Search results
Results from the WOW.Com Content Network
The spiral is started with an isosceles right triangle, with each leg having unit length.Another right triangle (which is the only automedian right triangle) is formed, with one leg being the hypotenuse of the prior right triangle (with length the square root of 2) and the other leg having length of 1; the length of the hypotenuse of this second right triangle is the square root of 3.
The Ulam spiral or prime spiral is a graphical depiction of the set of prime numbers, devised by mathematician Stanisław Ulam in 1963 and popularized in Martin Gardner's Mathematical Games column in Scientific American a short time later. [1] It is constructed by writing the positive integers in a square spiral and specially marking the prime ...
The left side of this identity describes a square number, while the right side describes a triangular number, so the result is a square triangular number. Falcón and Díaz-Barrero (2006) proved another identity relating Pell numbers to squares and showing that the sum of the Pell numbers up to P 4n +1 is always a square:
The following other wikis use this file: Usage on bh.wikipedia.org प्लास्टिक नंबर; Usage on ca.wikipedia.org Nombre plàstic
The length of the side of a larger square to the next smaller square is in the golden ratio. For a square with side length 1, the next smaller square is 1/φ wide. The next width is 1/φ², then 1/φ³, and so on. There are several comparable spirals that approximate, but do not exactly equal, a golden spiral. [2]
Physical scientists often use the term root mean square as a synonym for standard deviation when it can be assumed the input signal has zero mean, that is, referring to the square root of the mean squared deviation of a signal from a given baseline or fit. [8] [9] This is useful for electrical engineers in calculating the "AC only" RMS of a signal.
A matrix B is said to be a square root of A if the matrix product BB is equal to A. [1] Some authors use the name square root or the notation A 1/2 only for the specific case when A is positive semidefinite, to denote the unique matrix B that is positive semidefinite and such that BB = B T B = A (for real-valued matrices, where B T is the ...
Visualisation of the complex roots of y = ax 2 + bx + c: the parabola is rotated 180° about its vertex (orange). Its x -intercepts are rotated 90° around their mid-point, and the Cartesian plane is interpreted as the complex plane ( green ).