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To represent a given number as a location numeral, that number is expressed as a sum of powers of two and then each power of two is replaced by its corresponding digit (letter). For example, when converting from a decimal numeral: 87 = 1 + 2 + 4 + 16 + 64 = 2 0 + 2 1 + 2 2 + 2 4 + 2 6 = abceg
Reversing the digits to modern-day usage of descending order of decimal places, we get 314159265358979324 which is the value of pi (π) to 17 decimal places, except the last digit might be rounded off to 4. This verse encrypts the value of pi (π) up to 31 decimal places.
For example, one can multiply a sine that is less than 0.5 by some power of two or ten to bring it into the range [0.5,1]. After finding that logarithm in the radical table, one adds the logarithm of the power of two or ten that was used (he gives a short table), to get the required logarithm. [1]: p. 36
That is, fractions aren't difficult to compare if the numerator is 1 (e.g., 1 ⁄ 2 is larger than 1 ⁄ 3, which in turn is larger than 1 ⁄ 4). However, comparisons become more difficult when both numerators and denominators are mixed: 3 ⁄ 4 is larger than 5 ⁄ 7 , which in turn is larger than 2 ⁄ 3 , though this cannot be determined by ...
By 1586, Bürgi was able to calculate sines at arbitrary precision, using several algorithms, one of which he called Kunstweg. He supposedly used these algorithms to calculate a «Canon Sinuum», a table of sines to 8 places in steps of 2 arc seconds. Nothing more is known on this table, and some authors have speculated that its range was only ...
The 9's complement of any one-digit decimal number d is 9-d. So the 9's complement of 4 is 5 and the 9's complement of 9 is 0. Similarly, the 11's complement of 3 is 8. In a decimal machine with n dials the 9's complement of a number A is: = and therefore the 9's complement of (A-B) is:
Sometimes, [1] y̆ is written in place of y̑ , even though the former symbol denotes an extra-short in the official IPA. Some languages, though, have a palatal approximant that is unspecified for rounding, and therefore cannot be considered the semivocalic equivalent of either [y] or its unrounded counterpart .