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In geometry, an octagon (from Ancient Greek ὀκτάγωνον (oktágōnon) 'eight angles') is an eight-sided polygon or 8-gon. A regular octagon has Schläfli symbol {8} [ 1 ] and can also be constructed as a quasiregular truncated square, t {4}, which alternates two types of edges. A truncated octagon, t {8} is a hexadecagon, {16}.
Ratio. In mathematics, a ratio (/ ˈreɪʃ (i) oʊ /) shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4) and ...
A truncated square is an octagon, t{4}={8}. A quasitruncated square, inverted as {4/3}, is an octagram, t{4/3}={8/3}. [2] The uniform star polyhedron stellated truncated hexahedron, t'{4,3}=t{4/3,3} has octagram faces constructed from the cube in this way. It may be considered for this reason as a three-dimensional analogue of the octagram.
If this diagonal is oriented vertically with a height of 1, then the first five slices above occur at heights r, 3 / 8 , 1 / 2 , 5 / 8 , and s, where r is any number in the range 0 < r ≤ 1 / 4 , and s is any number in the range 3 / 4 ≤ s < 1.
Lagrange's discovery implies that the canonical continued fraction expansion of the square root of every non-square integer is periodic and that, if the period is of length p > 1, it contains a palindromic string of length p − 1. In 1813 Gauss derived from complex-valued hypergeometric functions what is now called Gauss's continued fractions ...
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 .
In mathematics, the Farey sequence of order n is the sequence of completely reduced fractions, either between 0 and 1, or without this restriction, [a] which when in lowest terms have denominators less than or equal to n, arranged in order of increasing size. With the restricted definition, each Farey sequence starts with the value 0, denoted ...
Example (inch, coarse): For size 7 ⁄ 16 (this is the diameter of the intended screw in fraction form)-14 (this is the number of threads per inch; 14 is considered coarse), 0.437 in × 0.85 = 0.371 in. Therefore, a size 7 ⁄ 16 screw (7 ⁄ 16 ≈ 0.437) with 14 threads per inch (coarse) needs a tap drill with a diameter of about 0.371 inches.
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