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Given a triangle DeltaA_1A_2A_3, the points A_1, I, and J_1 lie on a line, where I is the incenter and J_1 is the excenter corresponding to A_1. Furthermore, the circle with ...

The excentral-hexyl ellipse is the ellipse passing through vertices of the excentral and hexyl triangles (P. Moses, pers. comm., Jan. 29, 2005). It has center at the ...

A binomial coefficient (N; k) is said to be exceptional if lpf(N; k)>N/k. The following table gives the exception binomial coefficients which are also good binomial ...

A Jordan algebra which is not isomorphic to a subalgebra.

The kurtosis excess of a distribution is sometimes called the excess, or excess coefficient. In graph theory, excess refers to the quantity e=n-n_l(v,g) (1) for a v-regular ...

The radical circle of the excircles has center at the Spieker center X_(10) and radius R_E=1/2sqrt((a^2b+ab^2+a^2c+abc+b^2c+ac^2+bc^2)/(a+b+c)). Its circle function is ...

A method which can be used to solve any quadratic congruence equation. This technique relies on the fact that solving x^2=b (mod p) is equivalent to finding a value y such ...

Also known as the difference of squares method. It was first used by Fermat and improved by Gauss. Gauss looked for integers x and y satisfying y^2=x^2-N (mod E) for various ...

A disjunction that is true if only one, but not both, of its arguments are true, and is false if neither or both are true, which is equivalent to the XOR connective. By ...

If the tangents at B and C to the circumcircle of a triangle DeltaABC intersect in a point K_1, then the circle with center K_1 and which passes through B and C is called the ...