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The second Brocard Cevian triangle is the Cevian triangle of the second Brocard point. It has area Delta_2=(2a^2b^2c^2)/((a^2+b^2)(b^2+c^2)(c^2+a^2))Delta, where Delta is the ...

Let j, r, and s be distinct integers (mod n), and let W_i be the point of intersection of the side or diagonal V_iV_(i+j) of the n-gon P=[V_1,...,V_n] with the transversal ...

A topological space X is semilocally simply connected (also called semilocally 1-connected) if every point x in X has a neighborhood U such that any loop L:[0,1]->U with ...

In discrete percolation theory, site percolation is a percolation model on a regular point lattice L=L^d in d-dimensional Euclidean space which considers the lattice vertices ...

Smale (1958) proved that it is mathematically possible to turn a sphere inside-out without introducing a sharp crease at any point. This means there is a regular homotopy ...

Let a spherical triangle be drawn on the surface of a sphere of radius R, centered at a point O=(0,0,0), with vertices A, B, and C. The vectors from the center of the sphere ...

A hypotrochoid generated by a fixed point on a circle rolling inside a fixed circle. The curves above correspond to values of a=0.1, 0.2, ..., 1.0. Additional attractive ...

The Stammler circle is the circumcircle of the Stammler triangle. Unexpectedly, it has center at the circumcenter O (X_3) of the reference triangle and radius 2R (Ehrmann and ...

The standard form of a line in the Cartesian plane is given by ax+by=c for real numbers a,b,c in R. This form can be derived from any of the other forms (point-slope form, ...

Given a point set P={x_n}_(n=0)^(N-1) in the s-dimensional unit cube I=[0,1)^s, the star discrepancy is defined as D_N^*(P)=sup_(J in Upsilon^*)D(J,P), (1) where the local ...