When the outer Soddy circle has positive curvature, both Soddy centers are equal detour points.When the outer Soddy circle has negative curvature, its center is the isoperimetric point: the triangles ABP2, BCP2, and CAP2 have equal perimeter.
In geometry, the Soddy circles of a triangle are two circles associated with any triangle in the plane. Their centers are the Soddy centers of the triangle. They are all named for Frederick Soddy, who rediscovered Descartes' theorem on the radii of mutually tangent quadruples of circles.
Any triangle has three externally tangent circles centered at its vertices. Two more circles, its Soddy circles, are tangent to the three circles centered at the vertices; their centers are called Soddy centers. The line through the Soddy centers is the Soddy line of the triangle. These circles are related to many other notable features 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.
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These circles are the Soddycirclesof △ABC. The circle with the smaller radius is the inner Soddycircle and its center is called the inner Soddy point...
inversive geometry is the study of inversion, a transformation of the Euclidean plane that maps circles or lines to other circles or lines and that preserves...
the GEOS circle is derived from the intersection of four lines that are associated with a generalized triangle: the Euler line, the Soddy line, the orthic...
radius of the outer Soddycircleof any right triangle is equal to its semiperimeter. The outer Soddy center is located at D, where ACBD is a rectangle...
geometry, tangent circles (also known as kissing circles) are circles in a common plane that intersect in a single point. There are two types of tangency: internal...
center of the inner Soddycircleofatriangle and the additional distance travelled by the detour is equal to the diameter of the inner SoddyCircle. The...
given circles α and β, then there is an infinite number of closed Steiner chains of n circles; and any circle tangent to α and β in the same way is a member...
de Δ", pp. 58–59. Vandeghen, A. (1964), "Mathematical Notes: Soddy'sCircles and the De Longchamps Point ofaTriangle", The American Mathematical Monthly...
form a Steiner chain tangent to the two Soddy'scircles. Either Soddycircle, when taken together with the three given circles, produces a set of four...
circle Complex geometry Conic section Focus Circle List ofcircle topics Thales' theorem Circumcircle Concyclic Incircle and excircles ofatriangle Orthocentric...
of the Triangle and the Circle (2nd ed.), Courier Dover Publications, p. 295, ISBN 9780486458052. Vandeghen, A. (1964), "Mathematical Notes: Soddy's Circles...
right), circles and triangles. Alternative periodic tables are often developed to highlight or emphasize chemical or physical properties of the elements...
alter the values of the y by small amounts to try to minimise the polynomial in terms of the y. Equilateral dimension Spherical code Soddy's hexlet Cylinder...
For example, when describing the motion ofa drum skin, one can consider D {\displaystyle D} to be a disk (circle) on the plane R 2 {\displaystyle \mathbb...
integration around the boundary ofa rectangle in the complex plane. 1822 – Irisawa Shintarō Hiroatsu analyzes Soddy's hexlet in a Sangaku. 1823 – Sophie Germain's...
symbols are triangles, circles, and other geometrical figures, without whose help it is humanly impossible to comprehend a single word of it, and without...
chemist, the co-discoverer of chemical element protactinium (1913). He is also known for the Fajans' rules, Fajan's and Soddy's law, Fajans–Paneth–Hahn Law...
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