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Also bear in mind that the fraction 2/3 is the single exception, used in addition to integers, that Ahmes uses alongside all (positive) rational unit fractions to express Egyptian fractions. The 2/n table can be said to partially follow an algorithm (see problem 61B) for expressing 2/n as an Egyptian fraction of 2 terms, when n is composite.
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 .
The Rhind Mathematical Papyrus, [1] [2] an ancient Egyptian mathematical work, includes a mathematical table for converting rational numbers of the form 2/ n into Egyptian fractions (sums of distinct unit fractions ), the form the Egyptians used to write fractional numbers. The text describes the representation of 50 rational numbers.
An Egyptian fraction is a finite sum of distinct unit fractions, such as That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from each other. The value of an expression of this type is a positive rational number ; for instance the Egyptian fraction ...
However, the blue triangle has a ratio of 5:2 (=2.5), while the red triangle has the ratio 8:3 (≈2.667), so the apparent combined hypotenuse in each figure is actually bent. With the bent hypotenuse, the first figure actually occupies a combined 32 units, while the second figure occupies 33, including the "missing" square.
In geometry, a golden rectangle is a rectangle whose side lengths are in the golden ratio, : +, which is : (the Greek letter phi), where is approximately 1.618.. Golden rectangles exhibit a special form of self-similarity: All rectangles created by adding a square to a side, or removing a square from an end, of a golden rectangle are golden rectangles as well.
Number Forms is a Unicode block containing Unicode compatibility characters that have specific meaning as numbers, but are constructed from other characters. They consist primarily of vulgar fractions and Roman numerals. In addition to the characters in the Number Forms block, three fractions (¼, ½, and ¾) were inherited from ISO-8859-1 ...
Packing different rectangles in a rectangle: The problem of packing multiple rectangles of varying widths and heights in an enclosing rectangle of minimum area (but with no boundaries on the enclosing rectangle's width or height) has an important application in combining images into a single larger image. A web page that loads a single larger ...
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