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The Lucas central triangle (a term coined here for the first time) is the triangle DeltaL_AL_BL_C formed by the centers of the Lucas circles of a given reference triangle ...

There are two different definitions of the mid-arc points. The mid-arc points M_(AB), M_(AC), and M_(BC) of a triangle DeltaABC as defined by Johnson (1929) are the points on ...

An oval is a curve resembling a squashed circle but, unlike the ellipse, without a precise mathematical definition. The word oval derived from the Latin word "ovus" for egg. ...

A perpendicular bisector CD of a line segment AB is a line segment perpendicular to AB and passing through the midpoint M of AB (left figure). The perpendicular bisector of a ...

A principal bundle is a special case of a fiber bundle where the fiber is a group G. More specifically, G is usually a Lie group. A principal bundle is a total space E along ...

The Stammler circles are the three circles (apart from the circumcircle), that intercept the sidelines of a reference triangle DeltaABC in chords of lengths equal to the ...

A congruence of the form f(x)=0 (mod n) where f(x) is an integer polynomial (Nagell 1951, p. 73).

A compositeness certificate is a piece of information which guarantees that a given number p is composite. Possible certificates consist of a factor of a number (which, in ...

The sum-of-factorial powers function is defined by sf^p(n)=sum_(k=1)^nk!^p. (1) For p=1, sf^1(n) = sum_(k=1)^(n)k! (2) = (-e+Ei(1)+pii+E_(n+2)(-1)Gamma(n+2))/e (3) = ...

Let the residue from Pépin's theorem be R_n=3^((F_n-1)/2) (mod F_n), where F_n is a Fermat number. Selfridge and Hurwitz use R_n (mod 2^(35)-1,2^(36),2^(36)-1). A ...