“How The Square Root Of 2 Became A Number”, Quanta (https://www.quantamagazine.org/how-the-square-root-of-2-became-a-number-20240621/).
On HN: https://news.ycombinator.com/item?id=40750230
#Numbers #IrrationalNumbers #Mathematics #Maths #PythagorasTheorem #Dedekind #Cantor #History #Reals #Irrationals
Pi, an irrational number. How can you create it with 2 rational numbers?
22/7
333/106
355/113
...
...
312689/99532
How many more are there?
1/5: "Man, I was trying to reason with pi the other day. Cloud't do it."
1/2: "Oh, you can't reason with pi."
1/5: "How come?"
1/2: "Pi is irrational."
#math #MathJoke #IrrationalNumbers #RationalNumbers #dadjoke #joke
In 1768, Johann Heinrich Lambert and Ferdinand von Lindemann proved that it is impossible to ”square the circle.” #Poetry #Science #History #Mathematics #Pi #IrrationalNumbers #Lambert #vonLindemann (https://sharpgiving.com/thebookofscience/items/p1768.html)
XD
But....now I wonder if there is such a thing as "finding an infinite non-repeating sequence in reverse" and if that applies to digits of irrational numbers!
Surely not right? XD
But...I mean it would still have an infinite number of digits, and never repeat..
And we think of "a circle of infinite radius" as a line, and other things as "at infinity looking back"...
dlfkjfldkfjdlfk *is* it possible?
Why π^π^π^π could be an #integer (for all we know!)
https://www.youtube.com/watch?v=BdHFLfv-ThQ&ab_channel=Stand-upMaths
#Pi #Maths #Math #Mathematics #Algebra #Fractions #IrrationalNumbers #TranscendentalNumbers #Computing #LargeNumbers #Computation #ComputingPower
A lovely post on Dirichlet’s approximation theorem, which allows you to approximate irrational number with rational numbers with small denominators with guarantees on how close the irrational number is the approximation.
https://www.quantamagazine.org/how-rational-math-catches-slippery-irrational-numbers-20200310/
#Mathematics #Numbers #RationalNumbers #IrrationalNumbers #NumericalApproximations
