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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 ...

Let P_i=x_i:y_i:z_i be trilinear points for i=1, 2, 3. The A-vertex of the unary cofactor triangle is then defined as the point y_2z_3-z_2y_3:z_2x_3-x_2z_3:x_2y_3-y_2x_3, and ...

A triangle formed by the arcs of three geodesics on a smooth surface.

An optical illusion, illustrated above, in which the eye perceives a white upright equilateral triangle where none is actually drawn.

The triangle coefficient is function of three variables written Delta(abc)=Delta(a,b,c) and defined by Delta(abc)=((a+b-c)!(a-b+c)!(-a+b+c)!)/((a+b+c+1)!), (Shore and Menzel ...

The Curry triangle, also sometimes called the missing square puzzle, is a dissection fallacy created by American neuropsychiatrist L. Vosburgh Lions as an example of a ...

The Schwarz triangles are spherical triangles which, by repeated reflection in their indices, lead to a set of congruent spherical triangles covering the sphere a finite ...

The Penrose triangle, also called the tribar (Cerf), tri-bar (Ernst 1987), impossible tribar (Pappas 1989, p. 13), or impossible triangle, is an impossible figure published ...

A curve of constant width constructed by drawing arcs from each polygon vertex of an equilateral triangle between the other two vertices. The Reuleaux triangle has the ...

The condition that j takes on the values j=j_1+j_2,j_1+j_2-1,...,|j_1-j_2|, denoted Delta(j_1j_2j).