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Some examples of almost integers are high powers of the golden ratio = +, for example: = + = + = + The fact that these powers approach integers is non-coincidental, because the golden ratio is a Pisot–Vijayaraghavan number.
An almost integer is a number that is very close to an integer. Near-solutions to Fermat's last theorem provide a number of high-profile almost integers. In the season 7, episode 6 ("Treehouse of Horror VI") segment entitled Homer^3 of the animated televsion program The Simpsons, the equation 1782^(12)+1841^(12)=1922^(12) appears at one point in the background.
This example shows how to find almost integers, or numbers that are very close to integers, using variable-precision arithmetic in Symbolic Math Toolbox™. This example searches for almost integers (or near-integers) that have the form exp (π n) or exp (π n) for the integers n = 1, ..., 200. First, consider a well-known example of an almost ...
De nition 2.1. A number is called an algebraic integer if it is the root of some polynomial of the form f (x ) = x n + a n 1 x n 1 + + a 1 x + a 0; where the coe cients a i are all integers. If f (x ) is the minimal polynomial for some algebraic integer , then the roots of f (x ) other than are called the Galois conjugates of .
Mar 2, 2019 · Informally speaking, an "almost integer" is a real number very close to an integer. There are some known ways to construct such examples in a systematic way. One is through the use of certain algebraic numbers called Pisot numbers. These numbers $\alpha$ have the property that their powers can get arbitrarly close to integers, that is:
An almost integer is a number that is very close to an integer. Surprising examples are given by \sin(11) = -0.999990206,\dots which equals -1 to within 5 digits and ...
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Mar 28, 2013 · Almost integers are mathematical equations that are almost equal to a whole number, ... Take the number twenty, for example. A nice and round small integer. ... Mathematics is generally considered ...
