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Topic: BUSTED! Re: Myth-busting pentagons by compass & straight edge.
Replies: 9   Last Post: Aug 23, 2013 11:11 PM

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Louis Talman

Posts: 5,100
Registered: 12/27/05
Re: BUSTED! Re: Myth-busting pentagons by compass & straight edge.
Posted: Aug 23, 2013 11:11 PM
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On Fri, 23 Aug 2013 10:49:30 -0600, Robert Hansen <> wrote:

> On newer calculators this trick doesn't work as well as it used to

A similar does work---but not as well as it used to---on the TI-83 Plus.
Put the machine in degree mode and enter the number 23. Take the sine.
Then take the cosine of the result. And then the tangent of that. Then
take the arctangent of the result, followed by the arccosine of that, and,
finally, the arcsine. The result isn't 23, but it's pretty close. Back
in the early seventies, the result would have been about 24, or even 25.

If you work things out, you'll find that 23 degrees is very nearly optimal
for this kind of bad behavior with those three functions---though I
discovered it purely by accident a few days after acquiring my first
hand-held calculator in about 1971. I knew the guy who'd written the
algorithms for that machine. I mentioned it, and he said, with a grimace,
"Everybody seems to find 23."

- --Louis A. Talman
Department of Mathematical and Computer Sciences
Metropolitan State University of Denver


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