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Each subsequent row of Pascal's triangle is obtained by adding the two entries diagonally above. This follows immediately from the binomial coefficient identity (n; r) = ...

A curve composed exclusively of circular arcs.

Given three noncollinear points, construct three tangent circles such that one is centered at each point and the circles are pairwise tangent to one another. Then there exist ...

Let a, b, and c be the sides of a spherical triangle, then the spherical defect is defined as D=2pi-(a+b+c).

A closed geometric figure on the surface of a sphere which is formed by the arcs of great circles. The spherical polygon is a generalization of the spherical triangle. If ...

A triangular grid, also called an isometric grid (Gardner 1986, pp. 209-210), is a grid formed by tiling the plane regularly with equilateral triangles.

The triangular inequalities are the inequalities |x-y|<=z<=x+y for real numbers (x,y,z) (Messiah 1962, p. 1056). If these inequalities hold for any one permutation of ...

Construction of the angle pi/6=30 degrees produces a 30-60-90 triangle, which has angles theta=pi/6 and 2theta=pi/3. From the above diagram, write y=sintheta for the vertical ...

The triquetra is a geometric figure consisting of three mutually intersecting vesica piscis lens shapes, as illustrated above. The central region common to all three lenses ...

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