A few side questions

An enlightening discussion about pi and tau.

A few side questions

by metric man » Sun Dec 25, 2011 1:53 pm

Hi everyone,

I have a few historiographical questions that I would like to ask.

When going to Joseph Lindenberg's article, "Tau Before It Was Cool," I see a reference to a certain Peter Harremoës. When I click on that hyperlink, the only thing that I get is a reference to the medieval Persian mathematician al-Kashi. That is fine, of course, but I would like to know if this biographical sketch is the only contribution by Peter Harremoës to the tau debate. I am not discounting the value of the biography. But since I am trying to familiarize myself with as many facets to the controversy as I can, I am just curious if Peter Harremoës has even more to say regarding tau.

Second, the Wikipedia entry on al-Kashi alternatively uses the name al-Kashi and al-Kashani. Why do these variations exist? Which is preferable?

Third and finally, in Peter Harremoës' article on al-Kashi (or, of course, al-Kashani), right in the beginning I see a reference to Gregory's constant. What is that?

Thank you all.
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Re: A few side questions

by josephlindenberg » Tue Dec 27, 2011 3:36 am

Peter's page has a lot more than history. The main characteristic I notice about it is that he has such an extensive collection of formulas with tau replacing pi. But I certainly agree that he's the history expert/buff in the group.

Prior to August 17, Peter's page was titled "Gregory's constant τ" to honor the 17th/18th century mathematician David Gregory, who was thought to be the earliest known person to seem to recognize that circumference/radius was the important number. Back when other people were using "π/δ" to signify "perimeter/diameter", he used "π/ρ" to signify "perimeter/radius". But in early August, I was reading Wikipedia's page about "Approximations of pi". They list major historical calculations of pi, and I noticed it said that in the 15th century, al-Kashi calculated 2pi, not pi. I figured that might be a sign that he used 2pi in the rest of his work too. But I'm not a history buff, so I just sent an email around letting people know I'd come across this. Peter dug into it and found that indeed, al-Kashi had used circumference/radius in his work. (I don't know what symbol(s) he actually used.) So since al-Kashi was first, Peter transferred the honor to him. Gregory's constant became al-Kashi's constant. But I guess Peter hasn't gotten around to changing all the places on his web page where he uses the term.

Yeah, I find the different forms of al-Kashi's name strange too. His full name is quite long, so they shorten it, but use only the portion that tells what city he's from, Kashan. Maybe al-Kashi and al-Kashani are like Delawarean and Delawarite?

Earlier this year, I see Peter worked to prepare/soften the ground at Wikipedia. The math mavens there have been very dismissive of the whole tau idea. They really resisted introducing the topic, so from what I can see, Peter found ways to highlight the importance of 2pi, without actually calling it tau, which they wouldn't have tolerated. It's actually pretty funny when I'll be reading a Wikipedia page on a related topic and come across one of these entries. I'll think, hey, that really clearly points out the importance of 2pi. Then I'll get suspicious, look at the revision history, and sure enough, Peter wrote it.
PI is the SEMICIRCLE constant, not the circle constant . . . http://sites.google.com/site/taubeforeitwascool
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Re: A few side questions

by metric man » Tue Dec 27, 2011 6:34 pm

Thank you josephlinberg for your answers.

Given this information, I looked up David Gregory on Wikipedia, but there was no mention of his role in tau (or 2pi) in that article. But now I understand more of the story.
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Re: A few side questions

by josephlindenberg » Tue Dec 27, 2011 10:55 pm

Bob Palais mentions it at the end of his 2001 essay. He cites page 292 of Pi: A Source Book as his source.

http://www.amazon.com/Pi-Source-Book-Lennart-Berggren/dp/0387949240
If you click on the "Click to LOOK INSIDE!" link, then search for David Gregory, then hover over where it says page 292, you can see the relevant quote.
PI is the SEMICIRCLE constant, not the circle constant . . . http://sites.google.com/site/taubeforeitwascool
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Re: A few side questions

by josephlindenberg » Sat Jan 07, 2012 12:19 am

josephlindenberg wrote:Earlier this year, I see Peter worked to prepare/soften the ground at Wikipedia.

I noticed today that Peter's work on this at Wikipedia actually stretches clear back to May 2010.
PI is the SEMICIRCLE constant, not the circle constant . . . http://sites.google.com/site/taubeforeitwascool
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