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A connected labeled graph with n graph edges in which all graph vertices can be labeled with distinct integers (mod n) so that the sums of the pairs of numbers at the ends of ...

A device consisting of two coupled pendula, usually oscillating at right angles to each other, which are attached to a pen. The resulting motion can produce beautiful, ...

Let s_i be the orders of singular points on a curve (Coolidge 1959, p. 56). Harnack's first theorem states that a real irreducible curve of order n cannot have more than ...

A linkage which draws the inverse of a given curve. It can also convert circular to linear motion. The rods satisfy AB=CD and BC=DA, and O, P, and P^' remain collinear while ...

Any one of the eight Apollonius circles of three given circles is tangent to a circle H known as a Hart circle, as are the other three Apollonius circles having (1) like ...

A Hasse diagram is a graphical rendering of a partially ordered set displayed via the cover relation of the partially ordered set with an implied upward orientation. A point ...

The hat is a caret-shaped symbol commonly placed on top of variables to give them special meaning. The symbol x^^ is voiced "x-hat" (or sometimes as "x-roof") in mathematics, ...

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).

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 ...

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