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The Curry triangle, also sometimes called the missing square puzzle, is a dissection fallacy created by American neuropsychiatrist L. Vosburgh Lions as an example of a ...

The equation x^p=1, where solutions zeta_k=e^(2piik/p) are the roots of unity sometimes called de Moivre numbers. Gauss showed that the cyclotomic equation can be reduced to ...

Consider two cylinders as illustrated above (Hubbell 1965) where the cylinders have radii r_1 and r_2 with r_1<=r_2, the larger cylinder is oriented along the z-axis, and ...

The maximum number of pieces into which a cylinder can be divided by n oblique cuts is given by f(n) = (n+1; 3)+n+1 (1) = 1/6(n+1)(n^2-n+6) (2) = 1/6(n^3+5n+6), (3) where (a; ...

Let G be a group of group order h and D be a set of k elements of G. If the set of differences d_i-d_j contains every nonzero element of G exactly lambda times, then D is a ...

A directed strongly regular graph is a simple directed graph with adjacency matrix A such that the span of A, the identity matrix I, and the unit matrix J is closed under ...

A number of attractive 2-compounds of the regular dodecahedron can be constructed. The first (left figures) has the symmetry of the cube and arises by combining two regular ...

A point traced out twice as a closed curve is traversed. The maximum number of double points for a nondegenerate quartic curve is three. An ordinary double point is also ...

The elongated pentagonal gyrobirotunda is a convex equilateral gyrobirotunda having regular pentagonal upper and lower birotundas arranged rotated 1/10 of a turn with respect ...

Is there a planar convex set having two distinct equichordal points? The problem was first proposed by Fujiwara (1916) and Blaschke et al. (1917), but long defied solution. ...