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For example, Yasodhara in his Jayamangala commentary on Kamasutra [2] gives descriptions of methods known by the names Kautilya and Muladeviya. The ciphers described in the Jayamangala commentary are substitution ciphers : in Kautiliyam the letter substitutions are based on phonetic relations, and Muladeviya is a simplified version of Kautiliyam.
Rules for calculating the periods of repeating decimals from rational fractions were given by James Whitbread Lee Glaisher in 1878. [5] For a prime p, the period of its reciprocal divides p − 1. [6] The sequence of recurrence periods of the reciprocal primes (sequence A002371 in the OEIS) appears in the 1973 Handbook of Integer Sequences.
A pentatope number is a number in the fifth cell of any row of Pascal's triangle starting with the five-term row 1 4 6 4 1 . The sum of the reciprocals of the pentatope numbers is 4 / 3 . Sylvester's sequence is an integer sequence in which each member of the sequence is the product of the previous members, plus one.
For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The reciprocal function, the function f(x) that maps x to 1/x, is one of the simplest examples of a function which is its own inverse (an involution). Multiplying by a number is the same as dividing by its reciprocal and vice versa ...
Then if we denote the lengths of the parallel sides as a and b and half the length of the segment through the diagonal intersection as c, the sum of the reciprocals of a and b equals the reciprocal of c. [4] The special case in which the integers whose reciprocals are taken must be square numbers appears in two ways in the context of right ...
In particular, the step 4c = 0 + 4 + 0 + 8 + ⋯ is not justified by the additive identity law alone. For an extreme example, appending a single zero to the front of the series can lead to a different result.
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These lists may have encompassed nidana 1–4, 5–8, and 8-12. [138] Schumann also proposes that the 12 nidanas are extended over three existences, and illustrates the succession of rebirths. While Buddhaghosa and Vasubandhu maintain a 2-8-2 schema, Schumann maintains a 3-6-3 scheme.