5 ms·
The Pi You Know Is A Lie
- aston 18y agoYeah man. I love this paper. All of the equations look so much prettier without 2 in front of pi everywhere.
- mhartl 18y agoI independently 'discovered' this a few years back, basically on the grounds that there are infinitely many shapes with constant diameter but only one (the circle) with constant radius. It stands to reason that the ratio of a circle's circumference to its diameter contains a spurious factor of 2; it must be that the ratio of circumference to radius is the more fundamental quantity. This discovery was almost enough to make me want to memorize an embarrassing number of digits of 2π; 6.28 is really pathetic. (What's embarrassing, you say? Try 3.141592653589793238462643383279502884197169399...)
- llimllib 18y agoHow are you defining diameter? http://mathworld.wolfram.com/Diameter.html http://mathworld.wolfram.com/Diameter.html only defines it for circular and spherical objects.
- mhartl 18y agohttp://en.wikipedia.org/wiki/Curve_of_constant_width http://en.wikipedia.org/wiki/Curve_of_constant_width
- pc 18y agoPDF: http://www.math.utah.edu/~palais/pi.pdf http://www.math.utah.edu/~palais/pi.pdf
- eyudkowsky 18y agoThat's what I entered, but it came out on Scribd!
- 0x44 18y agohttp://news.ycombinator.com/item?id=179721 http://news.ycombinator.com/item?id=179721
- Alex3917 18y agoI dislike the current system because it attributes a violation of copyright to the submitter that they're not actually responsible for. In practice it's not a real issue, it's just kind of tacky. It would be better if all submitted PDFs were turned into Scribd documents, but each user had a profile option for whether to change their PDF links to point to the Scribd doc or to leave it pointing to the original download.
- jsn 18y agoor they might just add a hyperlinked "[pdf]" or "[scribd]" after the original link, pointing to scribdified version. internets ignoring my choice of pdf viewer -- that sure feels wrong. oh well, greasemonkey to rescue.
- Xichekolas 18y agoAlready done: http://userscripts.org/scripts/show/25039 http://userscripts.org/scripts/show/25039
- jsn 18y agomy version (http://userscripts.org/scripts/show/26925 http://userscripts.org/scripts/show/26925) was there 1 minute before that :)
- Xichekolas 18y ago
- dnaquin 18y agoVolume of the n-ball? Generally, what I would consider the defining equation for pi. Has no factor of 2? V_n = pi^(n/2)R^n / Gamma(n/2+1) = C_n R^n C_n = pi^k/k! for even n=2k C_n = 2^(k+1)k!pi^k / (2k+1)! for odd n=2k+1 Of course we could just change the definition of gamma, but I prefer gamma as an extension of factorial.
- mwerty 18y agoAlmost as bad as negatively charged electrons.
- aneesh 18y agoI don't see why this is such a big deal. Scaling by a factor of 2 doesn't make any of the math lose it's beauty. The underlying math is still the same. Calling 30 minutes "an hour" doesn't make time go faster. It's all semantics, really. Anyway, pi is so engrained in our mathematics that the costs of switching would surely be higher than any superficial, aesthetic benefits.
- akd 18y agoThe author knows this, and was making a merely aesthetic point which you seem to have sucked all the fun out of.
- dhbradshaw 18y agoI think the aesthetics are important. You can see further when they are better.
- lvecsey 18y agoThe three legged symbol is pretty good, but maybe papers could just set the value of pi at the introduction.
- tlrobinson 18y agoIndiana once tried to pass a law saying pi actually equals 3.2 http://www.straightdope.com/classics/a3_341.html http://www.straightdope.com/classics/a3_341.html
- gills 18y agoThat's interesting. I'm not trying to hijack the thread here, but the non-standard scrolling in Scribd bugs me. When I use two-finger drag on the macbook pro to scroll, scribd just doesn't move like a normal page.
- dnaquin 18y agoYes! Bothered me as well.
- axod 18y agoIs scribd an improvement for windows users or something? It seems that for most people here it's an anoyance and a worse user experience than just linking to the pdf. Does it solve some problem I'm missing? edit: Try zooming all the way in. You're in for some hideously unreadable fuzzy font rendering... why oh why.
- whacked_new 18y agoHoly... Eliezer Yudkowsky? Why, hello...!
- technoguyrob 18y agoWowsers, that's a good point. I didn't know he's on YC, that's great.
- eyudkowsky 18y agoAw, shucks.
- xirium 18y agoFrom the article: The proper value, which does deserve all of the reverence and adulation bestowed upon the current imposter, is the number now unfortunately known as 2pi. Does this mean we can have 2pi day on Jun 28?