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What is the algorithm of pushing and gathering?
What is the algorithm of pushing? Shoelace formula.

Shoelace formula, also called Gaussian area formula, is a mathematical algorithm, which can find the area of a simple polygon in a certain area. Polygons are planes in Cartesian coordinates described by their vertices.

Users cross multiply the corresponding coordinates to find the area around the polygon, and subtract the area from the surrounding polygons to find the area of the polygon. It is called shoelace formula because the coordinates that make up a polygon are constantly cross-multiplied, just like tying shoelaces. -The above is from Wikipedia in en.wikipedia.org/wiki/Shoelace_formula..

Why is it called shoelace formula? This is because it is wound like a shoelace in the calculation process. For example, a polygon (triangle) with three vertices A: (X 1, Y 1), B: (X2, Y2) and C: (X3, Y3) is calculated in this way.

Johann Carl Friedrich Gauss (German: Johann Karl Friedrich Gao? ; ? , English: Gauss, Latin: Carolus Fridericus Gauss,1April 30, 777-1February 23, 855), a famous German mathematician, physicist, astronomer, geometer and geodesist, graduated from Caroline Institute (now Brunswick Polytechnic University).

Gauss was born in Brunswick. 1796, Gauss proved that the ruler can be a regular heptagon. 1807, Gauss became a professor at the University of G? ttingen and director of the G? ttingen Observatory. During the period of1818-1826, the geodetic work in hanover principality was mainly Gaussian. 1840, gauss and Weber drew the world's first map of the earth's magnetic field. ?

Gauss is considered as one of the most important mathematicians in the world and enjoys the reputation of "prince of mathematics".