- Almost integer
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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 , for example:
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:
where the non-coincidence can be better appreciated when expressed in the common simple form[2]:
where : and the reason for the squares being due to certain Eisenstein series. The constant is sometimes referred to as Ramanujan's constant.
Almost integers involving the mathematical constants pi and e have often puzzled mathematicians. An example is
To date, no explanation has been given for why Gelfond's constant ( ) is nearly identical to ,[1] which is therefore regarded to be a mathematical coincidence.
Another example is
Also consider π in cubic expressions
or
where the second one is obvious from the first one.
Also consider π in quadratic expressions
or
where the second one is obvious from the first one.
Here are more examples:
External links
References
Categories:- Number stubs
- Integers
- Recreational mathematics
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