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A polygon whose vertices are points of a point lattice. Regular lattice n-gons exists only for n=3, 4, and 6 (Schoenberg 1937, Klamkin and Chrestenson 1963, Maehara 1993). A ...

A space-filling function which maps a one-dimensional interval into a two-dimensional area. Plane-filling functions were thought to be impossible until Hilbert discovered the ...

Proportionally cutting circles are circles that intersect the sidelines of a reference triangle DeltaABC such that length of the chords that are cut off have lengths mua, ...

Given a general quadratic curve Ax^2+Bxy+Cy^2+Dx+Ey+F=0, (1) the quantity X is known as the discriminant, where X=B^2-4AC, (2) and is invariant under rotation. Using the ...

There are nine possible types of isolated singularities on a cubic surface, eight of them rational double points. Each type of isolated singularity has an associated normal ...

A presentation of a group is a description of a set I and a subset R of the free group F(I) generated by I, written <(x_i)_(i in I)|(r)_(r in R)>, where r=1 (the identity ...

Let K be a number field and let O be an order in K. Then the set of equivalence classes of invertible fractional ideals of O forms a multiplicative Abelian group called the ...

In continuum percolation theory, the so-called germ-grain model is an obvious generalization of both the Boolean and Boolean-Poisson models which is driven by an arbitrary ...

Let G be a group and S be a topological G-set. Then a closed subset F of S is called a fundamental domain of G in S if S is the union of conjugates of F, i.e., S= union _(g ...

The tower of Hanoi (commonly also known as the "towers of Hanoi"), is a puzzle invented by E. Lucas in 1883. It is also known as the Tower of Brahma puzzle and appeared as an ...