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The hat polykite is an aperiodic monotile discovered by Smith et al. (2023). It is illustrated above in an aperiodic tiling (Smith et al. 2023).

The Hatzel graph is a planar hypohamiltonian graph on 57 vertices that was the smallest known example of such a graph until the discovery of the Zamfirescu graph on 48 ...

The axioms formulated by Hausdorff (1919) for his concept of a topological space. These axioms describe the properties satisfied by subsets of elements x in a neighborhood ...

Informally, self-similar objects with parameters N and s are described by a power law such as N=s^d, where d=(lnN)/(lns) is the "dimension" of the scaling law, known as the ...

Let X be a metric space, A be a subset of X, and d a number >=0. The d-dimensional Hausdorff measure of A, H^d(A), is the infimum of positive numbers y such that for every ...

For n>=3, there exist no additive finite and invariant measures for the group of displacements in R^n.

The construction of polyhedra using identical building blocks. The illustrations above show such constructions for the cuboctahedron, octahedron rhombic dodecahedron, and ...

The havercosine, also called the haversed cosine, is a little-used trigonometric function defined by havercosz = vercosz (1) = 1/2(1+cosz), (2) where vercosz is the vercosine ...

The haversine, also called the haversed sine, is a little-used entire trigonometric function defined by hav(z) = 1/2vers(z) (1) = 1/2(1-cosz) (2) = sin^2(1/2z), (3) where ...

The plane figure formed by a sequence of circles C_1, C_2, C_3, ... that are all tangent to each other at the same point and such that the sequence of radii converges to ...