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It can be shown that all Pythagorean triples can be obtained, with appropriate rescaling, from the basic Platonic sequence (a, (a 2 − 1)/2 and (a 2 + 1)/2) by allowing a to take non-integer rational values. If a is replaced with the fraction m/n in the sequence, the result is equal to the 'standard' triple generator (2mn, m 2 − n 2, m 2 + n ...
With a the shorter and b the longer legs of a triangle and c its hypotenuse, the Pythagoras family of triplets is defined by c − b = 1, the Plato family by c − b = 2, and the Fermat family by | a − b | = 1. The Stifel sequence produces all primitive triplets of the Pythagoras family, and the Ozanam sequence produces all primitive triples ...
[6]: p.7 For example, parent (3, 4, 5) has excircle radii equal to 2, 3 and 6. These are precisely the inradii of the three children (5, 12, 13), (15, 8, 17) and (21, 20, 29) respectively. If either of A or C is applied repeatedly from any Pythagorean triple used as an initial condition, then the dynamics of any of a , b , and c can be ...
An open reading frame (ORF) is a reading frame that has the potential to be transcribed into RNA and translated into protein. It requires a continuous sequence of DNA which may include a start codon, through a subsequent region which has a length that is a multiple of 3 nucleotides, to a stop codon in the same reading frame.
The term sister group is used in phylogenetic analysis, however, only groups identified in the analysis are labeled as "sister groups".. An example is birds, whose commonly cited living sister group is the crocodiles, but that is true only when discussing extant organisms; [3] [4] when other, extinct groups are considered, the relationship between birds and crocodiles appears distant.
Molecular phylogenetics (/ m ə ˈ l ɛ k j ʊ l ər ˌ f aɪ l oʊ dʒ ə ˈ n ɛ t ɪ k s, m ɒ-, m oʊ-/ [1] [2]) is the branch of phylogeny that analyzes genetic, hereditary molecular differences, predominantly in DNA sequences, to gain information on an organism's evolutionary relationships. From these analyses, it is possible to determine ...
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 word pedigree is a corruption of the Anglo-Norman French pé de grue or "crane's foot", either because the typical lines and split lines (each split leading to different offspring of the one parent line) resemble the thin leg and foot of a crane [3] or because such a mark was used to denote succession in pedigree charts.