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A rectangle which cannot be built up of squares all of different sizes is called an imperfect rectangle. A rectangle which can be built up of squares all of different sizes ...

A quotient-difference table is a triangular array of numbers constructed by drawing a sequence of n numbers in a horizontal row and placing a 1 above each. An additional "1" ...

Let two spheres of radii R and r be located along the x-axis centered at (0,0,0) and (d,0,0), respectively. Not surprisingly, the analysis is very similar to the case of the ...

The regular octahedron, often simply called "the" octahedron, is the Platonic solid with six polyhedron vertices, 12 polyhedron edges, and eight equivalent equilateral ...

Also known as the Serret-Frenet formulas, these vector differential equations relate inherent properties of a parametrized curve. In matrix form, they can be written [T^.; ...

A function built up of a finite combination of constant functions, field operations (addition, multiplication, division, and root extractions--the elementary operations)--and ...

Gaussian elimination is a method for solving matrix equations of the form Ax=b. (1) To perform Gaussian elimination starting with the system of equations [a_(11) a_(12) ... ...

Infinity, most often denoted as infty, is an unbounded quantity that is greater than every real number. The symbol infty had been used as an alternative to M (1000) in Roman ...

What space-filling arrangement of similar cells of equal volume has minimal surface area? This questions arises naturally in the theory of foams when the liquid content is ...

Marion's theorem (Mathematics Teacher 1993, Maushard 1994, Morgan 1994) states that the area of the central hexagonal region determined by trisection of each side of a ...