics) An n-dimensional Euclidian space with n > 3.


grad

(geometry, trigonometry) Abbreviation of gradian.


cuboctahedron

cuboctahedron (plural cuboctahedrons or cuboctahedra)

cuboctahedrons (plural)
cuboctahedra (plural)

Blend of cube + octahedron, reflecting the fact that it can be regarded both as a rectified cube and a rectified octahedron.

There are just two polyhedra that will fulfill these conditions: the cuboctahedron and the icosidodecahedron (Diagram 3.3).

1976, Hugh Kenner, Geodesic Math and how to Use it, page 21:

In the case of perfect, symmetric L1₀ cuboctahedra, two of the (001)-surfaces have to be terminated completely with either iron or platinum.

2008, M. E. Gruner, Georg Rollmann, Alfred Hucht, Peter Entel, “Structural and Magnetic Proprties of Transition Metal Nanoparticles from First Principles”, in Rolf Haug, editor, Advances in Solid State Physics 47, page 124:

Octahedra are also needed to make the packing of square-sharing cuboctahedra space filling (Fig. 2.4(c)).

2009, Walter Steurer, Sofia Deloudi, Crystallography of Quasicrystals: Concepts, Methods and Structures, page 54:

2015, Ke Jiang, Antoliy O. Pinchuk, Chapter Two: Noble Metal Nanomaterials: Synthetic Routes, Fundamental Properties, and Promising Applications, Robert E. Camley, Robert L. Stamps (editors), Solid State Physics, Volume 66, Elsevier, page 151,
Yang and coworkers have prepared Pt cuboctahedrons and cubes by reducing K₂PtCl₄ with H₂ generated in situ from the hydrolysis of NaBH₄ in the presence of tetradecyltrimethylammonium bromide as a surfactant [157,158].

(geometry) An Archimedean solid that has fourteen faces (eight triangular and six square) and is both isogonal and isotoxal.

kuboktaedri

polyhedron with 8 triangular and 6 square faces


spherical

en-adj

spherical (comparative more spherical, superlative most spherical)

more spherical (comparative)
most spherical (superlative)

English spheric + -al (see sphere), from Latin sphericus (+ -al), from Ancient Greek σφαιρικός (sphairikós).

The ability of a segment of a glass sphere to magnify whatever is placed before it was known around the year 1000, when the spherical segment was called a reading stone, essentially what today we might term a frameless magnifying glass or plain glass paperweight.

2013 September-October, Henry Petroski, “The Evolution of Eyeglasses”, in American Scientist:

(geometry, not comparable) Of, or pertaining to, spheres.


transcendental function

en-noun

transcendental function (plural transcendental functions)

An analytic function is transcendental (i.e., is a transcendental function) if and only if its Riemann surface is noncompact.

algebraically independent
algebraically independent

(mathematical analysis) Any function that is algebraically independent of its variable(s); a function which does not satisfy a polynomial equation whose coefficients are themselves polynomials.


Fourier transform

Fourier transform (plural Fourier transforms)

Named after French mathematician and physicist Jean Baptiste Joseph Fourier, who initiated the study of what is now harmonic analysis.

Fourier transforms are not limited to acting on functions of time, but the domain of the original function is commonly called the time domain.

The Fourier transform of a function of time is a complex function of frequency, whose magnitude (absolute value) represents the amount of that frequency present in the original function, and whose argument is the phase offset of the basic sinusoid in that frequency.

Since a separate integration is needed to give each point of the transformed function, the process would become extremely tedious if it were to be attempted manually and many ingenious devices have been invented for preforming Fourier transforms mechanically, electrically, acoustically and optically.

2002, J. F. James, A Student's Guide to Fourier Transforms, 2nd edition, Cambridge University Press, page 116:

2005, Emmanuel Letellier, Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras, Springer, Lecture Notes in Mathematics 1859, page 1,
The trigonometric sums of 𝒢^F are thus (up to a scalar) the Fourier transforms of the characteristic functions of the G^F!!-orbits of 𝒢^F.

2012, David Brandwood, Fourier Transforms in Radar and Signal Processing, Artech House, 2nd Edition, page 1,
The Fourier transform is a valuable theoretical technique, used widely in fields such as applied mathematics, statistics, physics, and engineering.

electrical engineering
electrical engineering

(mathematical analysis, harmonic analysis, physics, electrical engineering) A particular integral transform that when applied to a function of time (such as a signal), converts the function to one that plots the original function's frequency composition; the resultant function of such a conversion.

Fourier transform
Jean Baptiste Joseph Fourier

Fouriertransformatie

mathematics: a type of integral transform


scroll

From Middle English scrowle, scrolle, from earlier scrowe, scrouwe (influenced by Middle English rolle), from Old French escroe, escrowe, escrouwe (“scroll, strip of parchment”), from Frankish *skrōda (“a shred”), from Proto-Germanic *skraudō, from *skrew- (“to cut; cutting tool”), extension of *(s)ker- (“to cut”). Doublet of shred and escrow.


trigonometric function

trigonometric function (plural trigonometric functions)

(trigonometry) Any function of an angle expressible as the ratio of two of the sides of a right triangle that has that angle (e.g., sine), or that subtracts 1 from such a ratio or subtracts such a ratio from 1 (e.g., coversed sine).


cosecant

LL-Q1860 (eng)-Flame, not lame-cosecant.wav

(trigonometry) In a right triangle, the reciprocal of the sine of an angle. Symbols: cosec, csc


cotangent

LL-Q1860 (eng)-Flame, not lame-cotangent.wav

(trigonometry) In a right triangle, the reciprocal of the tangent of an angle. Symbols: cot, ctg, or ctn


transverse

Late Middle English, from Latin trānsversus (“turned across; going or lying across or crosswise”). Doublet of transversal.

der

(geometry) (of an intersection) Not tangent, so that a nondegenerate angle is formed between the two things intersecting. (For the general definition, see Transversality (mathematics).)


transverse

(geometry) The longer, or transverse, axis of an ellipse.


triangular

en-adj

triangular (comparative more triangular, superlative most triangular)

more triangular (comparative)
most triangular (superlative)

/tɹaɪˈæŋ.ɡjə.lə/

/tɹaɪˈæŋ.ɡjʊ.lə/

/tɹaɪˈæŋ.ɡjə.lɚ/

From Middle English triangulare, trianguler, triangulere, from Old French triangulaire, triangulier and Latin triangulāris.

Having a triangle as a base; as, a triangular prism, a triangular pyramid.


isotropy

en-noun

isotropy (countable and uncountable, plural isotropies)

down this road, as they watched, came a wagon, then a couple of riders, then a coach and another wagon, in daylight which slowly lost its stark isotropy and was flowed into by clouds and chimney smoke and even episodes of weather

2006, Thomas Pynchon, Against the Day, Vintage, published 2007, page 478:

(geometry, physics) The property of being identical, or having the same physical properties, in all directions.


Laplace distribution

exponential distribution
exponential distribution

(statistics) A probability distribution consisting of two exponential distributions, one positive and one negative.


probability distribution

probability distribution (plural probability distributions)

(statistics) A distribution of all possible values of a random variable together with an indication of their probabilities.


exponential distribution

exponential distribution (plural exponential distributions)

The exponential distribution is a basic distribution for constructing a number of other distributions. For example, the gamma distribution is obtained from the distribution of the sum of random variables where each variable follows an exponential distribution.

1998, Vijay Singh, Entropy-Based Parameter Estimation in Hydrology, Kluwer Academic, page 49:

In addition, PH distributions provide a simple framework to demonstrate how one can extend many simple results on exponential distributions to more complex models without losing computational tractability.

1999, G. Latouche, V. Ramaswami, Introduction to Matrix Analytic Methods in Stochastic Modeling, Society for Industrial and Applied Mathematics, page 33:

The exponential distribution was introduced briefly in Chapter 3 in connection with the Poisson discrete probability distribution function. There it was shown that if the number of failures in a given time period t was Poisson distributed, then the time to failure is distributed as an exponential distribution.

2012, Kenneth S. Stephens, Reliability Data Analysis with Excel and Minitab, ASQ Quality Press, page 145:

(statistics) Any of a class of continuous probability distributions used to model the time between events that occur independently at a constant average rate.


