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Place two solid spheres of radius 1/2 inside a hollow sphere of radius 1 so that the two smaller spheres touch each other at the center of the large sphere and are tangent to ...

A cubic number is a figurate number of the form n^3 with n a positive integer. The first few are 1, 8, 27, 64, 125, 216, 343, ... (OEIS A000578). The protagonist Christopher ...

Consider the process of taking a number, multiplying its digits, then multiplying the digits of numbers derived from it, etc., until the remaining number has only one digit. ...

The Pierce expansion, or alternated Egyptian product, of a real number 0<x<1 is the unique increasing sequence {a_1,a_2,...} of positive integers a_i such that ...

An integer j(n) is called a jumping champion if j(n) is the most frequently occurring difference between consecutive primes <=n (Odlyzko et al. 1999). This term was coined by ...

Given a map with genus g>0, Heawood showed in 1890 that the maximum number N_u of colors necessary to color a map (the chromatic number) on an unbounded surface is N_u = ...

The 13 Archimedean solids are the convex polyhedra that have a similar arrangement of nonintersecting regular convex polygons of two or more different types arranged in the ...

Any two rectilinear figures with equal area can be dissected into a finite number of pieces to form each other. This is the Wallace-Bolyai-Gerwien theorem. For minimal ...

The 6-polyiamonds illustrated above.

The result of a matrix multiplication.