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A version of the liar's paradox, attributed to the philosopher Epimenides in the sixth century BC. "All Cretans are liars... One of their own poets has said so." This is not ...

There exists a triangulation point Y for which the triangles BYC, CYA, and AYB have equal Brocard angles. This point is a triangle center known as the equi-Brocard center and ...

1. A straight line segment can be drawn joining any two points. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line ...

Each of the sacred unit fractions which the ancient Egyptians attributed to the six parts of the eye of the god Horus: 1/2, 1/4, 1/8, 1/16, 1/32, and 1/64. These fractions, ...

Gödel's second incompleteness theorem states no consistent axiomatic system which includes Peano arithmetic can prove its own consistency. Stated more colloquially, any ...

The great dodecahemidodecahedron is the uniform polyhedron with Maeder index 70 (Maeder 1997), Wenninger index 107 (Wenninger 1989), Coxeter index 86 (Coxeter et al. 1954), ...

The great icosihemidodecahedron is the uniform polyhedron with Maeder index 71 (Maeder 1997), Wenninger index 106 (Wenninger 1989), Coxeter index 85 (Coxeter et al. 1954), ...

The great retrosnub icosidodecahedron, also called the great inverted retrosnub icosidodecahedron is the uniform polyhedron with Maeder index 74 (Maeder 1997), Wenninger ...

The great snub icosidodecahedron is the uniform polyhedron with Maeder index 57 (Maeder 1997), Wenninger index 116 (Wenninger 1989), Coxeter index 88 (Coxeter et al. 1954), ...

Grelling's paradox, also known as the Grelling-Nelson paradox or heterological paradox, is a semantic paradox that arises by defining "heterological" to mean "a word which ...