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A constant-curvature surface which can be given parametrically by x = rcosphi (1) y = rsinphi (2) z = (ln[tan(1/2v)]+a(C+1)cosv)/(sqrt(C)), (3) where phi = ...
A siteswap is a sequence encountered in juggling in which each term is a positive integer, encoded in binary. The transition rule from one term to the next consists of ...
Given a triangle DeltaABC with inner and outer Soddy centers S and S^', respectively, the inner Soddy triangle DeltaPQR (respectively, outer Soddy triangle DeltaP^'Q^'R^') is ...
A spheroid is an ellipsoid having two axes of equal length, making it a surface of revolution. By convention, the two distinct axis lengths are denoted a and c, and the ...
The radical circle of the Stammler circles has center at the nine-point center N, which is Kimberling center X_5. The radius is given by R_S = sqrt(R^2+ON^2) (1) = ...
The Steiner circle is the central circle with center at the nine-point center X_5 and radius R_S=3/2R, where R is the circumradius of the reference triangle. It is the ...
Let a and b be nonzero integers such that a^mb^n!=1 (except when m=n=0). Also let T(a,b) be the set of primes p for which p|(a^k-b) for some nonnegative integer k. Then ...
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 ...
In nonstandard analysis, the limitation to first-order analysis can be avoided by using a construction known as a superstructure. Superstructures are constructed in the ...
Given a Lucas sequence with parameters P and Q, discriminant D!=0, and roots a and b, the Sylvester cyclotomic numbers are Q_n=product_(r)(a-zeta^rb), (1) where ...

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