Sungura wrote:But holy duck people that doesnt mean pi is wrong.
Yes it does! It's as bad as
(US) customary units and current going the wrong way.
Celebrate the 14th of March with baked goods all you like, but don't pretend it's that day specifically
that is related to a circle constant. Using the month number as the integer part and the day number as two decimal places? Ludicrous! Even Xanthir's suggestion is better (for people using the slash as a separator)!
Or like Vihart proposed in one of her pi day videos: celebrate every full turn (tau radians) of the Earth. Two pie every day!
Or maybe I misunderstood and she meant every turn around the Sun. In that case you get two pie every year, but the day on which it happens doesn't matter. Yes, it can be 03-14, but 06-28, 01-01 and your birthday (which is a pie day anyway) are equally valid. Hell, why not celebrate it four
times a year with half
a pie to demonstrate how silly π is.
Eebster the Great wrote:But now we have a factor of 2! Sometimes! Surely that's worth getting upset about. Now let me grab my calendar reform proposal and collection of infographics showing how dumb MDY dates are.
I shall be celebrating Pi Day on the 31st
of April, as I have done every year!
But March 14 is the better day because of ISO 8601.
Soupspoon wrote:He means that putting the digits 31415926… into YYYYMMDD hhmmss doesn't easily work.
Well just like we conveniently drop the year already and use month/day numbers that are really modulo 12/28/29/30/31 (rather than modulo 100) as digits, why not conveniently drop a leading zero in the month or day? A super pi day every century on __31-_4-15 _9:26:53
and super-mega-awesome pi day on 3141-_5-_9 _2:_6:53
While looking through the tau manifesto (again) I came across a long section about volumes of hyperballs
which left me very much unconvinced. The formulation with the gamma function ( π^(n/2) / Γ(n/2+1)
eq.14) is elegant and clearly extends to non-integer dimensions. However it leaves me puzzled as to what those n/2
s are doing there, let alone why
powers of π and Γ are showing up.
I liked the quadrant formulation ( 2^n * λ^⌊n/2⌋ / n!!
eq.28) with λ a quarter turn, but again, no (geometric) argument for the n/2
nor the double factorial.
Sweeping through a single quadrant in polar coordinates gives a nice looking integral ∫_0^λ ∫_0^λ ... (sin θ_n)^n*(sin θ_(n-1))^(n-1)*...*sin θ_1
. (Incidentally, today I learned what a Jacobian is, or at least what its determinant means.) However, the antiderivatives of (sin x)^n are horrible and their integrals are, of course, gamma functions with half-integers
Does anyone have a good explanation for why the volume (or surface) of an n-ball is the way it is?