re: pi day given that pi is a famous attractor for maths cranks i was wondering if there's ever been someone who took the observation that the square root of ten is surprisingly close to pi and decided to insist this must be literally exactly true. There's ancient texts using that value for pi, but I wouldn't count those as being cranks; that would require them to insist on that past widespread agreement by the mathematical community that it's wrong
the best example i've found so far is jospeh scaliger, a non-mathematician that claimed to prove that the square of the circumference of the circle is ten times the square of the diameter, which if true would mean Ď²=10. however, the same source also has him proposing a method of squaring the circle that implies Ď=sqrt(3)*9/5 (apparently he squares this disagreement because he thinks the classic formula for the area of a circle of Ďr² is wrong).
i think this counts, surely 'the ratio of the circumference to the diameter' is the more central definition of pi, but it seems theoretically possible the guy was bad enough at following the mathematical implications of his claims that he would not agree that Ď=sqrt(10) despite believing something obviously mathematically equivalent. and i can't read latin so i can't go through the relevant text and see how close he comes to literally saying so.
so now i'm curious if there's more examples of people insisting that Ď=sqrt(10)
close? that's off by over 0.02!
which is less than 0.7% relative error! pretty close
22/7 is closer!
yeah infinitely many numbers are closer, that's how the reals work
i didn't say "sqrt(10) is the most convenient approximation of pi using common operations and small numbers", i just said it's surprisingly close. implicitly, close enough to attract maths cranks, which, have you seen the sort of values "pi isn't actually transcendental" cranks have argued? the indiana pi bill went for 3.2
I think 22/7 makes a pretty good benchmark for "close to pi". like, you gotta at least get the 3.14 part right
"close to pi" criteria: any number N where 3.14 ⤠N < 3.145
you're going to break matt parker's heart :(
Fun fact: Ď = sqrt(g) (as in 9.81) was the original definition of the meter! If it's good enough for French people who wanted to adapt an old standard to modern times, it should be good enough for "close enough as a quick estimate" I feel.
22/7 is actually the closest you can get in 4 characters or less so I don't think "closer than 22/7" is achievable (plus, â10 is way more convenient to write than 22/7 so I'm not surprised it's worse)
â31 â 3.1414






















