Seven circles theorem
Encyclopedia
In geometry
, the seven circles theorem is a theorem about a certain arrangement of seven circle
s in the Euclidean plane. Specifically, given a chain of six circles all tangent
to a seventh circle and each tangent to its two neighbors, the three lines
drawn between the six points of tangency with 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).
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, the seven circles theorem is a theorem about a certain arrangement of seven circle
Circle
A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....
s in the Euclidean plane. Specifically, given a chain of six circles all tangent
Tangent
In geometry, the tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point. More precisely, a straight line is said to be a tangent of a curve at a point on the curve if the line passes through the point on the curve and has slope where f...
to a seventh circle and each tangent to its two neighbors, the three lines
Line (geometry)
The notion of line or straight line was introduced by the ancient mathematicians to represent straight objects with negligible width and depth. Lines are an idealization of such objects...
drawn between the six points of tangency with the seventh circle all pass through the same point
Point (geometry)
In geometry, topology and related branches of mathematics a spatial point is a primitive notion upon which other concepts may be defined. In geometry, points are zero-dimensional; i.e., they do not have volume, area, length, or any other higher-dimensional analogue. In branches of mathematics...
. Though elementary in nature, this theorem was not discovered until 1974 (by Evelyn, Money-Coutts, and Tyrrell).
External links
- Java applet by Michael Borcherds showing The Seven Circles Theorem made using GeoGebra.