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What is the longest ladder that can be moved around a right-angled hallway of unit width? For a straight, rigid ladder, the answer is 2sqrt(2), which allows the ladder to ...

An odious number is a nonnegative number that has an odd number of 1s in its binary expansion. The first few odious numbers are therefore 1, 2, 4, 7, 8, 11, 13, 14, 16, 19, ...

The parabididiminished rhombicosidodecahedron is a convex equilateral solid that is Johnson solid J_(820). The unit parabididiminished rhombicosidodecahedron ...

The paragyrate diminished rhombicosidodecahedron is a convex equilateral solid that is Johnson solid J_(77). The unit paragyrate diminished rhombicosidodecahedron has volume ...

The theory of natural numbers defined by the five Peano's axioms. Paris and Harrington (1977) gave the first "natural" example of a statement which is true for the integers ...

The pentagonal gyrobicupola is a convex equilateral solid that is Johnson solid J_(31). The unit pentagonal gyrobicupola has volume V=1/3(5+4sqrt(5)) (1) and Dehn invariant D ...

The pentagonal orthocupolarotunda is a convex equilateral solid that is Johnson solid J_(32). The unit pentagonal orthocupolarotunda has volume V=1/3(5+4sqrt(5)) (1) and Dehn ...

Any entire analytic function whose range omits two points must be a constant function. Of course, an entire function that omits a single point from its range need not be a ...

In its simplest form, the principle of permanence states that, given any analytic function f(z) defined on an open (and connected) set U of the complex numbers C, and a ...

Quantization is a nonlinear process which generates additional frequency components (Thompson et al. 1986). This means that the signal is no longer band-limited, so the ...