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In the above figure, let DeltaABC be a right triangle, arcs AP and AQ be segments of circles centered at C and B respectively, and define a = BC (1) b = CA=CP (2) c = BA=BQ. ...

Given rods of length 1, 2, ..., n, how many distinct triangles T(n) can be made? Lengths for which l_i>=l_j+l_k (1) obviously do not give triangles, but all other ...

Given a triangle with angles (pi/p, pi/q, pi/r), the resulting symmetry group is called a (p,q,r) triangle group (also known as a spherical tessellation). In three ...

The tribonacci constant is ratio to which adjacent tribonacci numbers tend, and is given by t = (x^3-x^2-x-1)_1 (1) = 1/3(1+RadicalBox[{19, -, 3, {sqrt(, 33, )}}, ...

The functions (also called the circular functions) comprising trigonometry: the cosecant cscx, cosine cosx, cotangent cotx, secant secx, sine sinx, and tangent tanx. However, ...

A minimal surface discovered by L. P. M. Jorge and W. Meeks III in 1983 with Enneper-Weierstrass parameterization f = 1/((zeta^3-1)^2) (1) g = zeta^2 (2) (Dickson 1990). ...

A tripod is a tree having exactly three tree leaves (Pirnazar and Ullman 2002). The numbers of tripods on n=1, 2, ... vertices are 0, 0, 0, 1, 1, 2, 3, 4, 5, 7, 8, 10, 12, ...

By way of analogy with the eban numbers, uban numbers are defined as numbers whose English names do not contain the letter "u" (i.e., "u" is banned). Note that this ...

Find nontrivial solutions to sigma(x^2)=sigma(y^2) other than (x,y)=(4,5), where sigma(n) is the divisor function. Nontrivial solutions means that solutions which are ...

The n-wheel complement graph W^__n is the graph complement of the n-wheel graph. For n>4, W^__n is isomorphic to the graph disjoint union of a circulant graph ...