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A graph G whose line graph is L(G) is called the root graph R(L(G)) of L(G). In order words, R(L(G))=G. The root graph of a connected graph is unique except for K_3=C_3 (the ...

In plane geometry, a chord is the line segment joining two points on a curve. The term is often used to describe a line segment whose ends lie on a circle. The term is also ...

In the case of a general surface, the distance between two points measured along the surface is known as a geodesic. For example, the shortest distance between two points on ...

The triangle with edge lengths 3, 4, and 5 is the right triangle with smallest possible integer lengths and corresponds to the Pythagorean triple (3,4,5) where the legs have ...

Five point geometry is a finite geometry subject to the following three axioms: 1. there exist exactly five points, 2. each two distinct points have exactly one line on both ...

A cubic curve invented by Diocles in about 180 BC in connection with his attempt to duplicate the cube by geometrical methods. The name "cissoid" first appears in the work of ...

The meeting point of lines that connect corresponding points from homothetic figures. In the above figure, O is the homothetic center of the homothetic figures ABCDE and ...

Draw the perpendicular line from the intersection of the two small semicircles in the arbelos. The two circles C_1 and C_2 tangent to this line, the large semicircle, and ...

The Tixier point X_(476) is the reflection of the focus of the Kiepert parabola (X_(110)) in the Euler line. It has equivalent trilinear center functions X_(476) = ...

The complex plane is the plane of complex numbers spanned by the vectors 1 and i, where i is the imaginary number. Every complex number corresponds to a unique point in the ...