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The Thomson problem is to determine the stable equilibrium positions of n classical electrons constrained to move on the surface of a sphere and repelling each other by an ...

If a plane cuts the sides AB, BC, CD, and DA of a skew quadrilateral ABCD in points P, Q, R, and S, then (AP)/(PB)·(BQ)/(QC)·(CR)/(RD)·(DS)/(SA)=1 both in magnitude and sign ...

Let the probabilities of various classes in a distribution be p_1, p_2, ..., p_k, with observed frequencies m_1, m_2, ..., m_k. The quantity ...

The circumsphere of given set of points, commonly the vertices of a solid, is a sphere that passes through all the points. A circumsphere does not always exist, but when it ...

Consider a convex plane curve K with perimeter L, and the set of points P exterior to K. Further, let t_1 and t_2 be the perpendicular distances from P to K (with ...

The Evans conic is the conic section passing through the Fermat points X and X^', the inner and outer Napoleon points N and N^', and the isodynamic points S and S^' of a ...

Divide a set of data into two groups (high and low) of equal size at the statistical median if there is an even number of data points, or two groups consisting of points on ...

The Jerabek center is the center of the Jerabek hyperbola. It is Kimberling center X_(125), which has equivalent triangle center functions alpha_(125) = cosAsin^2(B-C) (1) ...

The Kiepert center is the center of the Kiepert hyperbola. It is Kimberling center X_(115), which has equivalent triangle center functions alpha_(115) = ((b^2-c^2)^2)/a (1) ...

Relationships between the number of singularities of plane algebraic curves. Given a plane curve, m = n(n-1)-2delta-3kappa (1) n = m(m-1)-2tau-3iota (2) iota = ...