See circle of Apollonius on Wiktionary
Download JSON data for circle of Apollonius meaning in All languages combined (3.6kB)
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"etymology_text": "Named for the ancient Greek geometer and astronomer Apollonius of Perga (ca 262—ca 190 BCE).",
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"ref": "1934, Tôhoku Mathematical Journal, volumes 39-40, page 264",
"text": "In the present paper an attempt is made to find for the tetrahedron the analogues of the circles of Apollonius of the triangle.",
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"ref": "1995, Howard Whitley Eves, College Geometry, page 165",
"text": "It follows that O lies on the circle of Apollonius for A and C and ratio OT/OC, and on the circle of Apollonius for B and C and ratio OT/OC. Point O is thus found at the intersections, if any exist, of these two circles of Apollonius. The details are left to the reader.",
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"ref": "1996, A. C. Thompson, Minkowski Geometry, page 126",
"text": "More generally, the locus of points z such that #x5C;left#x5C;vertx-z#x5C;right#x5C;vert#x3D;#x5C;alpha#x5C;left#x5C;verty-z#x5C;right#x5C;vert is a circle of Apollonius which has x and y as inverse points and which cuts each circle through x and y orthogonally.[…]They show loci analogous to circles of Apollonius and the locus of points equidistant from two given points when the norm is an #x5C;mathcal#x7B;l#x7D;#x5F;p-norm.",
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"glosses": [
"The figure (a generalised circle) definable as the locus of points P such that, for given points A, B and C, =/(\\frac)."
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"(geometry) The figure (a generalised circle) definable as the locus of points P such that, for given points A, B and C, =/(\\frac)."
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"Any of eight circles (including degenerate cases) that, for a given set of three circles, solve the problem of Apollonius (i.e., intersect each circle tangentially)."
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"(geometry) Any of eight circles (including degenerate cases) that, for a given set of three circles, solve the problem of Apollonius (i.e., intersect each circle tangentially)."
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"etymology_text": "Named for the ancient Greek geometer and astronomer Apollonius of Perga (ca 262—ca 190 BCE).",
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"ref": "1995, Howard Whitley Eves, College Geometry, page 165",
"text": "It follows that O lies on the circle of Apollonius for A and C and ratio OT/OC, and on the circle of Apollonius for B and C and ratio OT/OC. Point O is thus found at the intersections, if any exist, of these two circles of Apollonius. The details are left to the reader.",
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"ref": "1996, A. C. Thompson, Minkowski Geometry, page 126",
"text": "More generally, the locus of points z such that #x5C;left#x5C;vertx-z#x5C;right#x5C;vert#x3D;#x5C;alpha#x5C;left#x5C;verty-z#x5C;right#x5C;vert is a circle of Apollonius which has x and y as inverse points and which cuts each circle through x and y orthogonally.[…]They show loci analogous to circles of Apollonius and the locus of points equidistant from two given points when the norm is an #x5C;mathcal#x7B;l#x7D;#x5F;p-norm.",
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"(geometry) The figure (a generalised circle) definable as the locus of points P such that, for given points A, B and C, =/(\\frac)."
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"(geometry) Any of eight circles (including degenerate cases) that, for a given set of three circles, solve the problem of Apollonius (i.e., intersect each circle tangentially)."
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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-05-10 from the enwiktionary dump dated 2024-05-02 using wiktextract (a644e18 and edd475d). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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