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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.
In number theory, the Calkin–Wilf tree is a tree in which the vertices correspond one-to-one to the positive rational numbers.The tree is rooted at the number 1, and any rational number q expressed in simplest terms as the fraction a / b has as its two children the numbers 1 / 1+1/q = a / a + b and q + 1 = a + b / b .
The entire fraction may be expressed as a single composition, in which case it is hyphenated, or as a number of fractions with a numerator of one, in which case they are not. (For example, two-fifths is the fraction 2 / 5 and two fifths is the same fraction understood as 2 instances of 1 / 5 .) Fractions should always be ...
When speaking the numbers in fractions, the spatial/chronological numbering system is used for denominators larger than 2 (2 as the denominator of a fraction is "half" rather than "second"), with a denominator of 4 sometimes spoken as "quarter" rather than "fourth".
Can be built with two dragon curves. One of the six 2-rep-tiles in the plane (can be tiled by two copies of itself, of equal size). [13] 1.5850: 3-branches tree: Each branch carries 3 branches (here 90° and 60°). The fractal dimension of the entire tree is the fractal dimension of the terminal branches.
The Pythagoras tree is a plane fractal constructed from squares. Invented by the Dutch mathematics teacher Albert E. Bosman in 1942, [ 1 ] it is named after the ancient Greek mathematician Pythagoras because each triple of touching squares encloses a right triangle , in a configuration traditionally used to depict the Pythagorean theorem .
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