Pascal's theorem refers to the intersection of three opposite sides of a cone inscribed with a hexagon (including a degenerate hexagon), which is dual with Briansan's theorem and a generalization of Pappus's theorem. Theorem in about 1639 for the French mathematician Blaise Pascal (Blaise? Pascal, also known as Pascal's theorem, is an important theorem in projective geometry.

If a hexagon is inscribed with a quadratic curve (circle, ellipse, hyperbola, parabola), then the intersections of its three pairs of opposite sides are on the same straight line. Because of the existence of hexagon, there are many kinds of graphs of Pascal's theorem. Although they look completely different, they are all Pascal's theorems, and the methods of proof are the same.

Briansan theorem;

Brian theorem is a famous theorem in projective geometry, which asserts that the three diagonal points where six sides of a hexagon are tangent to a conic curve are called Brian points. The inverse theorem of Brian Sang's theorem also holds, that is, if the three diagonal points of a hexagon are * * *, then its six sides are tangent to a conic curve.

French mathematician Charles Julian Brianxiong (1783–1864) found that according to French pronunciation, Brianxiong should be translated as "Brianxiong". Nowadays, most translators of mathematical terms don't know French, so they are wrongly translated into "Brianchon" according to English pronunciation. This term has been widely known, so they follow it. Brian Sang's theorem is another famous theorem in projective geometry: the duality theorem of Pascal's theorem.