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The entries in the second and third columns of Row 11, unlike those of all other rows except possibly Row 15, contain a common factor. It is possible that 45 and 1 15 are to be understood as 3/4 and 5/4, which is consistent with the standard (0.75,1,1.25) scaling of the familiar (3,4,5) right triangle in Babylonian mathematics.
A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") is a rational number written as a / b or , where a and b are both integers. [9] As with other fractions, the denominator (b) cannot be zero. Examples include 1 2 , − 8 5 , −8 5 , and 8 −5 .
Germanium (32 Ge) has five naturally occurring isotopes, 70 Ge, 72 Ge, 73 Ge, 74 Ge, and 76 Ge. Of these, 76 Ge is very slightly radioactive, decaying by double beta decay with a half-life of 1.78 × 10 21 years [4] (130 billion times the age of the universe). Stable 74 Ge is the most common isotope, having a natural abundance of approximately ...
Isotopes of thallium (81Tl) Thallium (81 Tl) has 41 isotopes with atomic masses that range from 176 to 216. 203 Tl and 205 Tl are the only stable isotopes and 204 Tl is the most stable radioisotope with a half-life of 3.78 years. 207 Tl, with a half-life of 4.77 minutes, has the longest half-life of naturally occurring Tl radioisotopes.
The Chinese mathematician Liu Hui in 263 CE computed π to between 3.141 024 and 3.142 708 by inscribing a 96-gon and 192-gon; the average of these two values is 3.141 866 (accuracy 9·10 −5). He also suggested that 3.14 was a good enough approximation for practical purposes.
[3] Alternatively, it can be described as the tuning of the syntonic temperament [1] in which the generator is the ratio 3:2 (i.e., the untempered perfect fifth), which is ≈ 702 cents wide. The system dates back to Ancient Mesopotamia;. [4] (See Music of Mesopotamia § Music theory.)
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In mathematical terms, Hamming codes are a class of binary linear code. For each integer r ≥ 2 there is a code-word with block length n = 2r − 1 and message length k = 2r − r − 1. Hence the rate of Hamming codes is R = k / n = 1 − r / (2r − 1), which is the highest possible for codes with minimum distance of three (i.e., the minimal ...