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A hyperbola for which the asymptotes are perpendicular, also called an equilateral hyperbola or right hyperbola. This occurs when the semimajor and semiminor axes are equal. ...

A semiperfect magic cube, sometimes also called an "Andrews cube" (Gardner 1976; Gardner 1988, p. 219) is a magic cube for which the cross section diagonals do not sum to the ...

A Pisot number is a positive algebraic integer greater than 1 all of whose conjugate elements have absolute value less than 1. A real quadratic algebraic integer greater than ...

In 1803, Malfatti posed the problem of determining the three circular columns of marble of possibly different sizes which, when carved out of a right triangular prism, would ...

The Engel expansion, also called the Egyptian product, of a positive real number x is the unique increasing sequence {a_1,a_2,...} of positive integers a_i such that ...

The recursive sequence defined by the recurrence relation a(n)=a(a(n-1))+a(n-a(n-1)) (1) with a(1)=a(2)=1. The first few values are 1, 1, 2, 2, 3, 4, 4, 4, 5, 6, ... (OEIS ...

Two rectangles, neither of which will fit inside the other, are said to be incomparable. This is equivalent to one rectangle being both longer and narrower. At least seven ...

The silver ratio is the quantity defined by the continued fraction delta_S = [2,2,2,...] (1) = 2+1/(2+1/(2+1/(2+...))) (2) (Wall 1948, p. 24). It follows that ...

The term "arbelos" means shoemaker's knife in Greek, and this term is applied to the shaded area in the above figure which resembles the blade of a knife used by ancient ...

The curlicue fractal is a figure obtained by the following procedure. Let s be an irrational number. Begin with a line segment of unit length, which makes an angle phi_0=0 to ...