Laplace operator

Laplace operator (plural Laplace operators)

1975, Various translators, V. Ja. Sikjrjavyĭ, A Quasidifferentiation Operator and Boundary Value Problems Connected With It, V. I. Averbvh, M. S. Birman, A. A. Blahin (editors), Transactions of the Moscow Mathematical Society for the Year 1972, Volume 27, [ТРУДЫ МОСКОВКОГО МАТЕМАҬИЧЕСКОГО ОБЩЕСТВА ТОМ 27 (1972)], American Mathematical Society, page 202,
The first notion of a Laplace operator for functionals on a Hilbert space was introduced by Levy in [l], and the idea was developed further in [2]. Levy's results depended on the posthumous work of Gateaux [3] in which the Dirichlet problem in Hilbert space was considered (without any concise definition of the Laplace operator).

Nevertheless, a systematic analysis of heat semigroups for Laplace operators on metric graphs is still missing.[…]Below we will prove an upper bound on the number of negative eigenvalues (Theorem 3.7) and a lower bound on the spectrum of Laplace operators (Theorem 3.10).

2006, Vadim Kostrykin, Robert Schrader, “Laplacians on Metric Graphs: Eigenvalues, Resolvents, and Semigroups”, in Gregory Berkolaiko, Robert Carlson, Stephen A. Fulling, Peter Kuchment, editors, Quantum Graphs and Their Applications: Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference, American Mathematical Society, page 201:

There are lots of approaches to get rational approximation of fractional order Laplace operator.[…]The rational function approximation gives direction to realize this fractional order Laplace operator in circuit impedance and admittance forms. This section gives insight into simple method of approximating the fractional Laplace operator.

2008, Shantanu Das, Functional Fractional Calculus for System Identification and Controls, Springer, page 153:

differential operator
differential operator

(mathematics, physics) A differential operator,denoted ∆ and defined on ℝⁿ as Δ=∑ᵢ₌₁ⁿ(∂²)/(∂x_i²), used in the modeling of wave propagation, heat flow and many other applications.

Laplace'i operaator

mathematics, physics: differential operator used in modeling of wave propagation, heat flow and many other applications


Laplace transform

Laplace transform (plural Laplace transforms)

Named after French polymath Pierre-Simon Laplace.

named-after

F(s)=∫₀ ᪲f(t)e⁻ˢᵗ,dt.

(mathematics) an integral transform of positive real function f(t) to a complex function F(s); given by:


coordinate system

en-noun

coordinate system (plural coordinate systems)

1992, D. H. Maling, Coordinate Systems and Map Projections, 2nd Edition, Pergamon Press, page 27,
In this chapter we review some of the fundamental ideas about the plane coordinate systems which are used in surveying and mapping, both from the viewpoint of studying the mathematics of map projections and the practical tasks which arise in cartography.

Note that the orientation of Squire's coordinate system relative to the physical coordinate system is changing as a function of wavenumbervector.

2003, Vejapong Juttijudata, Proper Orthogonal Decomposition in Squire's Coordinate System and Its Low-dimensional Model of Channel Turbulence, Cornell University, page 22:

In Chapter 1 the choice of the origin and orientation of the analysis Cartesian coordinate system was made arbitrarily.[…]Note that nothing was said about the origins of the above two Cartesian coordinate systems.

2008, Bruce K. Donaldson, Analysis of Aircraft Structures, 2nd edition, Cambridge University Press, page 38:

(geometry, mathematical analysis) A method of representing the position of any individual point in a space of given dimensionality as a tuple of numerical coordinates.

نِظَامُ إِحْدَاثِيَّاتٍ

method of representing points in a space


rotation

rotation (countable and uncountable, plural rotations)

/ɹoʊˈteɪʃən/

Borrowed from Latin rotatiō. By surface analysis, rotate + -ion.

The function mapping (x,y) to (−y,x) is a rotation.

(mathematics, geometry) An operation on a metric space that is a continuous isometry and fixes at least one point.


hypocycloid

From hypo- (“below or inside”) + cycloid.

(geometry) The locus of a point on the circumference of a circle that rolls without slipping inside the circumference of another circle.


astroid

From Ancient Greek ἄστρον (ástron, “a star”) + εἶδος (eîdos, “form, likeness”).

(geometry) A hypocycloid with four cusps.


epicycloid

From epi- (“above or outside”) + cycloid.

(geometry) The locus of a point on the circumference of a circle that rolls without slipping on the circumference of another circle.


cycloid

In the firſt Courſe there was a Shoulder of Mutton, cut into an Æquilateral Triangle, a Piece of Beef into a Rhomboides, and a Pudding into a Cycloid.

1726 October 28, [Jonathan Swift], “The Humours and Dispositions of the Laputians Described. […]”, in Travels into Several Remote Nations of the World. […] [Gulliver’s Travels], volume II, London: […] Benj[amin] Motte, […], →OCLC, part III (A Voyage to Laputa, Balnibarbi, Glubbdubdribb, Luggnagg, and Japan), page 20:

(geometry) The locus of a point on the circumference of a circle that rolls without slipping on a fixed straight line.

cicloide

geometry: locus of a point on the circumference of a rolling circle


escape velocity

escape velocity (plural escape velocities)

The gravitational force exerted by a planet determines its surface gravity and escape velocity.

1996, Thomas Arny, Explorations: An Introduction to Astronomy, McGraw-Hill Science, page 74:

(astrophysics) The minimum speed needed to escape the gravitational field of a planet or other body.


trident

PIE word
 *tréyes
From Latin tridēns, from tri- (“three”) + dēns (“tooth”).

(geometry) A curve of third order of the form:


icosasphere

(geometry) A geometric figure with twenty or more triangular faces producing a semi-spherical solid.


equivalence

equivalence (countable and uncountable, plural equivalences)

From French équivalence, from Medieval Latin aequivalentia.

(geometry) A number in intersection theory. A positive-dimensional variety sometimes behaves formally as if it were a finite number of points; this number is its equivalence.


lozenge

From Middle English losenge, from Old French losenge (“rhombus”), from Old French *lose (“flag-stone”), from Vulgar Latin *lausa.

Wherein the decussis is made within a longilaterall square, with opposite angles, acute and obtuse at the intersection; and so upon progression making a Rhombus or Lozenge figuration [...].

1658, Sir Thomas Browne, The Garden of Cyrus, Folio Society, published 2007, page 167:

How the junior partner of Hobbs and Dobbs leads her smiling to the carriage with the lozenge upon it, and the fat wheezy coachman!

1848, William Makepeace Thackeray, chapter 9, in Vani8ty Fair:

The floor is constructed from marble lozenges and triangles of every imaginable hue: yellow and pink and all manner of mottled and blotched shades, framed in white.

2004, Richard Fortey, The Earth, Folio Society, published 2011, page 14:

(shapes, heraldry) A quadrilateral with sides of equal length (rhombus), having two acute and two obtuse angles.


serpentine

From Middle English serpentine, from Old French serpentin, from Latin serpentīnus, from serpēns (“serpent”), equivalent to serpent + -ine.

(mathematics) Any of several related cubic curves; anguinea


enclosing

(geometry) Of a region, containing all points of a given set within its bounds.


arctangent

(trigonometry) Any of several single-valued or multivalued functions that are inverses of the tangent function. Symbol: arctan, tan⁻¹


latus rectum

latus rectum (plural latera recta or latus rectums)

latera recta (plural)
latus rectums (plural)

(geometry) The line drawn through a focus of a conic section parallel to the directrix and terminated both ways by the curve. It is the parameter of the principal axis.


cubewano

From Acronym of QB1. + -o.
Derived from QB1 ("cue bee one"), short for (15760) 1992 QB1, the first such object discovered

(astronomy) Any Kuiper belt object whose orbit is not determined by resonance with Neptune (orbit ~ 40-50 AU).


round angle

Two angles whose sum is a straight angle are called supplemental; two angles whose sum is a round angle we may call explemental.

1893, William Benjamin Smith, Introductory Modern Geometry of Point, Ray, and Circle, MacMillan, page 31:

(geometry) An angle of 360 degrees; a full circle.


acute-angled

(geometry) Of a triangle, having three acute angles.


perigon

(geometry) A round angle; a full circle.


obtuse-angled

(geometry) Of a triangle, having an obtuse angle.


