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The regular decagon is constructible 10-sided regular polygon with Schläfli symbol {10}. The inradius r, circumradius R, and area can be computed directly from the formulas ...

A proof or demonstration is said to be rigorous if the validity of each step and the connections between the steps is explicitly made clear in such a way that the result ...

dN^^+kappa_idr=0, where N^^ is the unit normal vector and kappa_i is one of the two principal curvatures.

The Seiberg-Witten equations are D_Apsi = 0 (1) F_A^+ = -tau(psi,psi), (2) where tau is the sesquilinear map tau:W^+×W^+->Lambda^+ tensor C.

Sinai billiards is the reflection of a ray of light by an arrangement of perfectly reflecting circles in the plane (Trott 2004, pp. 28-30). The path is extremely sensitive to ...

The mean square deviation of the best local fit straight line to a staircase cumulative spectral density over a normalized energy scale.

A spheroidal harmonic is a special case of an ellipsoidal harmonic that satisfies the differential equation d/(dx)[(1-x^2)(dS)/(dx)]+(lambda-c^2x^2-(m^2)/(1-x^2))S=0 on the ...

A three-dimensional knot spun about a plane in four dimensions. Unlike suspended knots, spun knots are smoothly embedded at the poles.

A stack is a data structure which is a special kind of list in which elements may be added to or removed from the top only. These actions are called a push or a pop, ...

The topological entropy of a map M is defined as h_T(M)=sup_({W_i})h(M,{W_i}), where {W_i} is a partition of a bounded region W containing a probability measure which is ...