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A plane curve is a curve that lies in a single plane. A plane curve may be closed or open. Curves which are interesting for some reason and whose properties have therefore ...

Circumscribe a triangle about a circle, another circle around the triangle, a square outside the circle, another circle outside the square, and so on. The circumradius and ...

"Spikey" is the logo of Wolfram Research, makers of Mathematica and the Wolfram Language. In its original (Version 1) form, it is an augmented icosahedron with an ...

Find the minimum size square capable of bounding n equal squares arranged in any configuration. The first few cases are illustrated above (Friedman). The only packings which ...

Surface area is the area of a given surface. Roughly speaking, it is the "amount" of a surface (i.e., it is proportional to the amount of paint needed to cover it), and has ...

The angular twist theta of a shaft with given cross section is given by theta=(TL)/(KG) (1) (Roark 1954, p. 174), where T is the twisting moment (commonly measured in units ...

There are two common definitions of the trapezium. The American definition is a quadrilateral with no parallel sides; the British definition is a quadrilateral with two sides ...

A triangle center function (sometimes simply called a center function) is a nonzero function f(a,b,c) that is homogeneous f(ta,tb,tc)=t^nf(a,b,c) (1) bisymmetry in b and c, ...

A twin Pythagorean triple is a Pythagorean triple (a,b,c) for which two values are consecutive integers. By definition, twin triplets are therefore primitive triples. Of the ...

Wang's conjecture states that if a set of tiles can tile the plane, then they can always be arranged to do so periodically (Wang 1961). The conjecture was refuted when Berger ...