SSA

SSA (countable and uncountable, plural SSAs)

(geometry) Initialism of side side angle (a geometric proof reason)


ovoid

From Latin ōvum (“egg”) + -oid (“resembling”).


conical

en-adj

conical (comparative more conical, superlative most conical)

more conical (comparative)
most conical (superlative)

He anſwers, That this Motion is Conical; and judgeth, that by the Conick path all the Phænomena of Comets can, without any inconveniency, be readily ſolved; even of that, which (by Hiſtory) in fifty days, paſſed through more then the 12 Signs of the Zodiack; And of that, which in two days run through eight Signs: and of another, which in 48 days poſted through all the Signs, contra ſeriem.

1665 November 6, “An Account of Hevelius his Prodromus Cometicus, together with some Animadversions made upon it by a French Philosopher”, in Henry Oldenburg, editor, Philosophical Transactions, volume I, number 6:

(geometry) Of or relating to a cone or cones.


circle segment

circular segment
circular segment#English


differential

[dɪfəˈɹənʃəɫ]

(differential geometry, of a smooth map ϕ between smooth manifolds) The pushforward or total derivative of ϕ: a linear map from the tangent space at a point x in ϕ's domain to the tangent space at ϕ(x) which is, in a technical sense, the best linear approximation of ϕ at x; denoted operatorname d!ϕₓ.


circular arc

A continuous section of the circumference of a circle.


homothetic

homoteettinen

economics: depending on the ratio of prices

(mathematics, geometry) for a geometric figure that is the image of another figure under an homothety.


polyhedral

polyhedral (comparative more polyhedral, superlative most polyhedral)

more polyhedral (comparative)
most polyhedral (superlative)

(mathematics, geometry) Of, pertaining to or derived from a polyhedron.

(geometry, of a solid or surface) Having multiple planar faces or facets.

poliedrico

(geometry) having multiple planar faces or facets


sinus

Learned borrowing from Latin sinus (“a bent surface, curve, hollow”). Doublet of sine.

lbor

(anatomy, zootomy) A pouch or cavity in a bone or other tissue, especially one in the bones of the face or skull connecting with the nasal cavities (the paranasal sinus).


flex

en-noun

flex (countable and uncountable, plural flexes)

From Latin flexus, past participle of flecto (“to bend”).

(countable, geometry) A point of inflection.


AAS

AAS (countable and uncountable, plural AASs)

(geometry) Initialism of angle-angle-side triangular congruency.


sphericon

(geometry) A solid constructed by slicing a bicone with 90-degree apices through a plane containing both of them, rotating one half by 90 degrees, and reconnecting them; the resulting shape has a single continuous face, and two edges.

esfericón

(geometry) a solid constructed by slicing a bicone


supplement

From Latin supplementum (“that which is added to supply a shortage”), from supplere (“to provide something”).

der

(geometry) An angle that, when added to a given angle, makes 180°; a supplementary angle.


taxicab geometry

From the distance travelled by a taxicab in a grid of streets that cross at right angles to each other.

non-Euclidean geometry
non-Euclidean geometry

(geometry) A non-Euclidean geometry in which the distance between two points is the sum of the absolute differences between their corresponding coordinates.


apsis

From Latin apsis, hapsis, from Ancient Greek ἁψίς (hapsís, “arch, vault”). See also apse.

Like Henry's collegiate church […] the cathedral is a cruciform basilica of the double bay system with four square bays in the central nave, western transoms, a quadrum for the choir, an apsis, and a transept with auxiliary apses.

2019, A Companion to Medieval Lübeck, page 96:

(architecture) A recess or projection, with a dome or vault, at the east end of a church; an apse.

(astronomy) Either of the points in the elliptical orbit of a planet, comet, or moon where it is closest or furthest from the body it orbits; examples are perihelion, aphelion, perigee, and apogee


epicycle

From Latin epicyclus, from Ancient Greek ἐπίκυκλος (epíkuklos), from ἐπί (epí, “upon”) + κύκλος (kúklos, “circle”).

Is it not [Philosophie], that […] teacheth miserie, famine and sicknesse to laugh? Not by reason of some imaginarie Epicicles, but by naturall and palpable reasons.

(astronomy) A small circle whose centre is on the circumference of a larger circle; in Ptolemaic astronomy it was seen as the basis of revolution of the "seven planets", given a fixed central Earth.

епицикъл

a small circle whose centre is on the circumference of a larger circle

(geometry) Any circle whose circumference rolls around that of another circle, thus creating a hypocycloid or epicycloid.

episykli

any circle whose circumference rolls around that of another circle

(organic chemistry) A ring of atoms joining parts of an already cyclic compound

If two chronicles seemed contradictory, instead of trying to choose between them, a rationalization (epicycle) was devised to cover both.

1978, The Journal of the Siam Society, volumes 66-67, page 152:

Rather than solve the theoretical problem of how to produce a method of political ethics, the contractarian device introduces an unnecessary theoretical epicycle into what is otherwise a coherent account of social justice in particular and political morality in general.

1998, Paul Joseph Kelly, Impartiality, Neutrality and Justice: Re-reading Brian Barry’s Justice as Impartiality, page 12:

(figuratively) An ad hoc complication added to a model to make it fit the known data


non-Euclidean geometry

en-noun

non-Euclidean geometry (plural non-Euclidean geometries)

(geometry) Any system of geometry not based on the set of axioms of Euclidean geometry, which is based on the three-dimensional space of common experience.


Euclidean geometry

(geometry) The familiar geometry of the real world, based on the postulate that through any two points there is exactly one straight line.

欧几里德几何

Ōujǐlǐdé jǐhé


limaçon of Pascal

limaçon of Pascal (plural limaçons of Pascal)


nef

Short for numerically effective; introduced by Miles Reid.

[…] this condition is the numerical consequence of the condition that for some m#x3E;0, the linear system #x7C;mD#x7C; is effective and free; thus nef = "numerically (effective and free)".

1983, Miles Reid, “Minimal Models of Canonical 3-Folds”, in Advanced Studies in Pure Mathematics, volume 1, page 131:

(algebraic geometry) Of a line bundle on a complete algebraic variety over a field: such that the degree of its restriction to every algebraic curve in the variety is non-negative.


domino

1801, borrowed from French domino (1771), originally the term for a hooded garment, itself from Medieval Latin domino, oblique case of dominus (“lord, master”); compare Medieval Latin dominicale (“a kind of veil”).

cog

(geometry) A polyomino made up of two squares.


Euclidean

Named after Euclid, who established the principles of plane geometry.

(geometry) Adhering to the principles of traditional geometry, in which parallel lines are equidistant.


limaçon

From French limaçon, ultimately from Latin limax (“snail”).

(geometry) A plane curve with polar equation ρ=a+b, sin ,θ or ρ=a+b, cos ,θ, of which the cardioid is a special case.


cardioid

(geometry) An epicycloid with exactly one cusp; the plane curve with polar equation ρ=1+ cos ,θ - approximately heart-shaped


n-omino

(geometry) A polyomino made up of n squares.


hexomino

(geometry) A polyomino made up of six squares.


tetromino

/tɛˈtɹɒmɪnəʊ/

/tɛˈtɹɑːmɪnoʊ/

(geometry) A polyomino made up of four squares connected edge to edge.


octomino

(geometry) A polyomino made up of eight squares.


heptomino

(geometry) A polyomino made up of seven squares.


nonomino

(geometry) A polyomino made up of nine squares.


monomino

(geometry) The polyomino made up of one square.


pentomino

PIE word
 *pénkʷe
pent(a)- + (poly)omino

(geometry) A polyomino made up of five square units. When packing pentominoes into three-dimensional shapes, the square units commonly are expanded into cubes instead of being flattened.


decomino

(geometry) A polyomino made up of ten squares.


tromino

/ˈtɹɑmɪˌnoʊ/

(geometry) A polyomino made up of three squares connected edge to edge.


polyform

(geometry) A plane or solid figure constructed by joining together identical polygons edge to edge.


polydrafter

From poly- + draft + -er, from drafting triangle.

