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- ...n-loop transfer function <math>G(s) = 1/(s+0.5)</math>in blue with M and N circles overlaid in the plot. The M circle with M = 0.45 is highlighted in red and ...the [[Nichols plot]]) of the associated open-loop transfer function. Hall circles have been introduced in control theory by Albert C. Hall in his thesis.<ref ...5 KB (732 words) - 23:21, 12 December 2024
- ...gent lines often involve [[radial line]]s and [[orthogonality|orthogonal]] circles. ...thus, {{mvar|T}} is the midpoint of the line segment OG. Two intersecting circles of the same radius ''R''>''r'' are drawn, centered on {{mvar|O}} and {{mvar ...34 KB (5,451 words) - 18:16, 29 November 2024
- ...ered [[Descartes' theorem]] on the radii of mutually tangent quadruples of circles. ...of the triangle. They can be generalized to additional triples of tangent circles centered at the vertices in which one circle surrounds the other two. ...11 KB (1,610 words) - 15:37, 6 February 2024
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- ...three given circles have eight Hart circles associated with them. The Hart circles are named after their discover, [[Andrew Searle Hart]]. They can be seen as [[Category:Circles]] ...2 KB (278 words) - 07:19, 2 June 2024
- {{Short description|Circle in the arbelos congruent to the twin circles}} [[Image:Archimedes' Circles.svg|thumb|300px|Archimedes' twin circles. The large semicircle has unit diameter, BC = 1–''r'', and AB = ''r'' = AB/ ...4 KB (663 words) - 00:40, 9 January 2025
- ...rt between these two formulations of the problem, the square side for unit circles will be {{math|''L'' {{=}} 2 + {{sfrac|2|''d<sub>n</sub>''}}}}. ...i-magdeburg.de/packing/csq/csq.html|title=The best known packings of equal circles in a square |author=Eckard Specht |date=20 May 2010 |access-date=25 May 201 ...5 KB (682 words) - 18:22, 30 December 2024
- ...n-loop transfer function <math>G(s) = 1/(s+0.5)</math>in blue with M and N circles overlaid in the plot. The M circle with M = 0.45 is highlighted in red and ...the [[Nichols plot]]) of the associated open-loop transfer function. Hall circles have been introduced in control theory by Albert C. Hall in his thesis.<ref ...5 KB (732 words) - 23:21, 12 December 2024
- ...at goes through the centers of the two [[Soddy circles of a triangle|Soddy circles]] of that triangle. ...ublished a proof of a special case of [[Descartes' theorem]] about tangent circles as a poem in [[Nature (journal)|Nature]] in 1936. ...2 KB (251 words) - 08:34, 3 January 2025
- {{short description|On rays from a point to a line, with equal inscribed circles between adjacent rays}} [[Image:Incircles.JPG|thumb|360px|If the blue circles are equal, the green circles are also equal.]] ...4 KB (655 words) - 03:08, 2 March 2024
- ...ons are known for {{math|''n'' < 13}} and for any [[triangular number]] of circles, and conjectures are available for {{math|''n'' < 28}}.<ref name="Melissen" | title = Densest packings of congruent circles in an equilateral triangle ...6 KB (740 words) - 22:06, 21 January 2025
- ...isodynamic points are related to the three [[Apollonius circle|Apollonian circles]] associated with a triangle. ...ircle {{mvar|E}} referred to in the above definition is one of these eight circles touching the three excircles of triangle {{math|△''ABC''}}. In [[Encycloped ...4 KB (556 words) - 07:55, 13 May 2024
- {{Short description|In-depth exploration of circles, spheres, and inversive geometry by Julian Coolidge}} ...mpactification]], and considers Euclidean lines to be a degenerate case of circles, passing through the [[point at infinity]]. It identifies every circle with ...6 KB (784 words) - 21:57, 2 April 2024
- ...easuring the "distance" between two [[circle]]s, regardless of whether the circles cross each other, are tangent to each other, or are disjoint from each othe ...formation]].<ref name="bh"/><ref name="ampa"/><ref name="bq"/> One pair of circles can be transformed to another pair by a Möbius transformation if and only i ...8 KB (1,179 words) - 19:59, 5 September 2024
- ...a |first=Tomohiro |date=2000 |title=Optimal Packings of 8, 9, and 10 Equal Circles in an Isosceles Right Triangle |publisher=Japan Advanced Institute of Scien ! Number of circles ...3 KB (334 words) - 15:31, 22 October 2022
- '''Haruki's Theorem''' says that given three intersecting circles that only intersect each other at two points that the lines connecting the ...ion points.<ref>{{cite journal |title=On a metrical theorem in geometry of circles |first=Hiroshi |last=Haruki |year=1972 |journal=Colloquium Mathematicum |vo ...1 KB (200 words) - 04:39, 16 December 2024
- The centers of these circles relating to {{math|△''ABC''}} are all collinear–they fall on the [[Euler li Any two polar circles of two triangles in an [[orthocentric system]] are [[orthogonal]].<ref name ...3 KB (489 words) - 10:21, 3 October 2024
- ==Soddy circles== [[File:Inner and outer Soddy points 02.svg|thumb|250px|Inner and outer Soddy circles in the case where the outer Soddy point is an isoperimetric point in the se ...7 KB (1,069 words) - 04:55, 15 November 2024
- ...e 4 points.svg|thumb|upright=1.4|4 points <math>A,B,C,D</math> and 4 pedal circles intersecting in <math>S</math>]] [[Griffiths' theorem]] states that all the pedal circles for a points located on a line through the center of the triangle's circumc ...4 KB (628 words) - 00:53, 13 May 2024
- {{Short description|Theorem about circles through lattice points}} ...circles generated by Schinzel's construction are not the smallest possible circles passing through the given number of integer points,{{r|mathworld}} but they ...3 KB (458 words) - 00:59, 9 January 2025
- ...ered [[Descartes' theorem]] on the radii of mutually tangent quadruples of circles. ...of the triangle. They can be generalized to additional triples of tangent circles centered at the vertices in which one circle surrounds the other two. ...11 KB (1,610 words) - 15:37, 6 February 2024
- ...rrelated variables]] {{mvar|X}} and {{mvar|Y}}. The area contained by both circles is the [[joint entropy]] {{tmath|H(X,Y)}}. The circle on the left (red and ...ntropy {{tmath|H(x,y,z)}} of all three variables is the union of all three circles. It is partitioned into 7 pieces, red, blue, and green being the [[Conditio ...3 KB (498 words) - 07:20, 4 March 2024
- ...rincir/|archive-date=2020-03-18|first=Erich|last=Friedman|title=Circles in Circles|work=Erich's Packing Center}}</ref> ! scope="col" | Layout(s) of the<br><math>n</math> circles ...7 KB (904 words) - 08:36, 12 November 2024
- {{short description|About a common point of certain circles defined by an arbitrary triangle}} ...,C^*</math>, respectively. The theorem says that these three '''Musselman circles''' meet in a point <math>M</math>, that is the [[circle inversion|inverse]] ...5 KB (865 words) - 22:20, 2 November 2020