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A rounded rectangle is the shape obtained by taking the convex hull of four equal circles of radius r and placing their centers at the four corners of a rectangle with side ...

A quadrilateral which has an incircle, i.e., one for which a single circle can be constructed which is tangent to all four sides. Opposite sides of such a quadrilateral ...

The sinusoidal projection is an equal-area projection given by the transformation x = (lambda-lambda_0)cosphi (1) y = phi. (2) The inverse formulas are phi = y (3) lambda = ...

Find the surface enclosing the maximum volume per unit surface area, I=V/S. The solution is a sphere, which has I_(sphere)=(4/3pir^3)/(4pir^2)=1/3r. The fact that a sphere ...

The Newton-Cotes formulas are an extremely useful and straightforward family of numerical integration techniques. To integrate a function f(x) over some interval [a,b], ...

The n-ball, denoted B^n, is the interior of a sphere S^(n-1), and sometimes also called the n-disk. (Although physicists often use the term "sphere" to mean the solid ball, ...

The positions of the geometric centroid of a planar non-self-intersecting polygon with vertices (x_1,y_1), ..., (x_n,y_n) are x^_ = ...

A parametric latitude which gives a sphere equal surface area relative to an ellipsoid. The authalic latitude is defined by beta=sin^(-1)(q/(q_p)), (1) where ...

A lattice polygon formed by a three-choice walk. The anisotropic perimeter and area generating function G(x,y,q)=sum_(m>=1)sum_(n>=1)sum_(a>=a)C(m,n,a)x^my^nq^a, where ...

A dissection fallacy discovered by Dudeney (1958). The same set of tangram pieces can apparently produce two different figures, one of which is a proper subset of the other. ...