In
geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...
, the seven circles theorem is a theorem about a certain arrangement of seven
circle
A circle is a shape consisting of all point (geometry), points in a plane (mathematics), plane that are at a given distance from a given point, the Centre (geometry), centre. The distance between any point of the circle and the centre is cal ...
s in the
Euclidean plane
In mathematics, a Euclidean plane is a Euclidean space of Two-dimensional space, dimension two, denoted \textbf^2 or \mathbb^2. It is a geometric space in which two real numbers are required to determine the position (geometry), position of eac ...
. Specifically, given a chain of six circles all
tangent
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is, intuitively, the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points o ...
to a seventh circle and each tangent to its two neighbors, the three
lines drawn between opposite pairs of the points of tangency on the seventh circle all pass through the same
point. Though elementary in nature, this theorem was not discovered until 1974 (by Evelyn, Money-Coutts, and Tyrrell).
See also
*
Brianchon's theorem
In geometry, Brianchon's theorem is a theorem stating that when a hexagon is circumscribed around a conic section, its principal diagonals (those connecting opposite vertices) meet in a single point. It is named after Charles Julien Brianchon (1 ...
References
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External links
* {{MathWorld, title=Seven Circles Theorem, urlname=SevenCirclesTheorem
Interactive Appletby Michael Borcherds showing The Seven Circles Theorem made usin
GeoGebra
the Seven Circles Theoremby Stanley Rabinowitz, with a proof based on Ceva's theorems.
Seven Circles Theoremat
Cut-the-knot
Alexander Bogomolny (January 4, 1948 July 7, 2018) was a Soviet Union, Soviet-born Israeli Americans, Israeli-American mathematician. He was Professor Emeritus of Mathematics at the University of Iowa, and formerly research fellow at the Moscow ...
.
Theorems about circles
7 (number)