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An infinite sequence of circles such that every four consecutive circles are mutually tangent, and the circles' radii ..., R_(-n), ..., R_(-1), R_0, R_1, R_2, R_3, R_4, ..., ...

If the section function of a centered convex body in n-dimensional Euclidean space (n>=3) is smaller than that of another such body, is its volume also smaller? The solution ...

The Freemish crate, also called Escher's cube (Elber) or Hyzer's illusion (Pappas 1989, p. 13), is an impossible figure box that can be drawn but not built. It appears in ...

A pentomino is a 5-polyomino. There are 12 free pentominoes, 18 one-sided pentominoes, and 63 fixed pentominoes. The twelve free pentominoes are known by the letters of the ...

A toroidal polyhedron is a polyhedron with genus g>=1 (i.e., one having one or more holes). Examples of toroidal polyhedra include the Császár polyhedron and Szilassi ...

The simple process of voting leads to surprisingly counterintuitive paradoxes. For example, if three people vote for three candidates, giving the rankings A, B, C; B, C, A; ...

Given the above figure (without looking at the figure below!), determine how to disengage the two slotted cube halves without cutting, breaking, or distorting. One possible ...

A flexagon-like structure created by connecting the ends of a strip of four squares after folding along 45 degrees diagonals. Using a number of folding movements, it is ...

An (ordinary) torus is a surface having genus one, and therefore possessing a single "hole" (left figure). The single-holed "ring" torus is known in older literature as an ...

The utility problem posits three houses and three utility companies--say, gas, electric, and water--and asks if each utility can be connected to each house without having any ...