More advanced slide rules typically have a set of “folded” scales, that can sometimes save a calculation from ending up off scale. In theory, these should be offset by half the scale length, i.e. sqrt(10). However, since the folded scales also offer a convenient way to multiply with the offset factor, most slide rules offset them by π instead, since it’s almost the same as sqrt(10), and multiplication by π is a more useful thing to have around.
My first thought was "well of course it is, since pi is a little larger than 3" but it was cool to see an actual derivation of how much pi squared differs from 10 as a nice, closed form series.
I remember discovering that pi x 10^7 is very close to the number of seconds in a year while at uni.
One of my tutors was convinced this had to be more than coincidence, but I always figured it was just chance and a nice but sometimes useful shortcut...
You might be able to send someone down an amusing (to observers) rabbit hole of wrongness by telling them it is not exact because Earth’s orbit is not perfectly circular.
It cannot be anything but coincidence. While 365.25 days in a year is physics, a day consisting of 86,400 seconds is an entirely arbitrary human construct.
I was a little disappointed that the upper range of gravity on earth only goes to 9.8337. Just a little more and there would have been somewhere on earth that was an exact match.
It would have been the ideal (if chilly) place to start a cult.
Millions of years from now, a far off alien race will discover the remnants of Earth, go through our maths knowledge, and they will slap their foreheads because we chose pi rather than tau.
More advanced slide rules typically have a set of “folded” scales, that can sometimes save a calculation from ending up off scale. In theory, these should be offset by half the scale length, i.e. sqrt(10). However, since the folded scales also offer a convenient way to multiply with the offset factor, most slide rules offset them by π instead, since it’s almost the same as sqrt(10), and multiplication by π is a more useful thing to have around.
I like the 4-5-6 theorem:
Well, to five decimal places, anyway. Some other good ones: There are also famous "almost integers" such as this one discovered by Ramanujan: Which is an integer to 12 decimal places.Edit: I just remembered I have public JupyterLite notebooks for both of these:
https://notebooks.oranlooney.com/lab/index.html?path=fake_ma...
https://notebooks.oranlooney.com/lab/index.html?path=heegner...
The second fact, pi^2 ~= g, is famous enough that it has a separate section in Wikipedia [1].
[1] https://en.wikipedia.org/wiki/Mathematical_coincidence#Gravi...
And https://xkcd.com/1047/
I don’t see pi^2 ~= g in there… did I miss it somewhere?
Also https://xkcd.com/217/
My first thought was "well of course it is, since pi is a little larger than 3" but it was cool to see an actual derivation of how much pi squared differs from 10 as a nice, closed form series.
I remember discovering that pi x 10^7 is very close to the number of seconds in a year while at uni.
One of my tutors was convinced this had to be more than coincidence, but I always figured it was just chance and a nice but sometimes useful shortcut...
You might be able to send someone down an amusing (to observers) rabbit hole of wrongness by telling them it is not exact because Earth’s orbit is not perfectly circular.
Hah, that would be hilarious
You're such an evil person :D
I always liked the fact that 10! (10 factorial) is exactly the number of seconds in six weeks.
It cannot be anything but coincidence. While 365.25 days in a year is physics, a day consisting of 86,400 seconds is an entirely arbitrary human construct.
Get enough numbers, accept wide error bars, and some of them are going to overlap.
This first became apparent to me when I got a slide rule. Pi is often marked on the various scales and an x^2 scale is often nearby the x scale.
at this rate, pi square is close to 'g'
pi^2 ~ 10, well known to anyone who used slide rules.
If you don't unblock scripts from cdn.jsdelivr.net.cdn.cloudflare.net, the math code won't work.
I was a little disappointed that the upper range of gravity on earth only goes to 9.8337. Just a little more and there would have been somewhere on earth that was an exact match.
It would have been the ideal (if chilly) place to start a cult.
need a countdown for when it gets there
As an ex-physicist, pi^2 is 10. Like g.
I get it that this is a nice calculation with the Zeta function and everything, but 3 and a small something squared will be near 10 so it is 10.
Pi^0 is exactly 1.
You could be on something there.
I also noticed that e^(i*pi) gives an integer exactly.
987654321 / 123456789 = 8 (to the 7th decimal place) is another nice one
The author wants tau=2*pi, but in the Greek alphabet, tau has one vertical stroke, and pi has two.
So, visually in Greek, pi=2*tau would seem an improvement.
Oh, well.
Tau is tau over 1, pi is tau over 2. See also https://www.tauday.com/tau-manifesto#sec-conflict_and_resist...
pi's prevalence instead of tau is one of the strongest indicators that we live in a suboptimal timeline.
Then, convert the digits of pi to text to find how to achieve interdimensional travel to reach the optimal timeline.
Millions of years from now, a far off alien race will discover the remnants of Earth, go through our maths knowledge, and they will slap their foreheads because we chose pi rather than tau.