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For two lines in the plane with endpoints (x_1,x_2) and (x_3,x_4), the angle between them is given by costheta=((x_2-x_1)·(x_4-x_3))/(|x_2-x_1||x_4-x_3|). (1) The angle theta ...

A transformation in which all points along a given line L remain fixed while other points are shifted parallel to L by a distance proportional to their perpendicular distance ...

A foliation F of dimension p on a manifold M is transversely orientable if it is integral to a p-plane distribution D on M whose normal bundle Q is orientable. A p-plane ...

For every positive integer n, there exists a square in the plane with exactly n lattice points in its interior. This was extended by Schinzel and Kulikowski to all plane ...

The evolute of a circle is a degenerate point at the origin.

Pick any point P on a conic section, and draw a series of right angles having this point as their vertices. Then the line segments connecting the rays of the right angles ...

A point lattice which can be constructed from an arbitrary parallelogram of unit area. For any such planar lattice, the minimum distance c between any two points is a ...

The geodesics in a complete Riemannian metric go on indefinitely, i.e., each geodesic is isometric to the real line. For example, Euclidean space is complete, but the open ...

De Grey (2018) found the first examples of unit-distance graphs with chromatic number 5, thus demonstrating that the solution to the Hadwiger-Nelson problem (i.e., the ...

A point at which two polygon edges of a polygon meet.