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Define the packing density eta of a packing of spheres to be the fraction of a volume filled by the spheres. In three dimensions, there are three periodic packings for ...

Let a Cevian PC be drawn on a triangle DeltaABC, and denote the lengths m=PA^_ and n=PB^_, with c=m+n. Then Stewart's theorem, also called Apollonius' theorem, states that ...

The "ternary" Champernowne constant can be defined by concatenating the ternary representations of the integers C_3 = 0.(1)(2)(1,0)(1,1)(1,2)(2,0)..._3 (1) = ...

There are (at least) two mathematical constants associated with Theodorus. The first Theodorus's constant is the elementary algebraic number sqrt(3), i.e., the square root of ...

A Trott constant is a real number whose decimal digits are equal to the terms of its continued fraction. The first Trott constant (OEIS A039662) was discovered by M. Trott in ...

Any nonzero rational number x can be represented by x=(p^ar)/s, (1) where p is a prime number, r and s are integers not divisible by p, and a is a unique integer. The p-adic ...

A transformation formula for continued fractions (Lorentzen and Waadeland 1992) which can, for example, be used to prove identities such as ...

A conjecture due to Paul Erdős and E. G. Straus that the Diophantine equation 4/n=1/a+1/b+1/c involving Egyptian fractions always can be solved (Obláth 1950, Rosati 1954, ...

The Bolyai expansion of a real number x is a nested root of the form x=a_0-1+RadicalBox[{{a, _, 1}, +, RadicalBox[{{a, _, 2}, +, RadicalBox[{{a, _, 3}, +, ...}, m]}, m]}, m], ...

1 calcus=1/(2304).