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A half-space is that portion of an n-dimensional space obtained by removing that part lying on one side of an (n-1)-dimensional hyperplane. For example, half a Euclidean ...

Given a point P in the interior of a triangle DeltaA_1A_2A_3, draw the cevians through P from each polygon vertex which meet the opposite sides at P_1, P_2, and P_3. Now, ...

A derived polygon with side ratios chosen as r=1/2 so that inscribed polygons are constructed by connecting the midpoints of the base polygon. For a triangle P, the ...

Let j, r, and s be distinct integers (mod n), and let W_i be the point of intersection of the side or diagonal V_iV_(i+j) of the n-gon P=[V_1,...,V_n] with the transversal ...

The point about which an angle is measured is called the angle's vertex, and the angle theta associated with a given vertex is called the vertex angle. In a polygon, the ...

The lattice method is an alternative to long multiplication for numbers. In this approach, a lattice is first constructed, sized to fit the numbers being multiplied. If we ...

A Hadamard matrix is a type of square (-1,1)-matrix invented by Sylvester (1867) under the name of anallagmatic pavement, 26 years before Hadamard (1893) considered them. In ...

Clean tile is a game investigated by Buffon (1777) in which players bet on the number of different tiles a thrown coin will partially cover on a floor that is regularly ...

Let a_n and b_n be the perimeters of the circumscribed and inscribed n-gon and a_(2n) and b_(2n) the perimeters of the circumscribed and inscribed 2n-gon. Then a_(2n) = ...

A leg of a right triangle (i.e., a side adjacent the right angle) is also known as a cathetus (plural: catheti). While this usage is rather rare in English, the terms ...