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Inscribe two triangles DeltaA_1B_1C_1 and DeltaA_2B_2C_2 in a reference triangle DeltaABC such that A = ∠AB_1C_1=∠AC_2B_2 (1) B = ∠BC_1A_1=∠BA_2C_2 (2) C = ∠CA_1B_1=∠CB_2A_2. ...

The triangle line that passes through the inner and outer Soddy centers S and S^'. The Soddy line is central line L_(657) and has trilinear equation ...

The standard deviation sigma of a probability distribution is defined as the square root of the variance sigma^2, sigma = sqrt(<x^2>-<x>^2) (1) = sqrt(mu_2^'-mu^2), (2) where ...

f_p=f_0+1/2p(p+1)delta_(1/2)-1/2(p-1)pdelta_(-1/2) +(S_3+S_4)delta_(1/2)^3+(S_3-S_4)delta_(-1/2)^3+..., (1) for p in [-1/2,1/2], where delta is the central difference and ...

Given two circles with one interior to the other, if small tangent circles can be inscribed around the region between the two circles such that the final circle is tangent to ...

Given n points, find the line segments with the shortest possible total length which connect the points. The segments need not necessarily be straight from one point to ...

The Stevanovic circle is a central circle with center X_(650), which has center function alpha_(650)=cosB-cosC, (1) It has radius (2) It has circle function ...

A prime p is called a Wolstenholme prime if the central binomial coefficient (2p; p)=2 (mod p^4), (1) or equivalently if B_(p-3)=0 (mod p), (2) where B_n is the nth Bernoulli ...

Let three isoscelizers I_(AC)I_(AB), I_(BA)I_(BC), and I_(CA)I_(CB) be constructed on a triangle DeltaABC, one for each side. This makes all of the inner triangles similar to ...

The de Longchamps line is central line L_(32) with trilinear equation a^3alpha+b^3beta+c^3gamma=0 (Droussent 1953; Kimberling 1998, p. 150) which is the anticomplement of the ...