(geometry) A polyform made by joining N-2 triangles edge to edge in various arrangements, each of these triangles being a right triangle with angles 30°, 60° and 90°.


polycube

(geometry) A polyform made by joining one or more cubes face to face in various arrangements.


polyabolo

en-noun

polyabolo (plural polyabolos or polyaboloes)

polyabolos (plural)
polyaboloes (plural)

Blend of poly- + diabolo, from the resemblance of a diabolo in cross-section to two right isosceles triangles joined at the vertices of their right angles.

(geometry) A polyform made by joining right isosceles triangles edge to edge in various arrangements.


polystick

(geometry) A figure made by joining line segments of equal length end to end at right angles.


polyhex

(geometry) A polyform made by joining one or more regular hexagons edge to edge in various arrangements.


triomino

triomino (plural triominoes or triominos)

/tɹaɪˈɒmɪnəʊ/

/tɹaɪˈɑmɪˌnoʊ/

A polyomino made up of three squares connected edge to edge.


polyomino

polyomino (plural polyominos or polyominoes)

polyominos (plural)
polyominoes (plural)

poly- + (d)omino, as if the d were for di-, two, a domino being made up of two squares

(geometry) A plane polyform made by joining one or more squares edge to edge in various arrangements; a similar polyform made from triangles or hexagons (or any polygon that can tile a plane)


orbiter

The orbiters in her life in high likelihood like to talk about this and make themselves her emotional tampon and outlet.

2015, Jack N. Raven, Penetration: A Tactical Manual on Forming Deep Emotional Connections!:

(slang, seduction community) A person who constantly hangs around with someone they are attracted to, but too shy to talk to.


polyiamond

Blend of poly- + diamond, the polyiamond made up of two triangles being a diamond or rhombus.

equilateral triangle
equilateral triangle

(geometry) A polyform made by joining one or more equilateral triangles edge to edge in various arrangements. Every polyiamond corresponds to a polyhex,


moniamond

(geometry) The polyiamond made up of a single triangle.


n-iamond

(geometry) A polyiamond made up of n triangles.


pentiamond

(geometry) A polyiamond made up of five triangles.


triamond

(geometry) A polyiamond made up of three triangles.


tetriamond

(geometry) A polyiamond made up of four triangles.


hexiamond

(geometry) A polyiamond made up of six triangles.


trapezoidal

en-adj

trapezoidal (comparative more trapezoidal, superlative most trapezoidal)

more trapezoidal (comparative)
most trapezoidal (superlative)

In the shape of a trapezoid, or having some faces which have one pair of parallel sides.


isomorphism

en-noun

isomorphism (countable and uncountable, plural isomorphisms)

Isomorphism on Encyclopedia of Mathematics

Natural Isomorphism on Wolfram MathWorld

(group algebra) A bijection f such that both f and its inverse f⁻¹ are homomorphisms, that is, structure-preserving mappings.


prism

→ Japanese: プリズム (purizumu)

→ Korean: 프리즘 (peurijeum)

→ Thai: ปริซึม (bprí-sʉ̂m)

[ˈpʰɹ̠̊ɪzm̩]

Learned borrowing from Late Latin prisma (“(geometry) prism”), from Ancient Greek πρίσμᾰ (prísma, “anything sawn; sawdust; (Koine, geometry) prism”), from πρῐ́ζω (prízō) (a variant of πρῑ́ω (prī́ō, “to saw”), further etymology unknown) + -μᾰ (-ma, suffix forming neuter nouns denoting the effect or result of an action, etc.).

prizëm

transparent block used to reflect or refract light

(geometry) A polyhedron with parallel ends of the same polygonal shape and size, the other faces being parallelogram-shaped sides.

An object having the shape of a geometrical prism (sense 1).

(construction) A cutting (“open passage at a level lower than the surrounding terrain, dug for a canal, railway, or road to go through”) or an embankment shaped like a prism (sense 1) or a number of prisms, such that its volume can be easily calculated.

leikkaus

cutting or embankment shaped like a prism or number of prisms

(crystallography) A crystal in which the faces are parallel to the vertical axis.

prisma

[page 13] One of theſe Parts [of a piece of black paper] I painted vvith a red Colour and the other vvith a blevv. […] This Paper I vievved through a Priſm of ſolid Glaſs, vvhoſe tvvo Sides through vvhich the Light paſſed to the Eye vvere plane and vvell poliſhed, and contained an Angle of about Sixty Degrees: vvhich Angle I call the refracting Angle of the Priſm. […] [page 17] Theſe Experiments may ſuffice for the Colours of Natural Bodies. For in the Colours made by the Refraction of Priſms this Propoſition vvill appear by the Experiments vvhich are novv to follovv in the next Propoſition.

1704, I[saac] N[ewton], “[The First Book of Opticks. Part I.] Prop[osition] I. Theor[y] I. Lights which Differ in Colour, Differ also in Degrees of Refrangibility.”, in Opticks: Or, A Treatise of the Reflexions, Refractions, Inflexions and Colours of Light. […], London: […] Sam[uel] Smith, and Benj[amin] Walford, printers to the Royal Society, […], →OCLC, pages 13 and 17:

Here, avvful [Isaac] Newton, the diſſolving clouds / Form, fronting on the ſun, thy ſhovvery priſm; / And to the ſage-inſtructed eye unfold / The various tvvine of light, by thee diſclos'd / From the vvhite mingling maze.

a. 1749 (date written), James Thomson, “Spring”, in The Seasons, London: […] A[ndrew] Millar, and sold by Thomas Cadell, […], published 1768, →OCLC, page 10, lines 207–211:

(optics) A transparent block in the shape of a prism (sense 1), typically with triangular ends, used to reflect or refract light.

The beams, that thro' the Oriel shine, / Make prisms in every carven glass, […]

1842, Alfred Tennyson, “The Day-Dream”, in Poems. […], volume II, London: Edward Moxon, […], →OCLC, page 151:

(archaic) A spectrum produced by light being refracted through a prism.

(by extension, surveying) A retroreflector (“device which reflects light back to its source with minimal scattering”) which is usually attached to a surveying pole as a target for a total station which emits a light beam at the device and calculates how long it takes to be reflected back in order to measure distance.


fylfot

Uncertain, but likely from Middle English fillen (“to fill”) (from Old English fyllan) + fot (“foot”) (from Old English fōt), in reference to its use as a design to be placed at the bottom of stained-glass windows.

Morley: A year and a half ago I stumbled into your gingerbread office, a lost, frightened soul in terrified flight across the great yawning terror of doubt—a human being, in short!—and you chanted some hagridden formulas and danged some fylfots...

There was a coffee tray on top of it, and spilt coffee part hid the fylfot design of the tray.

1982, Anthony Burgess, The End of the World News:

A swastika, especially one with the arms bent in an anticlockwise direction.


vanishing point

en-noun

vanishing point (plural vanishing points)

At 8h 35' 4", the least dent possible, quite black, appeared in the sun's limb. And at 8h 35' 6", the limb was restored to its perfect form, there having been a small trembling light, between the narrow watery border of Venus and the vanishing point of contact in the sun's limb for these two seconds of time.

1762, Samuel Dunn, “Some Observations of the Planet Venus, on the Disk of the Sun, June 6th, 1761,”, in Philosophical Transactions (1683-1775), volume 52, page 192:

It might cut the tuberculosis deathrate to the vanishing point.

1923 June 25, “Tuberculosis at Bay”, in Time:

It hit 100 m.p.h. with ease and sped toward the vanishing point down Highway 93A.

2003 August 25, Sally B. Donnelly, “The Need for Speed”, in Time:

The situation in which, place where, or point in time when some object or phenomenon is no longer observable or notable.

katoamispiste

point when an object or phenomenon is no longer observable


resonance

resonance (countable and uncountable, plural resonances)

From Old French resonance (French résonance), from Latin resonantia (“echo”), from resonō (“I resound”).

The leiter-wagons contained great, square boxes, with handles of thick rope; these were evidently empty by the ease with which the Slovaks handled them, and by their resonance as they were roughly moved.

1897, Bram Stoker, Dracula, New York, N.Y.: Modern Library, →OCLC:

(uncountable) The quality of being resonant.

He passed on, and the lights and cries of the station dropped away, merged in a wider haze and a hollower resonance, as the train gathered itself up with a long shake and rolled out again into the darkness.

1912, Edith Wharton, The Reef, New York, N.Y.: D[aniel] Appleton and Company:

(countable) A resonant sound, echo, or reverberation, such as that produced by blowing over the top of a bottle.

