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(b-c)/a = (sin[1/2(B-C)])/(cos(1/2A)) (1) (c-a)/b = (sin[1/2(C-A)])/(cos(1/2B)) (2) (a-b)/c = (sin[1/2(A-B)])/(cos(1/2C)). (3)

Trigonometric identities which prove useful in the construction of map projections include (1) where A^' = A-C (2) B^' = 2B-4D (3) C^' = 4C (4) D^' = 8D. (5) ...

If (sinalpha)/(sinbeta)=m/n, then (tan[1/2(alpha-beta)])/(tan[1/2(alpha+beta)])=(m-n)/(m+n).

The number obtained by adding the reciprocals of the odd twin primes, B=(1/3+1/5)+(1/5+1/7)+(1/(11)+1/(13))+(1/(17)+1/(19))+.... (1) By Brun's theorem, the series converges ...

A gambling game played at carnivals in which a player may bet on any one of the numbers 1 through 6. Three dice are then rolled and, if his number appears, he receives back a ...

The Doro graph is a distance-transitive and Distance-Regular Graph on 68 vertices and with valency 12. It is the unique automorphic graph having intersection array ...

Define an emirpimes ("semiprime" spelled backwards) as a semiprime whose (base 10) reversal is a different semiprime. The first such number is 15, because 15 reversed is 51 ...

A shuffle of a deck of cards obtained by successively exchanging the cards in position 1, 2, ..., n with cards in randomly chosen positions. For 4<=n<=17, the most frequent ...

The Fischer groups are the three sporadic groups Fi_(22), Fi_(23), and Fi_(24)^'. These groups were discovered during the investigation of 3-transposition groups. The Fischer ...

One of the eight convex deltahedra built up from 16 equilateral triangles. It consists of two oppositely faced square pyramids rotated 45 degrees to each other and separated ...