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One name for the figure used by Euclid to prove the Pythagorean theorem.

Divide the sides of a quadrilateral into three equal parts. The figure formed by connecting and extending adjacent points on either side of a polygon vertex is a ...

The Yff central circle, a term coined here for the first time, is the circumcircle of the Yff central triangle.

The Yiu circle is the circumcircle of the Yiu triangle DeltaO_AO_BO_C. It has center function given by alpha=af(a,b,c), where f(a,b,c) is a 14th-order polynomial. Its radius ...

The Yiu triangle DeltaO_AO_BO_C is the triangle formed by the centers of the Yiu circles. It has area where f(a,b,c) is a 12th-order polynomial and Delta is the area of the ...

The binomial coefficient (n; k) is the number of ways of picking k unordered outcomes from n possibilities, also known as a combination or combinatorial number. The symbols ...

Ball tetrahedron picking is the selection of quadruples of points (corresponding to vertices of a general tetrahedron) randomly placed inside a ball. n random tetrahedra can ...

Any bounded planar region with positive area >A placed in any position of the unit square lattice can be translated so that the number of lattice points inside the region ...

Let n points xi_1, ..., xi_n be randomly distributed on a domain S, and let H be some event that depends on the positions of the n points. Let S^' be a domain slightly ...

Given four points chosen at random inside a unit cube, the average volume of the tetrahedron determined by these points is given by ...