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Sylvester's line problem, known as the Sylvester-Gallai theorem in proved form, states that it is not possible to arrange a finite number of points so that a line through ...

Watson (1939) considered the following three triple integrals, I_1 = 1/(pi^3)int_0^piint_0^piint_0^pi(dudvdw)/(1-cosucosvcosw) (1) = (4[K(1/2sqrt(2))]^2)/(pi^2) (2) = ...

Barycentric coordinates are triples of numbers (t_1,t_2,t_3) corresponding to masses placed at the vertices of a reference triangle DeltaA_1A_2A_3. These masses then ...

A portion of a disk whose upper boundary is a (circular) arc and whose lower boundary is a chord making a central angle theta<pi radians (180 degrees), illustrated above as ...

A curve with polar coordinates, r=b+asectheta (1) studied by the Greek mathematician Nicomedes in about 200 BC, also known as the cochloid. It is the locus of points a fixed ...

The word "convergent" has a number of different meanings in mathematics. Most commonly, it is an adjective used to describe a convergent sequence or convergent series, where ...

A series is said to be convergent if it approaches some limit (D'Angelo and West 2000, p. 259). Formally, the infinite series sum_(n=1)^(infty)a_n is convergent if the ...

A cylindrical wedge, also called a cylindrical hoof or cylindrical ungula, is a wedge cut from a cylinder by slicing with a plane that intersects the base of the cylinder. ...

Elder's theorem is a generalization of Stanley's theorem which states that the total number of occurrences of an integer k among all unordered partitions of n is equal to the ...

If P is a pedal point inside a triangle DeltaABC, and P_A, P_B, and P_C are the feet of the perpendiculars from P upon the respective sides BC, CA, and AB, then ...