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All Rational Approximations of Pi Are Useless

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Re: All Rational Approximations of Pi Are Useless

#111
post #107
post #39

Earlier quoted context omitted.

I would think most slide rules have a marker for pi that make this even easier.

Given how slide rules work, there would have to be a great number of marks, for the same reason that there cannot be only one unique ratio of integers that approximates Pi.

I do not think you have thought that through. You need only one mark for PI on every part of a sliderule to multiply or divide by pi. See for example http://en.wikipedia.org/wiki/File:Slide_rule_cursor.jpg

Re: All Rational Approximations of Pi Are Useless

#112
post #79

Earlier quoted context omitted.

No idea what you're talking about. I'm merely improving the typography.

From the original spec of the problem: "only the operators +, -, x, /, and ^ (exponentiation), and parenthesis for grouping"

It has to be presentable. Typography matters.

Re: All Rational Approximations of Pi Are Useless

#113
post #107

Earlier quoted context omitted.

Given how slide rules work, there would have to be a great number of marks, for the same reason that there cannot be only one unique ratio of integers that approximates Pi.

I do not think you have thought that through. You need only one mark for PI on every part of a sliderule to multiply or divide by pi. See for example http://en.wikipedia.org/wiki/File:Slide_rule_cursor.jpg

> I do not think you have thought that through.

My remark was only in the context of the present conversation, where Pi is representable by the ratios of various integers.

I used a lot of slide rules during my years as a NASA engineer, but none of those I owned had marks for physical constants -- too bad, because it's a very good idea.

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