(medicine) The sound produced by a hollow body part such as the chest cavity upon auscultation, especially that produced while the patient is speaking.

sympathetic vibration
sympathetic vibration

An increase in the strength or duration of a musical tone produced by sympathetic vibration.

(astronomy) An influence of the gravitational forces of one orbiting object on the orbit of another, causing periodic perturbations.

Resonance is a kind of relationship to the world, formed through affect and emotion, intrinsic interest, and perceived self-efficacy, in which subject and world are mutually affected and transformed.

2019 [2016], James Wagner, transl., Resonance, John Wiley & Sons, translation of Resonanz by Hartmut Rosa, →ISBN:

(sociology) A quality of human relationship with the world.


circumscribe

en-verb

circumscribe (third-person singular simple present circumscribes, present participle circumscribing, simple past and past participle circumscribed)

circumscribes (present singular third-person)
circumscribing (participle present)
circumscribed (participle past)
circumscribed (past)

From Latin circumscrībō, from circum (“around”) + scrībō (“write”). By surface analysis, circum- + scribe.

(geometry) To draw the smallest circle or higher-dimensional sphere that has (a polyhedron, polygon, etc.) in its interior.

описвам

to draw a circle, sphere, or higher-dimensional ball

piirtää ympyrä monikulmion kärkien kautta


trojan

/ˈtɹəʊd͡ʒən/

/ˈtɹoʊd͡ʒən/

(computing) Malware that appears to perform or actually performs a desired task for a user while performing a harmful task without the user's knowledge or consent.


annulus

Learned borrowing from Medieval Latin ānnulus, a misspelling of Latin ānulus (“ring, especially one worn on a finger”), from ānus (“ring”) (from Proto-Indo-European *h₁eh₂no- (“ring”)) + -ulus (diminutive suffix).
The plural form annuli is a learned borrowing from Medieval Latin ānnulī.

lbor

(geometry) The region in a plane between two concentric circles of different radii.


parallelepiped

/ˌpæɹəˌlɛləˈpaɪpɪd/

/ˌpæɹəlɛˈlɛpɪpɛd/

From Latin parallēlepipedum, from Ancient Greek παραλληλεπίπεδος (parallēlepípedos, “with parallel surfaces”), from παράλληλος (parállēlos, “parallel”) + ἐπίπεδος (epípedos, “plane”).

der

παραλληλεπίπεδος

A cuboid is a rectangular parallelepiped.

(geometry) A solid figure, having six faces, all parallelograms, all opposite faces being similar and parallel.


saddle

→ Japanese: サドル (sadoru)

Homer Tunnel
Milford Sound
Oxford English Dictionary

From Middle English sadel, from Old English sadol, from Proto-West Germanic *sadul, from Proto-Germanic *sadulaz (“saddle”). Further etymology uncertain, perhaps from Proto-Indo-European *sod-dʰlo-, from *sed- (“to sit”) + *-dʰlom (a variant of *-trom (suffix forming nouns denoting instruments or tools)), though the Oxford English Dictionary says this “presents formal difficulties”.
cognates
* Danish sadel
* Dutch zadel
* German Sattel
* Icelandic söðull
* Low German Sadel
* Russian седло́ (sedló)
* Saterland Frisian Soadel
* Scots sadil
* Swedish sadel
* West Frisian seal

saal

seat for a rider placed on the back of a horse or other animal

satula

something resembling a saddle in appearance or shape

satula

depression located along the axial trend of an anticline

Something resembling a saddle (sense 1) in appearance or shape.

(geometry) Synonym of saddle point (“a point in the range of a smooth function, every neighbourhood of which contains points on each side of its tangent plane”)


sector

Sector (Star Trek)
Sector (instrument)
sector

(geometry) Part of a circle, extending to the center; circular sector.


linear pair

(geometry) The two supplementary adjacent angles formed by two intersecting lines


absolute value

The absolute value |x| of a real number x is √, which is equal to x if x is non-negative, and −x if x is negative.

principal square root
principal square root

(mathematics) For a complex number a+bi, the principal square root of the sum of the squares of its real and imaginary parts, √. Denoted by | |.


line of centers

en-noun

line of centers (plural lines of centers)

(geometry) A line joining centers of figures.


polar

/ˈpəʊ̯lə(ɹ)/

[ˈpʰəʊ̯lə(ɹ)]

From Late Latin polāris, equivalent to pole + -ar.

(geometry) The line joining the points of contact of tangents drawn to meet a curve from a point called the pole of the line.


antilog

Shortening; see log (“logarithm”), equivalent to anti- + log.

Then the desired y path can be obtained by taking the antilog of #x5C;lny […]

2005, Alpha C. Chiang and Kevin Wainwright, Fundamental Methods of Mathematical Economics, fourth edition, McGraw-Hill, page 484:


mapping

mapping (countable and uncountable, plural mappings)

(mathematics) A function that maps every element of a given mathematical structure (eg: a set) to a unique element of another structure; a correspondence.

zobrazení

function that maps every element of a given set to a unique element of another set


antilogarithm

If x is the logarithm of y, then y is the antilogarithm of x.

(mathematics) The number of which a given number is the logarithm (to a given base).


alternate angles

(geometry) the internal angles made by two (parallel) lines with a third, on opposite sides of it.

the internal angles made by two (parallel) lines with a third, on opposite sides of it.
If the parallels AB, CD, are cut by the line EF, intersecting at points G and H, then the angles AGH, GHD, are called alternate angles (as also are the angles BGH and GHC).


antiparallel

(geometry) A line that forms equal angles with two other lines, but in opposite directions.


perturb

en-verb

perturb (third-person singular simple present perturbs, present participle perturbing, simple past and past participle perturbed)

perturbs (present singular third-person)
perturbing (participle present)
perturbed (participle past)
perturbed (past)

From Middle English perturben, from Old French perturber, from Latin perturbare (“throw into confusion, confuse, disorder, disturb”), from per (“through”) + turbare (“to confuse, disturb”).

der

(physics) To slightly modify the motion of an object.

(astronomy) To modify the motion of a body by exerting a gravitational force.

perturbar

(mathematics) To modify slightly, such as an equation or value.


tetrahemihexahedron

A concave uniform polyhedron with four triangular faces, three square faces, twelve edges and six vertices.


anharmonic

(geometry) Describing the section of a line by four points, A, B, C, D, when their mutual distances are such that AB divided by CB is not equal to AD divided by CD.


cupola

Borrowed from Italian cupola, from Latin cūpula (“little tub”); from Latin cūpa, cuppa (“cup”); named for its resemblance to a cup turned over.

(geometry) A solid formed by joining two polygons, one (the base) with twice as many edges as the other, by an alternating band of isosceles triangles and rectangles.


anteorbital

(astronautics) Referring to the period before orbit is achieved.


ogive

From late Middle English ogif, egeve, egeove, from Old French ogive, œgive, augive. Doublet of ogee.

distribution function
distribution function

(statistics) The curve of a cumulative distribution function.


quadrangle

/ˈkwɒdˌɹæŋ.ɡəl/

From Old French quadrangle, from Late Latin quadrangulum.

(geometry) A geometric shape with four angles and four straight sides; a four-sided polygon.


coincidence

en-noun

coincidence (countable and uncountable, plural coincidences)

From French coïncidence. By surface analysis, coincide + -ence.

(geometry) A fixed point of a correspondence; a point of a variety corresponding to itself under a correspondence.


deltohedron

deltohedron (plural deltohedra or deltohedrons)

deltohedra (plural)
deltohedrons (plural)

From delto- (combining form of deltoid) + -hedron.

affix

A polyhedron whose faces are kites (deltoids). The dual polyhedron of a regular n-gonal antiprism.


trapezohedron

en-noun

trapezohedron (plural trapezohedra or trapezohedrons)

trapezohedra (plural)
trapezohedrons (plural)

From trapezium + -hedron, with trapezium used in the US sense of a convex irregular quadrilateral.

The general form is called the tetragonal trapezohedron. In this case also there are both left- (Fig. 97) and right-handed (Fig. 98) forms.

1969, Carl W. Correns, translated by William D. Johns, Introduction to Mineralogy: Crystallography and Petrology, 2nd edition, page 40:

This trapezohedron, or antidiamond, is composed of ten quadrilaterals. In each quadrilateral, three of the angles are 108° and one is 36°.

