I like the 4-5-6 theorem:<p><pre><code> pi^4 + pi^5 = e^6
</code></pre>
Well, to five decimal places, anyway. Some other good ones:<p><pre><code> e^pi - pi = 20
sqrt(2) ln pi = phi
</code></pre>
There are also famous "almost integers" such as this one discovered by Ramanujan:<p><pre><code> e^(pi sqrt(163))
</code></pre>
Which is is almost an integer to 12 decimal places.
at this rate, pi square is close to 'g'
The second fact, pi^2 ~= g, is famous enough that it has a separate section in Wikipedia [1].<p>[1] <a href="https://en.wikipedia.org/wiki/Mathematical_coincidence#Gravitational_acceleration" rel="nofollow">https://en.wikipedia.org/wiki/Mathematical_coincidence#Gravi...</a>
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.<p>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.
Get enough numbers, accept wide error bars, and some of them are going to overlap.
pi^2 ~ 10, well known to anyone who used slide rules.
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.
987654321 / 123456789 = 8 (to the 7th decimal place) is another nice one
If you don't unblock scripts from cdn.jsdelivr.net.cdn.cloudflare.net, the math code won't work.
need a countdown for when it gets there
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.<p>It would have been the ideal (if chilly) place to start a cult.
Pi^0 is exactly 1.
As an ex-physicist, pi^2 is 10. Like g.<p>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.
The author wants tau=2*pi, but in the Greek alphabet, tau has one vertical stroke, and pi has two.<p>So, visually in Greek, pi=2*tau would seem an improvement.<p>Oh, well.
Tau is tau over 1, pi is tau over 2. See also <a href="https://www.tauday.com/tau-manifesto#sec-conflict_and_resistance" rel="nofollow">https://www.tauday.com/tau-manifesto#sec-conflict_and_resist...</a>
pi's prevalence instead of tau is one of the strongest indicators that we live in a suboptimal 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.
Then, convert the digits of pi to text to find how to achieve interdimensional travel to reach the optimal timeline.