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Roughly speaking, isospectral manifolds are drums that sound the same, i.e., have the same eigenfrequency spectrum. Two drums with differing area, perimeter, or genus can ...

The polar sine is a function of a vertex angle of an n-dimensional parallelotope or simplex. If the content of the parallelotope is P and the lengths of the n edges of the ...

Reverse Polish notation (RPN) is a method for representing expressions in which the operator symbol is placed after the arguments being operated on. Polish notation, in which ...

The turning of an object or coordinate system by an angle about a fixed point. A rotation is an orientation-preserving orthogonal transformation. Euler's rotation theorem ...

Suppose that f is an analytic function which is defined in the upper half-disk {|z|^2<1,I[z]>0}. Further suppose that f extends to a continuous function on the real axis, and ...

The Wythoff array is an interspersion array that can be constructed by beginning with the Fibonacci numbers {F_2,F_3,F_4,F_5,...} in the first row and then building up ...

The Tucker circles are a generalization of the cosine circle and first Lemoine circle which can be viewed as a family of circles obtained by parallel displacing sides of the ...

Sylvester's four-point problem asks for the probability q(R) that four points chosen at random in a planar region R have a convex hull which is a quadrilateral (Sylvester ...

If P is a pedal point inside a triangle DeltaABC, and P_A, P_B, and P_C are the feet of the perpendiculars from P upon the respective sides BC, CA, and AB, then ...

In general, the internal similitude center of two circles C_1=C(x_1,r_1) and C_2=C(x_2,r_2) with centers given in Cartesian coordinates is given by ...