On Tuesday (two days late for Pi Day), Veritasium posted the video below about calculations of Pi, from the days of Archimedes to the present. Some methods of calculation and approximation can be done on pen and paper, but like many things in mathmatics, massive breakthroughs were purely 20th century solutions made possible by computers.
“How I wish I could calculate Pi.”
3 . 1 4 1 5 9 2
How have I never heard that before tonight?
Cute mnemonic for pi! There are plenty of others, of course. The one I like is How I want a drink? Alcoholic, of course, after the heavy chapters involving quantum mechanics.
The mnemonic I remember is actually rather poetic, and also longer than many:
Now I, even I, would celebrate in rhymes unapt the great
Immortal Syracusan, rivaled nevermore
Who in his wond’rous lore, passed on before
Made the way straight, how to circles mensurate.
There’s a version of this on the Wikipedia Piphilology page, though the first half of the last line uses different words. This is the one I learned, and it rhymes better.
IIRC some mathematician persuaded his father to calculate pi to several hundred thousand decimal places. I had not realized that mathematicians were that sadistic.
Science Friday reports that James Grime of Numberphile claims we only need 39 digits of Pi to calculate the circumference of the galaxy.
3.14159265358979323846264338327950288420
And I’ve read (can’t cite a source) that only eight digits of Pi were necessary for building the 27km circumference of the Large Hadron Collider at CERN in Switzerland.
The 39 digits is to calculate “the circumference of the known universe to the width of a hydrogen atom”.
The diameter d of the observable universe is about 8.8×10^26 metres (93 billion light years), and the hydrogen atom is 5.3×10^(-11) m across, so the universe is 1.7×10^37 hydrogen widths across, and its circumference is about 5.3×10^37 hydrogen widths.
So yeah, we could know the circumference to the width of an H atom with 39 digits of π, but only if we also knew the diameter to 39 digits. Which I’m pretty sure we don’t know.
@3, “[S]ome mathematician persuaded his father to calculate pi to several hundred thousand decimal places”.
Whilst I have a vaguely-similar recollection, according to Ye Pffft! of All Knowledge, the most digits ever calculated by hand is 620 (1946, DF Ferguson). Since then, calculators (Ferguson holds several records here also) or computers have been used. Broadly, no-one has ever calculated π to “several hundred thousand decimal places” without using a computer. Whatever it is we(? I?) believe we are remembering, that ain’t it.
3.14 still works for me.
@ 5 blf
Blast it, there goes another mathematical urban legend. Could it be we are remembering Kerrich and the Law of Large Numbers ? It’s only 10,000 coin flips but still impressive.
That works if you can remember how to spell calcuelate. though i suppose being off by 0.00001 won’t affect anything i actually do 😛