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A prime can be a member of up to three prime triplets - for example, 103 is a member of (97, 101, 103), (101, 103, 107) and (103, 107, 109).When this happens, the five involved primes form a prime quintuplet.
[17] [18] While Boyer mentions Old Babylonian mathematics (c. 2000 BCE–1600 BCE) as a possible origin, the c. 1800 BCE Plimpton 322 tablet containing a table of triplets, however also states that Shulba sutras contain a formula not found in Babylon sources. [19] [1] KS Krishnan asserts that Shulba sutras predates Mesopotamian Pythagoras ...
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 ...
Such a triple is commonly written (a, b, c), a well-known example is (3, 4, 5). If ( a , b , c ) is a Pythagorean triple, then so is ( ka , kb , kc ) for any positive integer k . A triangle whose side lengths are a Pythagorean triple is a right triangle and called a Pythagorean triangle .
English-language haiku is an example of an unrhymed tercet poem. A poetic triplet is a tercet in which all three lines follow the same rhyme, AAA; triplets are rather rare; they are more customarily used sparingly in verse of heroic couplets or other couplet verse, to add extraordinary emphasis.
[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 ...
A set of triplets believed to be the first to graduate all together at the same university with first-class honours have said the moment was “bittersweet” after the loss of their father.
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