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The diagonal triangle of a complete quadrangle is the triangle formed by its three diagonal points. If the quadrangle is a cyclic quadrilateral, then the circle is the polar ...

11 11 1 11 2 2 11 2 4 2 11 3 6 6 3 11 3 9 10 9 3 11 4 12 19 19 12 4 11 4 16 28 38 28 16 4 11 5 20 44 66 66 44 20 5 11 5 25 60 110 126 110 60 25 5 1 (1) Losanitsch's triangle ...

Triangle picking is the process of picking triangles at random within a given shape in the plane, in space, or in a higher dimension. The most natural definition of a random ...

The trinomial triangle is a number triangle of trinomial coefficients. It can be obtained by starting with a row containing a single "1" and the next row containing three 1s ...

The number of different triangles which have integer side lengths and perimeter n is T(n) = P(n,3)-sum_(1<=j<=|_n/2_|)P(j,2) (1) = [(n^2)/(12)]-|_n/4_||_(n+2)/4_| (2) = ...

11 21 3 41 4 7 81 5 11 15 161 6 16 26 31 32 (1) The number triangle illustrated above (OEIS A008949) composed of the partial sums of binomial coefficients, a_(nk) = ...

A triangle ABC formed by three circular arcs. By extending the arcs into complete circles, the points of intersection A^', B^', and C^' are obtained. This gives the three ...

A monotone triangle (also called a strict Gelfand pattern or a gog triangle) of order n is a number triangle with n numbers along each side and the base containing entries ...

Every convex body B in the Euclidean plane with area A can be inscribed in a triangle of area at most equal to 2A (Gross 1918, Eggleston 1957). The worst possible fit ...

Given rods of length 1, 2, ..., n, how many distinct triangles T(n) can be made? Lengths for which l_i>=l_j+l_k (1) obviously do not give triangles, but all other ...