cylinder

→ Japanese: シリンダー (shirindā)

→ Korean: 실린더 (sillindeo)

From Middle French chilindre, cylindre, from Latin cylindrus, from Ancient Greek κύλινδρος (kúlindros), from κυλίνδω (kulíndō) "I roll or wallow" (intransitive). Doublet of calander and calender.

When the two-dimensional curve is a circle, the cylinder is called a circular cylinder. When the axis is perpendicular to the plane of the curve, the cylinder is called a right cylinder. In non-mathematical usage, both right and circular are usually implied.

(geometry) A surface created by projecting a closed two-dimensional curve along an axis intersecting the plane of the curve.


cubic

From Middle French cubique, equivalent to cube + -ic.


sphere

From Middle English spere, from Old French sphere, from Late Latin sphēra, earlier Latin sphaera (“ball, globe, celestial sphere”), from Ancient Greek σφαῖρα (sphaîra, “ball, globe”), of unknown origin. Not related to superficially similar Persian سپهر (sepehr, “sky”) .

uder

(mathematics) A surface in three dimensions consisting of all points equidistant from a center. .


torus

Borrowed from Latin torus (“a round, swelling, elevation, protuberance”).

bor

A 4-variable Karnaugh map can be thought of, topologically, as being a torus.

(geometry) The standard representation of such a space in 3-dimensional Euclidean space: a surface or solid formed by rotating a closed curve, especially a circle, about a line which lies in the same plane but does not intersect it (e.g. like a ring doughnut).

(topology) A topological space which is a product of two circles.

(topology, in combination, n-torus, 4-torus, etc.) The product of the specified number of circles.

A ring-shaped object, especially a large ring-shaped chamber used in physical research.


plane

→ Irish: plána

From Latin plānum (“flat surface”), a noun use of the neuter of plānus (“plain”). The word was introduced in the 17th century to distinguish the geometrical senses from the other senses of plain. Doublet of llano, piano, and plain.

հարթություն

geometry: flat surface extending infinitely in all directions

Mirrors in the compartments have been canted out of the vertical plane to reduce reflections to the passengers when seated.

1979 August, Graham Burtenshaw, Michael S. Welch, “O.V.S. Bulleid's SR loco-hauled coaches - 1”, in Railway World, page 396:

(geometry) A flat surface extending infinitely in all directions (e.g. horizontal or vertical plane).

(anatomy) An imaginary plane which divides the body into two portions.


surface

From French surface. Doublet of superficies.

(mathematics, geometry) The locus of an equation (especially one with exactly two degrees of freedom) in a more-than-two-dimensional space.

سَطْح

locus of an equation in a more-than-two-dimensional space


toroid

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(mathematics) A surface generated by a closed curve (especially a circle) rotating about, but not intersecting or containing, an axis in its own plane.


septic

Enriques states that it is possible to construct a family of septics with a singular curve of degree 7 and genus 4 having a triple point that degenerates to the above configuration[…].

2002, Ingrid C. Bauer, Fabrizio Catanese, Roberto Pignatelli, “Canonical Rings of Surfaces Whose Canonical System has Base Points”, in Ingrid C. Bauer et al., editors, Complex Geometry: Collection of Papers Dedicated to Hans Grauert, page 66:

Now consider the two septics C = U⁷ᵢ₌₁Cᵢ, D = U⁷ᵢ₌₁Dᵢ and note that for i = 1,2,3,4,5,6 the lines Cᵢ and Dᵢ are parallel, so that the intersection of two septics S' consists of 6⁶^([sic]) + 6 + 1 = 43 points and it is the singular set of a foliation of degree 6.

2003, Antonio Campillo, Santiago Encinas, “Two Dimensional Complete Ideals”, in Luchezar L. Avramov et al., editors, Commutative Algebra: Interactions with Algebraic Geometry: International Conference, page 71:

(mathematics) A mathematical object (function, curve, surface, etc.) of degree seven.


solid of revolution

en-noun

solid of revolution (plural solids of revolution)

A cylinder is a solid of revolution generated by rotating a rectangle about one of its axes.

A solid produced by taking a particular two-dimensional curve and rotating it through 360° about an axis. The curve will sweep out a surface, and the region inside the surface defines a solid.

omdrejningslegeme

solid produced rotating a two-dimensional curve through 360° about an axis


spheroid

en-adj

spheroid (comparative more spheroid, superlative most spheroid)

more spheroid (comparative)
most spheroid (superlative)

Of a shape similar to a squashed sphere.


spheroid

UFOs are reported as being either oblate (saucer-shaped) or prolate (cigar-shaped) spheroids.

A solid of revolution generated by rotating an ellipse about its major (prolate), or minor (oblate) axis.


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.


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.


pear-shaped

en-adj

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

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

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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.