2002, John Montroll, A Plethora of Polyhedra in Origami, page 105:

(geometry, crystallography) Any of a class of polyhedra that have kite-shaped faces and are dual polyhedra of antiprisms.

trapezopluredro

any of several forms of crystal with trapezia as faces

A trapezohedron has 24 equal faces, each a four-sided figure or trapezium. Unlike the forms already described, which are always the same, there are several different trapezohedrons, all having the same number of faces but differing in the angles between the faces.

1998, Cornelius S. Hurlbut Jr., W. Edwin Sharp, Dana's Minerals and How to Study Them (After Edward Salisbury Dana), page 23:

deltoidal icositetrahedron
deltoidal icositetrahedron

(crystallography) A deltoidal icositetrahedron.


rotunda

Learned borrowing from Latin rotunda, from rotundus (“round”). In the architectural sense, from Sancta Maria Rotunda (the name for a church in the Pantheon).

(geometry) A form of cupola that has pentagons rather than squares or rectangles.


curvature

curvature (countable and uncountable, plural curvatures)

From Latin curvare, from Latin curvatura. See also curve. Displaced native Old English ġebīeġednes.

A turtle drawing an ellipse would have to turn more per distance traveled to get around its “pointy” sides than to get around its flatter top and bottom. This notion of how “pointy something is,” expressed as the ratio of angle turned to distance traveled, is the intrinsic quantity that mathematicians call curvature.

1980, Harold Abelson, Andrea DiSessa, Turtle Geometry : The Computer as a Medium for Exploring Mathematics, Cambridge, Massachusetts: MIT Press, archived from the original on 2021-06-26, pages 13–14:

(mathematics) The extent to which a subspace is curved within a metric space.

kaarevuus

mathematics: the extent to which a subspace is curved within a metric space

(differential geometry) The extent to which a Riemannian manifold is intrinsically curved.

kaarevuus

differential geometry: of a Riemannian manifold


reflex

en-adj

reflex (comparative more reflex, superlative most reflex)

more reflex (comparative)
most reflex (superlative)

From Late Latin reflexus, past participle of reflectere (“to bend back”), equivalent to re- + flex. Photography sense is from noun sense meaning “reflection”. Compare English reflect.

A polygon is said to be convex when no one of its angles is reflex.

1878, James Maurice Wilson, Elementary Geometry, MacMillan, page 10:

An angle less than a right angle is said to be acute; one greater than a right angle but less than a straight angle is said to be obtuse; one greater than a straight angle but less than a perigon is said to be reflex or convex.

1895, David Eugen Smith, Wooster Woodruff Bernan, New Plane and Solid Geometry, page 7:

If the reflex region is the interior of the angle, the dihedral angle is reflex.

1958, Howard Fehr, “On Teaching Dihedral Angle and Steradian” in The Mathematics Teacher, v 51, National Council of Teachers of Mathematics, page 275

A reflex edge of a polyhedron is an edge where the inner dihedral angle subtended by two incident faces is greater than 180°.

1991, B. Falcidieno et al., “Configurable Representations in Feature-based Modelling”, in Eurographics '91: Proceedings, North-Holland, page 145:

We say that an angle is convex if it is not reflex.

2001, Esther M. Arkin et al., “On the Reflexivity of Point Sets”, in Algorithms and data structures: 7th International Workshop, WADS 2001: Proceedings, Springer, page 195:

P denotes a polygon and r the number of reflex vertices.

2004, Ana Paula Tomás and António Leslie Bajuelos, “Quadratic-Time Linear-Space Algorithms Generating Orthogonal Polygons with a Given Number of Vertices”, in Computational Science and Its Applications – ICCSA 2004 Proceedings, part 3, Springer, page 117

(geometry, of an angle) Having greater than 180 degrees but less than 360 degrees.


great icosihemidodecahedron

(geometry) A polyhedron having 26 faces, 30 vertices, 60 edges, six self-intersected faces, and six nonconvex faces.

大二十面半十二面体

だいにじゅうめんはんじゅうにめんたい


icosihemidodecahedron

small icosihemidodecahedron
small icosihemidodecahedron

great icosihemidodecahedron
great icosihemidodecahedron

(geometry) Either of two polyhedra, the small icosihemidodecahedron and the great icosihemidodecahedron.


versor

From Latin vertere, versus (“to turn”). See version.

(quaternion algebra) A quaternion of norm one.


bicuspid

Having two points or prominences; ending in two points; said of teeth, leaves, fruit, etc.


rondure

en-noun

rondure (countable and uncountable, plural rondures)

Borrowed from French rondeur (“roundness; round object”), from rond (“round”) + -eur (suffix forming agent nouns from verbs).

bor

(uncountable) The quality of being round; roundness.


isosceles

Borrowed from Latin īsoscelēs, from Ancient Greek ἰσοσκελής (isoskelḗs, “equal-legged”), from ἴσος (ísos, “equal”) + σκέλος (skélos, “leg”) + -ής (-ḗs, adjective suffix).

affix

Upon each exterior side draw an Isosceles Triangle of 480 Fathoms.

1693, Abel Swall, transl., The New Method of Fortification, as Practised by Monsieur de Vavban, Engineer General of France, 2nd edition, "A New Treatise of Fortification", page 96:

A right double pyramid is isosceles when the extremities of the vertex-edge are at the same distance from the plane of the base.

1914, Henry Parker Manning, Geometry of Four Dimensions, page 204:

To prepare for the application of his method, Saccheri made use of a figure with which we are already acquainted. This is the isosceles quadrilateral with the two base angles right angles.

1945, Harold E. Wolfe, Introduction to Non-Euclidean Geometry, page 31:

The polygon advantageously is an isosceles trapezoid or rectangle with the pivotal connections between the deck or superstructure and four hulls respectively at its corners.

1965 April 8, Newton B. Dismukes, “Multihull vessels (Patent US3316873A)”, in Google Patents:

The flowers were stuck inside a flower pot that was shaped like an isosceles polygon with a rectangular "edge."

2019 January 23, Altered Book Lover, “Funky Flowers”, in Blogspot:

(geometry) Having (at least) two sides of equal length, used especially of a triangle or trapezoid.

հավասարասրուն

having two sides of equal length, used especially of an isosceles triangle or trapezoid


bell-shaped

en-adj

bell-shaped (comparative more bell-shaped, superlative most bell-shaped)

more bell-shaped (comparative)
most bell-shaped (superlative)

Having a shape or cross-section like the cross-section of a bell.


pear-shaped

pear-shaped (comparative more pear-shaped, superlative most pear-shaped)

more pear-shaped (comparative)
most pear-shaped (superlative)

LL-Q1860 (eng)-Flame, not lame-pear-shaped.wav

Single egg laid directly on ledge, pear-shaped to prevent rolling off[.]

2009, Lars Svensson, Collins Bird Guide, page 210:

Having a shape of a (typical western) pear, or in cross-section, like the cross-section of a pear.

pear-shaped obesity versus apple-shaped obesity

Just as one should take sitting-up exercises every day to keep one's figure from going pear-shaped in the hips, one should spend at least a little time, even if it is only very little, sloughing off mental flabbiness by thinking, studying or just reading something that requires an exercising effort of the mind to understand, memorise or digest.

1936 March 21, Glen Innes Examiner, NSW, page 7, column 3:

Having gynoid fat distribution, not android fat distribution.

(slang, Commonwealth, UK, Ireland) Wrong, awry, usually in the phrase go pear-shaped.


hexagonal

Nuts in engineering are generally hexagonal.

(geometry) Having six edges, or having a cross-section in the form of a hexagon.

ষড়ভুজাকৃতি

geometry: having six edges, or having a cross-section in the form of a hexagon


deltoid

From Latin deltoideus, which was in turn from Ancient Greek adjective δελτοειδής (deltoeidḗs). See also: δέλτα (délta), the fourth letter of the Greek alphabet.

(anatomy) The deltoid muscle, a triangular muscle on the human shoulder.

(geometry) A kite (quadrilateral having two pairs of edges of equal length, the edges of each pair touching each other at one end).

(geometry) A deltoid curve (hypocycloid with three cusps).


deltoid

In the shape of the uppercase Greek letter delta (Δ); triangular.

