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The pedal circle with respect to a pedal point P of a triangle DeltaA_1A_2A_3 is the circumcircle of the pedal triangle DeltaP_1P_2P_3 with respect to P. Amazingly, the ...

Robertson's apex graph is the 15-vertex graph illustrated above constructed by Neil Robertson as an example of an apex graph that is not YDeltaY-reducible. The graph may be ...

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 ...

Every smooth manifold M has a tangent bundle TM, which consists of the tangent space TM_p at all points p in M. Since a tangent space TM_p is the set of all tangent vectors ...

Let P_i=x_i:y_i:z_i be trilinear points for i=1, 2, 3. The A-vertex of the unary cofactor triangle is then defined as the point y_2z_3-z_2y_3:z_2x_3-x_2z_3:x_2y_3-y_2x_3, and ...

The orthogonal polynomials defined variously by (1) (Koekoek and Swarttouw 1998, p. 24) or p_n(x;a,b,c,d) = W_n(-x^2;a,b,c,d) (2) = (3) (Koepf, p. 116, 1998). The first few ...

Select three points at random on the circumference of a unit circle and find the distribution of areas of the resulting triangles determined by these three points. The first ...

Just as the ratio of the arc length of a semicircle to its radius is always pi, the ratio P of the arc length of the parabolic segment formed by the latus rectum of any ...

Skewness is a measure of the degree of asymmetry of a distribution. If the left tail (tail at small end of the distribution) is more pronounced than the right tail (tail at ...

Let pi_(m,n)(x) denote the number of primes <=x which are congruent to n modulo m (i.e., the modular prime counting function). Then one might expect that ...