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The lines joining the vertices of a tetrahedron to the centroids of the opposite faces are called medians. Commandino's theorem states that the four medians of a tetrahedron ...

Let A, B, and C be three circles in the plane, and let X be any circle touching B and C. Then build up a chain of circles such that Y:CAX, Z:ABY, X^':BCZ, Y^':CAX^', ...

Let any finite or infinite set of points having no finite limit point be prescribed, and associate with each of its points a definite positive integer as its order. Then ...

Letting Lk be the linking number of the two components of a ribbon, Tw be the twist, and Wr be the writhe, then Lk(K)=Tw(K)+Wr(K). (Adams 1994, p. 187).

The perspectrix X of a pair of paralogic triangles DeltaA_1A_2A_3 and DeltaB_1B_2B_3 bisects the line joining the two orthocenters H_A and H_B (Johnson 1929, p. 259).

Let M be the midpoint of the arc AMB. Pick C at random and pick D such that MD_|_AC (where _|_ denotes perpendicular). Then AD=DC+BC.

If the lines joining corresponding points of two directly similar figures are divided proportionally, then the locus of the points of the division will be a figure directly ...

Let f_n(z) be a sequence of functions, each regular in a region D, let |f_n(z)|<=M for every n and z in D, and let f_n(z) tend to a limit as n->infty at a set of points ...

If one part of the total intersection group of a curve of order n with a curve of order n_1+n_2 constitutes the total intersection with a curve of order n_1, then the other ...

Willans' formula is a prime-generating formula due to Willan (1964) that is defined as follows. Let F(j) = |_cos^2[pi((j-1)!+1)/j]_| (1) = {1 for j=1 or j prime; 0 otherwise ...