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A set of n magic circles is a numbering of the intersections of the n circles such that the sum over all intersections is the same constant for all circles. The above sets of ...

Curves with Cartesian equation ay^2=x(x^2-2bx+c) with a>0. The above equation represents the third class of Newton's classification of cubic curves, which Newton divided into ...

Consider a second-order differential operator L^~u(x)=p_0(d^2u)/(dx^2)+p_1(du)/(dx)+p_2u, (1) where u=u(x) and p_i=p_i(x) are real functions of x on the region of interest ...

The power of a fixed point A with respect to a circle of radius r and center O is defined by the product p=AP×AQ, (1) where P and Q are the intersections of a line through A ...

The 10.1.2 equation A^(10)=B^(10)+C^(10) (1) is a special case of Fermat's last theorem with n=10, and so has no solution. No 10.1.n solutions are known with n<13. A 10.1.13 ...

Lee (1944) defines an authalic map projection to be one in which at any point the scales in two orthogonal directions are inversely proportional.

Clean tile is a game investigated by Buffon (1777) in which players bet on the number of different tiles a thrown coin will partially cover on a floor that is regularly ...

A map projection in which the distances between one or two points and every other point on the map differ from the corresponding distances on the sphere by only a constant ...

An authalic latitude given by phi_g=tan^(-1)[(1-e^2)tanphi]. (1) The series expansion is phi_g=phi-e_2sin(2phi)+1/2e_2^2sin(4phi)+1/3e_2^3sin(6phi)+..., (2) where ...

When applied to a system possessing a length R at which solutions in a variable r change character (such as the gravitational field of a sphere as r runs from the interior to ...