On a straight line, Ptolemy theorem also holds, also called euler theorem.
The inverse theorem of Ptolemy's theorem also holds: the sum of the products of two opposite sides of a convex quadrilateral is equal to the product of two diagonal lines, then this convex quadrilateral is inscribed in a circle.
Qin Sheng inequality was established by the Danish mathematician Qin Sheng from 1905 to 1906. A series of inequalities can be obtained by using Qin Sheng inequality, such as "power average inequality" and "weighted Qin Sheng inequality".
Descartes theorem: the intersection of a straight line and three pairs of opposite sides of a complete quadrilateral * and a conic curve circumscribed by the quadrilateral form a involutory four-point couple. The connecting line between a point and three pairs of vertices of a complete quadrilateral * and the tangent drawn from the point to the conic inscribed in the quadrilateral form a involutory four-ray coupling.
Fermat's last theorem:
When the integer n > 2, the indefinite equation about x, y and z.
x^n + y^n = z^n.
The integer solution of is trivial, that is,
When n is an even number: (0, m, m) or (m, 0, m)
When n is odd: (0, m, m) or (m, 0, m) or (m, -m, 0)
This theorem was originally called Fermat's conjecture, which was put forward by the French mathematician Fermat in the17th century.