The proof is not that ancient. Pi was proven to be irrational in 1761, and proven to be transcendental in 1882.
For a long time the problem was known as “squaring the circle”: Given a circle in a plane, construct a square with the same area using a compass and straightedge. This was a famous unsolved problem in mathematics from antiquity all the way through the renaissance.
A slight clarification in return: the constructible numbers are a strict subset of the algebraic (i.e. non-transcendental) real numbers.
(The constructible numbers are those numbers resulting from the closure of the rational numbers under square roots.)
This means that although the proof of pi’s transcendentality proved that squaring the circle is impossible, it could have been the case that pi was neither transcendental nor constructible. A simple example of such a number is the cube root of 2.
Oh sure, but in 6 years someone at a dinner party is gonna say “did you know there is no 6 in π” because they read my comment. At that moment my life’s purpose will be fulfilled.
Could anyone explain this joke plz?
π has an infinite amount of decimals.
So does every number:
6.000000…
We asume
Nope, the proof has been known since ancient times!
Thanks for the info :)
The proof is not that ancient. Pi was proven to be irrational in 1761, and proven to be transcendental in 1882.
For a long time the problem was known as “squaring the circle”: Given a circle in a plane, construct a square with the same area using a compass and straightedge. This was a famous unsolved problem in mathematics from antiquity all the way through the renaissance.
Thanks for the correction - misremembered that.
A slight clarification in return: the constructible numbers are a strict subset of the algebraic (i.e. non-transcendental) real numbers.
(The constructible numbers are those numbers resulting from the closure of the rational numbers under square roots.)
This means that although the proof of pi’s transcendentality proved that squaring the circle is impossible, it could have been the case that pi was neither transcendental nor constructible. A simple example of such a number is the cube root of 2.
There is no 6 in π
3.1415926… there is 6 in pi, I believe the joke is that it’s an irrational number so the line never stops
Oh sure, but in 6 years someone at a dinner party is gonna say “did you know there is no 6 in π” because they read my comment. At that moment my life’s purpose will be fulfilled.
Mischief managed.
I look forward to seeing that fact in an AI overview on google
Why you wanna make me blush?
3.1415926… there is 6 in pi, I believe the joke is that it’s an irrational number so the line never stops