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A triangle with side lengths a, b, and c and triangle area Delta satisfies a^2+b^2+c^2>=4sqrt(3)Delta. Equality holds iff the triangle is equilateral.

A nonconformal, equal-area projection which is a special case of the Bonne projection where one of the poles is taken as the standard parallel. Because of its heart shape, ...

A lune is a plane figure bounded by two circular arcs of unequal radii, i.e., a crescent. (By contrast, a plane figure bounded by two circular arcs of equal radius is known ...

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 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 similar construction can be done by initially erecting a square internally on the side BC. This leads to the A^--inscribed square. The triangle DeltaX^-Y^-Z^- of centers of ...

An inellipse inconic that is an ellipse. The locus of the centers of the ellipses inscribed in a triangle is the interior of the medial triangle. Newton gave the solution to ...

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 circumellipse is a circumconic of a triangle that is an ellipse. There is an amazing formula for the area of a circumellipse. Let d_A be the length of the chord of the ...