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For a semicubical parabola with parametric equations x = t^2 (1) y = at^3, (2) the involute is given by x_i = (t^2)/3-8/(27a^2) (3) y_i = -(4t)/(9a), (4) which is half a ...

The word net has several meanings in mathematics. It refers to a plane diagram in which the polyhedron edges of a polyhedron are shown, a point set satisfying certain ...

The number of nondecreasing lists {a_1,a_2,...,a_n} consisting of n elements 1<=a_i<=k is given by the binomial coefficient N(n,k)=(n+k-1; n-1). For example, there are six ...

A field automorphism of a field F is a bijective map sigma:F->F that preserves all of F's algebraic properties, more precisely, it is an isomorphism. For example, complex ...

There are several types of numbers that are commonly termed "lucky numbers." The first is the lucky numbers of Euler. The second is obtained by writing out all odd numbers: ...

The positive integers 216 and 12960000 appear in an obscure passage in Plato's The Republic. In this passage, Plato alludes to the fact that 216 is equal to 6^3, where 6 is ...

An equation of the form y=ax^3+bx^2+cx+d, (1) where the three roots of the equation coincide (and are therefore real), i.e., y=a(x-r)^3=a(x^3-3rx^2-3r^2x-r^3). (2) Loomis ...

A number x in which the first n decimal digits of the fractional part frac(x) sum to 666 is known as an evil number (Pegg and Lomont 2004). However, the term "evil" is also ...

The continued fraction for ln2 is [0; 1, 2, 3, 1, 6, 3, 1, 1, 2, 1, 1, 1, 1, 3, 10, ...] (OEIS A016730). It has been computed to 9702699208 terms by E. Weisstein (Aug. 21, ...

A Pythagorean triple is a triple of positive integers a, b, and c such that a right triangle exists with legs a,b and hypotenuse c. By the Pythagorean theorem, this is ...