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A subset B of a vector space E is said to be balanced if lambdaB subset= B whenever lambda is a scalar satisfying |lambda|<=1. Here, the notation lambdaB denotes the set ...

The Balthasart projection is a cylindrical equal-area projection that uses a standard parallel of phi_s=50 degrees.

Let f be a contraction mapping from a closed subset F of a Banach space E into F. Then there exists a unique z in F such that f(z)=z.

A Banach limit is a bounded linear functional f on the space ł^infty of complex bounded sequences that satisfies ||f||=f(1)=1 and f({a_(n+1)})=f({a_n}) for all {a_n} in ...

The circle through the cusp of the arbelos and the tangent points of the first Pappus circle, which is congruent to the two Archimedes' circles. If AB=r and AC=1, then the ...

A polyhex consisting of hexagons arranged along a line.

A polyiamond consisting of equilateral triangles arranged along a line.

A man of Seville is shaved by the Barber of Seville iff the man does not shave himself. Does the barber shave himself? This pseudoparadox was proposed by Bertrand Russell.

All curves of constant width of width w have the same perimeter piw.

The triangle center with triangle center function alpha=A.