(botany, of leaves) Of a triangular or roughly triangular shape and attached to the stem via the side.


triangulation

en-noun

triangulation (countable and uncountable, plural triangulations)

/tɹʌɪaŋɡjʊˈleɪʃn̩/

/ˌtɹaɪˌæŋɡjəˈleɪʃən/

From Medieval Latin triangulātiōnem (“triangulation”), from triangulāre (“to triangulate”) + -tiōnem (suffix forming nouns relating to some actions or the results of actions). Triangulāre is derived from triangulāris (“triangular”), from triangulus (“triangular; triangle”), from trēs (“three”) + angulus (“angle; corner”). The English word is analysable as triangulate + -ion, and is cognate with French triangulation.

refn

An engraving from a 16th-century treatise by Levinus Hulsius (1546–1606).

Regular triangulations are a class in-between lifting and lexicographic triangulations. Their main draw-back in the context of this paper is that regularity depends on the specific realization and not only on the oriented matroid.

2002 March, Francisco Santos, “Triangulations of Oriented Matroids”, in Memoirs of the American Mathematical Society, volume 156, number 741, Providence, R.I.: American Mathematical Society, →ISSN, →OCLC, chapter 5 (Lifting Triangulations), page 59:

A triangulation of a point configuration #x5C;mathbf#x7B;A#x7D;#x5C;in#x5C;mathbb#x7B;R#x7D;ᵈ is a collection of d-simplices all of whose vertices are points in #x5C;mathbf#x7B;A#x7D; that satisfies the following two properties: 1. The union of all these simplices equals conv(#x5C;mathbf#x7B;A#x7D;). (Union Property) 2. Any pair of these simplices intersects in a common face (possibly empty). (Intersection Property)

2010, Jésus A[ntonio] De Loera, Jörg Rambau, Francisco Santos, “Triangulations in Mathematics”, in Triangulations: Structures for Algorithms and Applications (Algorithms and Computation in Mathematics; 25), Heidelberg, Dordrecht: Springer Verlag, →DOI, →ISBN, →ISSN, definition 1.0.1, page 1:

(countable, geometry) A subdivision of a planar object into triangles, and by extension the subdivision of a higher-dimension geometric object into simplices.


antiprism

A polyhedron composed of two parallel copies of some particular polygon, connected by an alternating band of triangles.

反稜柱

a polyhedron composed of two parallel copies of some particular polygon, connected by an alternating band of triangles


L-shaped

Shaped like the letter L or its mirror image

A-shaped - B-shaped - C-shaped - D-shaped - E-shaped - F-shaped - G-shaped - H-shaped - I-shaped - J-shaped - K-shaped - L-shaped - M-shaped - N-shaped - O-shaped - P-shaped - Q-shaped - R-shaped - S-shaped - T-shaped - U-shaped - V-shaped - W-shaped - X-shaped - Y-shaped - Z-shaped


gamma function

The function itself was initially defined as an integral (in modern representation, Γ(x)=∫₀ ᪲e⁻ᵗtˣ⁻¹dt) for positive real x by Swiss mathematician Leonhard Euler in 1730. The name derives from the notation, Γ(x), which was introduced by Adrien-Marie Legendre (1752—1833) (he referred to it, however, as the Eulerian integral of the second kind). Both Euler's integral and Legendre's notation shift the argument with respect to the factorial, so that for integer n>0, Γ(n) = (n−1)!. Carl Friedrich Gauss preferred π(x), with no shift, but Legendre's notation prevailed. Generalisation to non-integer negative and to complex numbers was achieved by analytic continuation.

Chapter 3 deals with the p-adic gamma function.

1987, Kit Ming Yeung, Applications of p-adic gamma function to congruences of binomial coefficients, University of California, San Diego, page 3:

2002, M. Aslam Chaudhry, Syed M. Zubair, On a Class of Incomplete Gamma Functions with Applications, Chapman & Hall / CRC Press, page 2,
In particular, the exponential, circular, and hyperbolic functions are rational combinations of gamma functions.

We select one mathematical object, the gamma function, and show how it grew in concept and in content from the time of Euler to the recent mathematical treatise of Bourbaki, and how, in this growth, it partook of the general development of mathematics over the past two and a quarter centuries.

2007, Philip J. Davis, “Leonhard Euler's Integral: A Historical Profile of the Gamma Function”, in William Dunham, editor, The Genius of Euler: Reflections on His Life and Work, American Mathematical Society, page 167:

mathematical analysis
mathematical analysis

(mathematical analysis) A meromorphic function which generalizes the notion of factorial to complex numbers and has singularities at the nonpositive integers; any of certain generalizations or analogues of said function, such as extend the factorial to domains other than the complex numbers.

Adrien-Marie Legendre
American Mathematical Monthly
Carl Friedrich Gauss
Leonhard Euler

fonction gamma

function which generalizes the notion of a factorial

Euler integral of the second kind

function that extends the domain of the factorial


star polygon

(geometry) A geometric figure formed by connecting, with straight lines, every vertex of a p-sided regular polygon to the qth vertex beyond it (proceeding, consistently, either clockwise or anticlockwise).


ruled

(geometry, of a surface) Being a scroll; being such that through every point of S there is a straight line that lies on S.


hyperbolic tangent

en-noun

hyperbolic tangent (plural hyperbolic tangents)

tanh (x)=(sinh (x))/(cosh (x))=(eˣ-e⁻ˣ)/(eˣ+e⁻ˣ).

(mathematics) A hyperbolic function that is written in symbol tanh and defined as the following:


hyperbolic cosine

hyperbolic cosine (plural hyperbolic cosines)

(mathematics) A hyperbolic function that is written in symbol cosh and defined as the following: cosh (x)= tfrac 1 2(eˣ+e⁻ˣ).


hyperbolic sine

hyperbolic sine (plural hyperbolic sines)

(mathematics) A hyperbolic function that is the analogue of the sine function for hyperbolic spaces, taking in a hyperbolic angle as an argument and returning the y-coordinate for the corresponding point on the unit hyperbola. It is written in symbol sinh and can be represented as: sinh (x)= tfrac 1 2(eˣ-e⁻ˣ)


hyperbolic function

hyperbolic function (plural hyperbolic functions)

trigonometric function
trigonometric function

(mathematics) A set of functions that are analogs of the trigonometric functions for hyperbolic spaces.


Klein bottle

Calque of German Kleinsche Flasche, named after German mathematician Felix Klein (1849–1925), who first described such a surface in 1882.

named-after

A physical bottle, usually of blown glass, made to resemble the topological shape.


hyperbolic

hyperbolic partial differential equation

The hyperbolic cosine of zero is one.

hyperbolic function
hyperbolic function#English

trigonometric function
trigonometric function#English

Indicates that the specified function is a hyperbolic function rather than a trigonometric function.

A hyperbolic isometry f has two (distinct) fixed points on ∂ℋ.

2001, A. F. Beardon, "The Geometry of Riemann Surfaces", in, E. Bujalance, A. F. Costa, and E. Martínez, editors, Topics on Riemann Surfaces and Fuchsian Groups, Cambridge, page 6 http://books.google.com/books?id=RjbQdcP7DgwC&pg=PA6&dq=hyperbolic

(geometry, topology, of an automorphism) Whose domain has two (possibly ideal) fixed points joined by a line mapped to itself by translation.


quartic

LL-Q1860 (eng)-Flame, not lame-quartic.wav

(mathematics) An algebraic equation or function of the fourth degree.


cavernous

en-adj

cavernous (comparative more cavernous, superlative most cavernous)

more cavernous (comparative)
most cavernous (superlative)

Late Middle English cavernous, cavernose, borrowing from Old French caverneux or Latin cavernōsus (“full of hollows or cavities”), from caverna (“a hollow, cavity, cave”) + -ōsus (“-ous, -ose”, adjectival suffix); equivalent to cavern + -ous.

af

The last stop on the West Coast Main Line before you cross the border into Scotland, the strategically placed Carlisle Citadel is a station steeped in history. Opened on September 1 1847, the cavernous station was once home to seven railway companies in the pre-Grouping years.

