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Let T_1 be the point at which the J_1-excircle meets the side A_2A_3 of a triangle DeltaA_1A_2A_3, and define T_2 and T_3 similarly. Then the lines A_1T_1, A_2T_2, and A_3T_3 ...

The system of partial differential equations U_t = [V,W] (1) V_t = [W,U] (2) W_t = [U,V], (3) where [A,B] denotes the commutator.

A branch of mathematics which attempts to formalize the nature of the set using a minimal collection of independent axioms. Unfortunately, as discovered by its earliest ...

NAND, also known as the Sheffer stroke, is a connective in logic equivalent to the composition NOT AND that yields true if any condition is false, and false if all conditions ...

The first definition of the logarithm was constructed by Napier and popularized through his posthumous pamphlet (Napier 1619). It this pamphlet, Napier sought to reduce the ...

Let a spherical triangle have sides a, b, and c with A, B, and C the corresponding opposite angles. Then (sin[1/2(A-B)])/(sin[1/2(A+B)]) = (tan[1/2(a-b)])/(tan(1/2c)) (1) ...

Napier's bones, also called Napier's rods, are numbered rods which can be used to perform multiplication of any number by a number 2-9. By placing "bones" corresponding to ...

For b>a>0, 1/b<(lnb-lna)/(b-a)<1/a.

The Napoleon-Feuerbach cubic is the pivotal isogonal cubic with nine-point center N as the pivot point. It therefore has trilinear equation ...

The Napoleon crossdifference is the crossdifference of the Napoleon points. It has triangle center function alpha_(1510)=((b^2-c^2)[2cos(2A)-1])/a and is Kimberling center ...