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Squaring is the geometric construction, using only compass and straightedge, of a square which has the same area as a given geometric figure. Squaring is also called ...

In the triangle DeltaABC illustrated above, side c subtends angle ∠C. More generally, given a geometric object O in the plane and a point P, let A be the angle from one edge ...

Construction of the angle pi/4=45 degrees produces an isosceles right triangle. Since the sides are equal, sin^2theta+cos^2theta=2sin^2theta=1, (1) so solving for ...

Two circles may intersect in two imaginary points, a single degenerate point, or two distinct points. The intersections of two circles determine a line known as the radical ...

Square line picking is the selection of pairs of points (corresponding to endpoints of a line segment) randomly placed inside a square. n random line segments can be picked ...

The Grötzsch graph is smallest triangle-free graph with chromatic number four. It is identical to the Mycielski graph of order four, and is implemented as ...

In the case of a general surface, the distance between two points measured along the surface is known as a geodesic. For example, the shortest distance between two points on ...

The word "pole" is used prominently in a number of very different branches of mathematics. Perhaps the most important and widespread usage is to denote a singularity of a ...

A simplex, sometimes called a hypertetrahedron (Buekenhout and Parker 1998), is the generalization of a tetrahedral region of space to n dimensions. The boundary of a ...

Given a regular tetrahedron of unit volume, consider the lengths of line segments connecting pairs of points picked at random inside the tetrahedron. The distribution of ...