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The trigonometric formulas for pi/5 can be derived using the multiple-angle formula sin(5theta)=5sintheta-20sin^3theta+16sin^5theta. (1) Letting theta=pi/5 and x=sintheta ...

Trigonometric functions of npi/9 radians for n an integer not divisible by 3 (e.g., 40 degrees and 80 degrees) cannot be expressed in terms of sums, products, and finite root ...

A triply periodic function is a function having three distinct periods. Jacobi (1835) proved that a single-valued univariate function cannot have more than two distinct ...

There exist points A^', B^', and C^' on segments BC, CA, and AB of a triangle, respectively, such that A^'C+CB^'=B^'A+AC^'=C^'B+BA^' (1) and the lines AA^', BB^', CC^' ...

A multivariate normal distribution in three variables. It has probability density function (1) where (2) The standardized trivariate normal distribution takes unit variances ...

A figurate number which is constructed as an octahedral number with a square pyramid removed from each of the six graph vertices, TO_n = O_(3n-2)-6P_(n-1)^((4)) (1) = ...

The truncated pentakis dodecahedron is a polyhedron on 180 vertices, 270 edges, and 92 faces. Its canonical polyhedron has edges of three different lengths and faces ...

The truncated square pyramid is a special case of a pyramidal frustum for a square pyramid. Let the base and top side lengths of the truncated pyramid be a and b, and let the ...

A figurate number constructed by taking the (3n-2)th tetrahedral number and removing the (n-1)th tetrahedral number from each of the four corners, Ttet_n = ...

The truncated triangular prism is an undecagon obtained by truncation of a triangular prism. It has 18 vertices, 27 edges, and 11 faces. As a canonical polyhedron with unit ...