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The curve produced by fixed point P on the circumference of a small circle of radius b rolling around the inside of a large circle of radius a>b. A hypocycloid is therefore a ...

Diophantus's riddle is a poem that encodes a mathematical problem. In verse, it read as follows: 'Here lies Diophantus,' the wonder behold. Through art algebraic, the stone ...

The conjecture that there are only finitely many triples of relatively prime integer powers x^p, y^q, z^r for which x^p+y^q=z^r (1) with 1/p+1/q+1/r<1. (2) Darmon and Merel ...

Let there be three polynomials a(x), b(x), and c(x) with no common factors such that a(x)+b(x)=c(x). Then the number of distinct roots of the three polynomials is one or more ...

The Mercator projection is a map projection that was widely used for navigation since loxodromes are straight lines (although great circles are curved). The following ...

The Mordell conjecture states that Diophantine equations that give rise to surfaces with two or more holes have only finite many solutions in Gaussian integers with no common ...

A perfect cuboid is a cuboid having integer side lengths, integer face diagonals d_(ab) = sqrt(a^2+b^2) (1) d_(ac) = sqrt(a^2+c^2) (2) d_(bc) = sqrt(b^2+c^2), (3) and an ...

The Riemann theta function is a complex function of g complex variables that occurs in the construction of quasi-periodic solutions of various equations in mathematical ...

As defined by Gray (1997, p. 201), Viviani's curve, sometimes also called Viviani's window, is the space curve giving the intersection of the cylinder of radius a and center ...

The biharmonic operator, also known as the bilaplacian, is the differential operator defined by del ^4=(del ^2)^2, where del ^2 is the Laplacian. In n-dimensional space, del ...