This Demonstration considers expressions of the form
where
,
,
,
, and
are positive rational numbers or integers and
is one of the six trigonometric functions, sin, cos, tan, cot, sec, or csc. For any set of such parameters, the value
will never be an integer (nor even an algebraic number).
The goal of the hunt is to find values of the parameters such that
is as near as possible to an integer. Easy integers are excluded, like the sine or cosine of a small number, which can easily be made very close to 0 or 1. Using all possible slider combinations, more than
1030 possible values of
can be tested, allowing the hunter to be busy for weeks. How small can you make the difference between the value
and an integer?
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