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A twin Pythagorean triple is a Pythagorean triple (a,b,c) for which two values are consecutive integers. By definition, twin triplets are therefore primitive triples. Of the ...

Two points which are collinear with respect to a similitude center but are not homologous points. Four interesting theorems from Johnson (1929) follow. 1. Two pairs of ...

The Cairo tessellation is a tessellation appearing in the streets of Cairo and in many Islamic decorations. Its tiles are obtained by projection of a dodecahedron, and it is ...

Four or more points P_1, P_2, P_3, P_4, ... which lie on a circle C are said to be concyclic. Three points are trivially concyclic since three noncollinear points determine a ...

A 15_3 configuration of 15 lines and 15 points, with three lines through three points, three points on every line, and containing no triangles. It is illustrated above in two ...

Given two crossed ladders resting against two buildings, what is the distance between the buildings? Let the height at which they cross be h and the lengths of the ladders ...

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 ...

A cyclic polygon is a polygon with vertices upon which a circle can be circumscribed. Since every triangle has a circumcircle, every triangle is cyclic. It is conjectured ...

Let A_1, A_2, A_3, and A_4 be four points on a circle, and H_1, H_2, H_3, H_4 the orthocenters of triangles DeltaA_2A_3A_4, etc. If, from the eight points, four with ...

A principal vertex x_i of a simple polygon P is called an ear if the diagonal [x_(i-1),x_(i+1)] that bridges x_i lies entirely in P. Two ears x_i and x_j are said to overlap ...