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Almost integer : ウィキペディア英語版
Almost integer

In recreational mathematics an almost integer is any number that is very close to an integer. Well-known examples of almost integers are high powers of the golden ratio \phi=\frac\approx 1.618\,, for example:
* \phi^=\frac\approx 3571.00028\,
* \phi^=2889+1292\sqrt5 \approx 5777.999827\,
* \phi^=\frac\approx 9349.000107\,
The fact that these powers approach integers is non-coincidental, which is trivially seen because the golden ratio is a Pisot-Vijayaraghavan number.
Other occurrences of non-coincidental near-integers involve the three largest Heegner numbers:
* e^}\approx 147197952743.999998662454\,
* e^}=12^3(9^2-1)^3+744-2.225\cdots\times 10^\,
:e^\,
:e^\,
where
:21=3\times7, 231=3\times7\times11, 744=24\times 31\,
and the reason for the squares being due to certain Eisenstein series. The constant e^-\pi=19.999099979189\cdots\,
To date, no explanation has been given for why Gelfond's constant ( e^\, ) is nearly identical to \pi+20\,,〔Eric Weisstein, ("Almost Integer" ) at MathWorld〕 which is therefore considered a mathematical coincidence.
==See also==

*Schizophrenic number

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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