2019 November 20, Paul Stephen, “Lakes and lines offer scenery to savour”, in Rail, page 54:

Resembling a cavern in size, shape, or atmosphere.

cavernous eyes

While the filmmakers behind Dear Evan Hansen have maintained that their biggest motivation for adapting the popular Broadway musical was to immortalize Platt’s Tony-winning titular performance, what they’ve actually done by having the 27-year-old play a high school senior is highlight the stage show’s cavernous weaknesses while failing to transport just about any of its strengths to the new medium.

2021 September 22, Caroline Siede, “Dear Evan Hansen is a misfire on just about every level”, in AV Club:

Giving the impression of vast, dark depths.

(anatomy, zootomy) Composed largely of vascular sinuses and capable of dilating with blood to bring about the erection of a body part.

Having many caverns.
(dentistry) Having cavities.


verf

The regular polyhedra include the five Platonic solids and the four Kepler-Poinsot solids. Their faces are all regular and congruent as well as their vertices and edges. Their verfs are regular also.

2012, Jonathan Bowers, Uniform Polyhedra and Other Three Dimensional Shapes:


perversion

en-noun

perversion (countable and uncountable, plural perversions)

From Latin perversio, from pervertere (“corrupt”).


collinear

(geometry, of three or more points) Lying on the same straight line.


truncate

en-verb

truncate (third-person singular simple present truncates, present participle truncating, simple past and past participle truncated)

truncates (present singular third-person)
truncating (participle present)
truncated (participle past)
truncated (past)

/ˈtɹʌŋˌkeɪt/

From Latin truncātus, perfect passive participle of truncō (“maim, reduce to a trunk”); see trunk as a verb.

بَتَرَ

shorten something as if by cutting off part of it

(geometry) To replace a corner by a plane (or to make a similar change to a crystal).


gree

From Middle English gre, from Old French gré, from Latin gradum (“step”). Compare degree. Doublet of grade.


affine transformation

en-noun

affine transformation (plural affine transformations)

An affine transformation does not in general preserve angles between lines or distances between points, but it does preserve ratios of distances between points lying on a straight line.

Given an affine space X, every affine transformation on X can be represented as the composition of a linear transformation on X and a translation of X.

Examples of affine transformations include translation, scaling, homothety, similarity, reflection, rotation, shear and compositions of them in any combination and sequence.

Just as for plane transformations, we may show that the set of all affine transformations of space form a group.
Under an affine transformation of space, the image of a line is a line, and the image of a plane is a plane.

1965, P. S. Modenov, A. S. Parkhomenko, translated by Michael B. P. Slater, Geometric Transformations, Volume 1: Euclidean and Affine Transformations, Academic Press, page 145:

Theorem 15.2 A transformation such that the images of every three collinear points are themselves collinear is an affine transformation.
Are the affine transformations the same as those transformations for which the images of any three noncollinear points are themselves noncollinear? We shall see the answer is "Yes."

1982, George E. Martin, Transformation Geometry, Springer, page 169:

2004, Solomon Khmelnik, Computer Arithmetic of Geometrical Figures: Algorithms and Hardware Design, Mathematics in Computer Comp., page 8,
Most striking and well-known examples of affine transformation applications are computer tomography (see for instance [1]) and information compression for telecommunication systems (see [2]).
This book describes affine transformations (displacements, turns, scaling, shifts) of n-dimensional figures, where n=1,2,3,4.

(geometry, linear algebra) A geometric transformation that preserves lines and parallelism, but in general not lengths or angles; (more formally) an automorphism of an affine space: a mapping of an affine space onto itself that preserves both the dimension of any affine subspace and the ratio of the lengths of any pair of parallel line segments.

affine homomorphism

mappings from one space to a (generally) different one


affine geometry

affine geometry (countable and uncountable, plural affine geometries)

As an alternative to the axiomatic approach, affine geometry can be studied via the properties of affine transformations, which do not, in general, preserve distances or angles, but do preserve alignment of points and parallelism of lines.

The notion of parallelism remains central to affine geometry, in which the parallel postulate is replaced by Playfair's axiom, a version of the postulate that relies on neither distance nor angle size.

1940 [McGraw-Hill], E. T. Bell, The Development of Mathematics, 2017 [1992], Dover, page 265,
To include affine geometry, Menger (1935) imposed on lattices a reasonable axiom of parallelism.

1953 [Addison-Wesley], Dirk J. Struik, Lectures on Analytic and Projective Geometry, 2014, Dover, page 108,
And affine geometry itself can be considered as the geometry of all projective transformations which leave a line invariant.

Affine geometry is the geometry of an n-dimensional vector space together with its inhomogeneous linear structure.[…]Arbitrary affine linear maps take affine linear subspaces into one another, and also preserve collinearity of points, parallels and ratios of distances along parallel lines; all these are thus well defined notions of affine geometry.

2005, Miles Reid, Balazs Szendroi, Geometry and Topology, Cambridge University Press, page 62:

(geometry, uncountable) The branch of geometry dealing with what can be deduced in Euclidean geometry when the notions of line length and angle size are ignored.


truncation

truncation (countable and uncountable, plural truncations)

From Late Latin truncātiō, from Latin truncāre, past participle truncātus (“to cut off”). See truncate.

(geometry) The replacement of a solid angle by a plane, or a similar operation in other dimensions.


injection

injection (countable and uncountable, plural injections)

Nicolas Bourbaki
Éléments de mathématique

Borrowed from Middle French injection, from Latin iniectio. The mathematical sense is from French injection, introduced by Nicolas Bourbaki in their treatise Éléments de mathématique.

(mathematics) A relation on sets (X,Y) that associates each element of Y with at most one element of X.


loxodrome

Back-formation from loxodromic, from Ancient Greek λοξός (loxós, “oblique”) + δρόμος (drómos, “course”) via French.

(mathematics, nautical) A line on a surface (such as the Earth) that cuts all meridians at a constant angle (but not a right angle) – on Earth, the path followed by a ship or aircraft that maintains a constant course by the compass.


toric

en-adj

toric (comparative more toric, superlative most toric)

more toric (comparative)
most toric (superlative)

Pertaining to or shaped like a torus, or a section of a torus; toroidal.


harmonic

From Latin harmonicus, from Ancient Greek ἁρμονικός (harmonikós), from ἁρμονία (harmonía, “harmony”).

(mathematics) One of a class of functions that enter into the development of the potential of a nearly spherical mass due to its attraction.


inscribe

en-verb

inscribe (third-person singular simple present inscribes, present participle inscribing, simple past and past participle inscribed)

inscribes (present singular third-person)
inscribing (participle present)
inscribed (participle past)
inscribed (past)

Borrowed from Latin īnscrībō, from in- (“upon”) and scrībō (“to write”).

(geometry) To draw a circle, sphere, etc. inside a polygon, polyhedron, etc. and tangent to all its sides.


tet

(geometry, engineering) A tetrahedron; a tetrahedral finite element.


transfer function

en-noun

transfer function (plural transfer functions)

(systems theory) a mathematical representation of the relation between the input and output of a linear time-invariant system


eccentricity

eccentricity (countable and uncountable, plural eccentricities)

excentricitat

a ratio between distances in a conic section

Although the Celebrity was almost impervious to sarcasm, he was now beginning to exhibit visible signs of uneasiness, the consciousness dawning upon him that his eccentricity was not receiving the ovation it merited.

1897 December (indicated as 1898), Winston Churchill, chapter V, in The Celebrity: An Episode, New York, N.Y.: The Macmillan Company; London: Macmillan & Co., Ltd., →OCLC:

The quality of being eccentric or odd; any eccentric behaviour.


superellipsoid

(algebra, geometry) A closed surface, of which the sphere and ellipsoid are special cases, whose parametric equation is x = a.cos^(2/r)t, y = b.cos^(2/r)t, z = c.cos^(2/r)t.


superellipse

(algebra, geometry) a geometric shape constituting a transition between a rectangle and a circle; a closed curve, of which the circle and ellipse are special cases, whose parametric equation is x = a.cos^(2/r)t, y = b.cos^(2/r)t


radical center

(geometry) A point at which the radical lines of three circles meet.


radial

en-adj

radial (comparative more radial, superlative most radial)

more radial (comparative)
most radial (superlative)

From Medieval Latin radiālis (“radial”), from Latin radius.

What is the relationship between arc length and radial length?

(geometry) Of, or relating to a radius (line joining to a geometric centre).

radial velocity