The Pi You Know Is A Lie

http://www.scribd.com/vacuum?url=http://www.math.utah.edu/~palais/pi.pdf

by eyudkowsky • 18 years ago

60 29 18 years ago

aston• 18 years ago

Yeah man. I love this paper. All of the equations look so much prettier without 2 in front of pi everywhere.

mhartl2• 18 years ago

I 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• 18 years ago

How are you defining diameter? http://mathworld.wolfram.com/Diameter.html only defines it for circular and spherical objects.

mhartl2• 18 years ago

http://en.wikipedia.org/wiki/Curve_of_constant_width

pc• 18 years ago

PDF: http://www.math.utah.edu/~palais/pi.pdf

eyudkowsky2• 18 years ago

That's what I entered, but it came out on Scribd!

0x44• 18 years ago

http://news.ycombinator.com/item?id=179721

dnaquin2• 18 years ago

Volume 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• 18 years ago

Almost as bad as negatively charged electrons.

aneesh• 18 years ago

I 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• 18 years ago

The author knows this, and was making a merely aesthetic point which you seem to have sucked all the fun out of.

dhbradshaw• 18 years ago

I think the aesthetics are important. You can see further when they are better.

lvecsey• 18 years ago

The three legged symbol is pretty good, but maybe papers could just set the value of pi at the introduction.

tlrobinson• 18 years ago

Indiana once tried to pass a law saying pi actually equals 3.2

http://www.straightdope.com/classics/a3_341.html

gills• 18 years ago

That'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.

dnaquin2• 18 years ago

Yes! Bothered me as well.

axod• 18 years ago

Is 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.

eru• 18 years ago

It does not seem to improve matters on my Ubuntu, either.

volida• 18 years ago

it's not rendering a font, it's a non-vector image, stored with bad comrpession, therefore it will get blur if you zoom it.

astine• 18 years ago

Only guessing here, I think that it solves a copyright issue.

whacked_new• 18 years ago

Holy... Eliezer Yudkowsky? Why, hello...!

technoguyrob• 18 years ago

Wowsers, that's a good point. I didn't know he's on YC, that's great.

eyudkowsky2• 18 years ago

Aw, shucks.

xirium• 18 years ago

From 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?

The Pi You Know Is A Lie

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