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A large number defined as where the circle notation denotes "n in n squares," and triangles and squares are expanded in terms of Steinhaus-Moser notation (Steinhaus 1999, pp. ...

A derived polygon with side ratios chosen as r=1/2 so that inscribed polygons are constructed by connecting the midpoints of the base polygon. For a triangle P, the ...

The star figure {9/3} composed of three equilateral triangles rotated at angles 0 degrees, 40 degrees, and 80 degrees. It has been called the star of Goliath by analogy with ...

The pentagonal cupola is Johnson solid J_5. Its faces consist of 5 equilateral triangles, 5 squares, 1 pentagon, and one decagon. The surface area and volume of the ...

For n points in the plane, there are at least N_1=sqrt(n-3/4)-1/2 different distances. The minimum distance can occur only <=3n-6 times, and the maximum distance can occur ...

Polypons are polyforms obtained from dividing a regular triangular grid into 30-30-120 triangles, illustrated above. The numbers of polypons with n=1, 2, ... components are ...

The constant ratio by which all distances are increased (or decreased) in a similarity. A similarity with ratio of magnification equal to 1 is called an isometry.

The nth-order Sierpiński tetrahedron graph is the connectivity graph of black triangles in the nth iteration of the tetrix fractal. The first three iterations are shown ...

Given three noncollinear points, construct three tangent circles such that one is centered at each point and the circles are pairwise tangent to one another. Then there exist ...

A notation for large numbers defined by Steinhaus (1983, pp. 28-29). In this notation, denotes n^n, denotes "n in n triangles," and denotes "n in n squares." A modified ...