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

At this level Atman and Brahman are like a Klein bottle or a Möbius strip: there is no edge where one can say that this is Atman, but this is Brahman.

1981, William Irwin Thompson, The Time Falling Bodies Take to Light: Mythology, Sexuality and the Origins of Culture, London: Rider/Hutchinson & Co., page 222:

(topology) The closed manifold obtained by identifying the boundary components of the annulus so that the resultant surface is nonorientable.

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


level set

mathematical analysis
mathematical analysis

(mathematical analysis) The set of values x for which a real-valued function f(x) is equal to a given constant.


spherical lune

(geometry) A portion of the surface of a sphere cut off by two vertical planes through the centre of the sphere.


Euclidean plane

en-noun

Euclidean plane (plural Euclidean planes)


complex plane

(mathematics) a representation of the space of complex numbers


Riemann surface

Riemann surface (plural Riemann surfaces)

From Bernhard Riemann, German mathematician.

(mathematics) A one-dimensional complex manifold; a generalization of the complex plane.


ellipsoid

Polarizability can be imagined as a three-dimensional ellipsoid centred on the centre of the molecule, as shown in Figure 10.4.

2002, John Michael Hollas, Basic Atomic and Molecular Spectroscopy, page 133:

Because only ellipsoids of rotation have been adopted in practical geodesy and surveying and triaxial ellipsoids have been limited to theoretical studies, we will use the term ellipsoid for brevity to mean ellipsoid of rotation.

2004, Alfred Leick, GPS Satellite Surveying, 3rd edition, page 367:

As mentioned before, modern geodetic datums rely on the surfaces of geocentric ellipsoids to approximate the surface of the earth.

2010, Jan Van Sickle, Basic GIS Coordinates, 2nd edition, page 73:

Cartesian coordinates
Cartesian coordinates

(mathematics, geometry) A surface, all of whose cross sections are elliptic or circular (including the sphere), that generalises the ellipse and in Cartesian coordinates (x, y, z) is a quadric with equation x²/a² + y²/b² + z²/c² = 1.

উপবৃত্তাকার

surface all of whose cross sections are elliptic or circular


paraboloid

(mathematics) A surface having a parabolic cross section parallel to an axis, and circular or elliptical cross section perpendicular to the axis; especially the surface of revolution of a parabola.


spheroidal

en-adj

spheroidal (comparative more spheroidal, superlative most spheroidal)

more spheroidal (comparative)
most spheroidal (superlative)

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The buccal mass in milacids is spheroidal, and contains an oxygnathic jaw.

2004, G. M. Barker, Natural Enemies of Terrestrial Molluscs, page 299:


surface of revolution

en-noun

surface of revolution (plural surfaces of revolution)

A sphere is a surface of revolution of a circle around an axis which runs through the center of the circle.

A torus is a surface of revolution of a circle around an axis which is outside the circle.

(mathematics) A surface formed when a given curve is revolved around a given axis. If the resulting surface is a closed one, it also defines a solid of revolution.


helicoid

From Ancient Greek ἑλικοειδής (helikoeidḗs); morphologically, from helico- + -id.

(mathematics) A minimal surface in the form of a flattened helix


equipotential

A region whose every point has the same potential.


hyperbolic plane

hyperbolic plane (plural hyperbolic planes)

(mathematics) A topological space homeomorphic to a plane (or open disk) and equipped with a hyperbolic metric.


minimal surface

minimal surface (plural minimal surfaces)

(mathematics) Any surface that has the least possible surface area of those into which it could transform; typically the shapes of soap bubbles that span wire frames


gyroid

Coordinate term: lattice

(mathematics) An infinitely connected periodic minimal surface containing no straight lines.


cyclide

(mathematics) Any of a class of surfaces, described by quartic expressions, that are related to spherical surfaces


hyperboloid

A particular surface in three-dimensional Euclidean space, the graph of a quadratic with all three variables squared and their coefficients not all of the same sign.


isosurface

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an isosurface representing a concentration of 10 grams per cubic meter

(computer graphics, geometry) A surface that represents points of a constant value within a volume of space


horosphere

A modern scientific coinage, probably from a Latinized spelling of Ancient Greek ὅρος (hóros, “boundary”) (not to be confused with ὧρος (hôros, “year”), which gave rise to many time-related terms) + sphere

An n-1-dimensional hyperplane in hyperbolic n-dimensional space: it is (in the Poincaré disk) Euclidean-tangent at infinity to the boundary sphere or (in the upper-half-space model) Euclidean-parallel to the boundary hyperplane.


quadric

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(mathematics) A surface or curve whose shape is defined in terms of a quadratic equation

quadrique

surface whose shape is defined in terms of a quadratic equation


bicone

(geometry) The three-dimensional shape swept by revolving an isosceles triangle around its edge of unequal length, or by joining two identical right circular cones, base to base.


