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An affine isoperimetric inequality.

The vertical perspective projection is a map projection that corresponds to the appearance of a globe when directly viewed from some distance away with the z-axis of the ...

Several cylindrical equidistant projections were devised by R. Miller. Miller's projections have standard parallels of phi_1=37 degrees30^' (giving minimal overall scale ...

A map projection with transformation equations x = rhosintheta (1) y = rho_0-rhocostheta, (2) where rho = (G-phi) (3) theta = n(lambda-lambda_0) (4) rho_0 = (G-phi_0) (5) G = ...

Every convex body B in the Euclidean plane with area A can be inscribed in a triangle of area at most equal to 2A (Gross 1918, Eggleston 1957). The worst possible fit ...

The region lying between two concentric circles. The area of the annulus formed by two circles of radii a and b (with a>b) is A_(annulus)=pi(a^2-b^2). The annulus is ...

The van der Grinten projection is a map projection given by the transformation x = (1) y = sgn(phi)(pi|PQ-Asqrt((A^2+1)(P^2+A^2)-Q^2)|)/(P^2+A^2), (2) where A = ...

Enclose a sphere in a cylinder and cut out a spherical segment by slicing twice perpendicularly to the cylinder's axis. Then the lateral surface area of the spherical segment ...

A rotor is a convex figure that can be rotated inside a polygon (or polyhedron) while always touching every side (or face). The least area rotor in a square is the Reuleaux ...

The surface of revolution generated by the external catenary between a fixed point a and its conjugate on the envelope of the catenary through the fixed point is equal in ...