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Conversely the period of the repeating decimal of a fraction c / d will be (at most) the smallest number n such that 10 n − 1 is divisible by d. For example, the fraction 2 / 7 has d = 7, and the smallest k that makes 10 k − 1 divisible by 7 is k = 6, because 999999 = 7 × 142857. The period of the fraction 2 / 7 is ...
Trigonometry, in the form of a table of chord lengths in a circle, was probably used by Claudius Ptolemy of Alexandria to obtain the value of π given in the Almagest (circa 150 CE). [ 68 ] Advances in the approximation of π (when the methods are known) were made by increasing the number of sides of the polygons used in the computation.
This sequence takes a particularly simple form for prime k: 2 ⋅ 2 k − 1 − 1 / k . For example: 2 ⋅ 2 13 − 1 − 1 / 13 = 630 is the number of cycles of length 13. Since this case of the logistic map is chaotic for almost all initial conditions, all of these finite-length cycles are unstable.
Arithmetic values thought to have been represented by parts of the Eye of Horus. The scribes of ancient Egypt used two different systems for their fractions, Egyptian fractions (not related to the binary number system) and Horus-Eye fractions (so called because many historians of mathematics believe that the symbols used for this system could be arranged to form the eye of Horus, although this ...
More abstractly, the logistic function is the natural parameter for the Bernoulli distribution, and in this sense is the "simplest" way to convert a real number to a probability. In particular, it maximizes entropy (minimizes added information), and in this sense makes the fewest assumptions of the data being modeled; see § Maximum entropy .
This smaller form factor is similar to that used in an HDD by Rodime in 1983, which was the same size as the "half height" 3½" FDD, i.e., 1.63 inches high. Today, the 1-inch high ("slimline" or "low-profile") version of this form factor is the most popular form used in most desktops.
Water is one of the simplest molecules, composed of one oxygen and two hydrogen atoms, and can be found in all celestial bodies of the solar system. However, water is only useful for life in a liquid state, and extraterrestrial water is commonly found as water vapor or ice. Liquid water also has several properties that are beneficial for lifeforms.
The simplest way to explore lunar transfer trajectories is by the method of patched conics. The spacecraft is assumed to accelerate only under classical 2 body dynamics, being dominated by the Earth until it reaches the Moon's sphere of influence .