Re: Pi/3 the only fraction of the circle with a rational projection

In article
<2dd83b53-c414-4172-ac9c-c4dd7781a0e6@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
amado.alves@xxxxxxxxx wrote:

I find it extremely intriguing that a simple fraction of the circle
should project upon a simple fraction of the radius: sin(Pi/3) = 1/2.

And furthermore I intuit that this is the only projection with
integral fractions on both sides of the equation. (Ignoring the
geometrically trivial cases sin(0), sin(Pi/2), and the equivalent
cases cos(Pi/6), etc.)

Much more is known. I wrote a paper almost 20 years ago
in which I found all rational x, y, z, w such that
(sin pi x) (sin pi y) (sin pi z) (sin pi w) is rational.

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)
.

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