catenoid

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(geometry) A three-dimensional surface formed by rotation of a catenary

caténoïde

Three-dimensional surface formed by rotation of a catenary


sextic

(mathematics) An algebraic equation or function of the sixth degree, e.g. a polynomial of degree 6; a curve surface etc. describing such an equation or function, especially a quantic of the sixth degree.


pseudosphere

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(geometry) Any of various surfaces with constant negative Gaussian curvature.


conoid

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(geometry) A Catalan surface all of whose rulings intersect some fixed line


real plane

(set theory) The Cartesian product of two real lines.


tractricoid

(geometry) A surface formed by revolving a tractrix about its asymptote.


projective plane

projective plane (plural projective planes)

Generally, a projective plane of "order" N has N²+N+1 points, and the same number of lines.

2004, David S. Dummit with Richard M. Foote, chapter 6, in Abstract Algebra, page 210

(geometry) A plane in which any pair of distinct points determine a line and any pair of distinct lines intersect at a point.


superegg

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(geometry) A surface formed by rotating a superellipse about one of its axes.


ellipsoid of revolution

ellipsoid of revolution (plural ellipsoids of revolution)

An ellipsoid of revolution may be either prolate or oblate.

(geometry) A spheroid; a solid of revolution generated by rotating an ellipse about one of its axes.


Fano plane

Named after Gino Fano (1871–1952), an Italian mathematician.

(geometry) The finite projective plane of order 2, having the smallest possible number of points and lines, 7 each, with 3 points on every line and 3 lines through every point.


Gauss map

Named after German mathematician Carl Friedrich Gauss.

1969 [Van Nostrand], Robert Osserman, A Survey of Minimal Surfaces, 2014, Dover, Unabridged republication, page 73,
There exist complete generalized minimal surfaces, not lying in a plane, whose Gauss map lies in an arbitrarily small neighborhood on the sphere.

1985, R. G. Burns (translator), B. A. Dubrovin, A. T. Fomenko, S. P. Novikov, Modern Geometry― Methods and Applications: Part II: The Geometry and Topology of Manifolds, Springer, Graduate Texts in Mathematics, page 114,
14.2.2 Theorem The integral of the Gaussian curvature over a closed hypersurface in Euclidean n-space is equal to the degree of the Gauss map of the surface, multiplied by γₙ (the Euclidean volume of the unit (n-1)-sphere).

In §2 we use results of §1 for the study of Gauss maps of projective varieties. The classical Gauss map associates to each point of a nonsingular real affine hypersurface the unit vector of the external normal at this point.

2005, F. L. Zak, Tangents and Secants of Algebraic Varieties, American Mathematical Society, page 5:

differential geometry
differential geometry

(geometry, differential geometry) A map from a given oriented surface in Euclidean space to the unit sphere which maps each point on the surface to a unit vector orthogonal to the surface at that point.


Klein quartic

Named after German mathematician Felix Klein, who described it in 1878.

A compact Riemann surface of genus 3 with the highest possible order automorphism group for this genus, namely order 168 orientation-preserving automorphisms, and 336 automorphisms if orientation may be reversed.


Hurwitz surface

Hurwitz surface (plural Hurwitz surfaces)

(geometry) A compact Riemann surface with precisely 84(g − 1) automorphisms, where g is the genus of the surface. This number is maximal by virtue of Hurwitz's theorem on automorphisms.


real projective plane

real projective plane (plural real projective planes)

(geometry) A three-dimensional vector space over the field of real numbers in which one-dimensional linear subspaces are considered as “points” and two-dimensional linear subspaces are considered as “lines”. Equivalently, a sphere in which pairs of antipodal points are considered as “points” and great circles are considered as “lines”.


unduloid

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(geometry) A surface of revolution of an elliptic catenary


Cauchy horizon

(physics) A light-like boundary of the domain of validity of a Cauchy problem. One side of the horizon contains closed space-like geodesics and the other side contains closed time-like geodesics.


Fermat curve

Named after French mathematician Pierre de Fermat (1607-1665).

homogeneous coordinate
homogeneous coordinate

(mathematics) The algebraic curve in the complex projective plane defined in homogeneous coordinates (X:Y:Z) by the Fermat equation.


apple-shaped

en-adj

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

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

Having a shape of an apple, or in cross-section, like the cross-section of an apple.

Even at BMIs above 30, where obesity begins, men and women whose waist-to-hip ratio identified them as more pear-shaped were less likely to die -- of any cause and of cardiovascular causes -- than those with similar BMIs who were apple-shaped.

2015 September 11, Melissa Healy, “Pear-shaped vs. apple trumps body mass index as a measure of risk”, in Los Angeles Times:

Having android fat distribution, not gynoid fat distribution.