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Andrzej Kukla
1K posts
Andrzej Kukla
@Mathinity_
Recreational mathematician. Doing math for the plot ✦
Kraków, Poland Inscrit le Ekim 2020
235 Abonnements9.9K Abonnés
Continue celebrating π-day with this fun little integral! 🥳❤️ have fun!
π-day never ends.
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@INSPECTOLNZ Ok, then my proof must be wrong. Can you point in which point it doesn’t hold?
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@Mathinity_ Even a smaller value of actual «π»=π⁷⁶² is defined exactly:
0.999999(∞) is a fraction ¹/₁
This is why π is rational.
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Happy π-day! 🥳
To celebrate this day I’ve decided to show you how to prove the irrationality of π!
What is your favourite thing related to π? 🤔
Meanwhile, have a nice read!
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Andrzej Kukla retweeté
Simple!
Apery’s proof that ζ(3) is irrational can be modified to show that ζ(2)=π²/6 is irrational, by constructing sequences of integers Aₙ and Bₙ
0 ≠ ζ(2)-Aₙ/Bₙ = ο(1/Bₙ)
from which it follows that π² is irrational and hence π is irrational.
Andrzej Kukla@Mathinity_
Happy π-day! 🥳 To celebrate this day I’ve decided to show you how to prove the irrationality of π! What is your favourite thing related to π? 🤔 Meanwhile, have a nice read! 🧵[1/8]
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This Fibonacci sum identity embraces what I love about mathematics – it’s simple enough for everyone to understand it and it has A LOT of different proofs. But I bet you don’t know the proof I shared here. Enjoy! 🥹
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That got me thinking… can we prove it?
Anthony Bonato@Anthony_Bonato
“The vast majority of mathematics remains undiscovered.” This is commonly known thing, right?
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Andrzej Kukla retweeté
every known prime number is of the form n.
MathMatize Memes@MathMatize
Every known prime number more than 3 is of the type 2n±1.
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Late night snack (integral) delivered right to your door (notebook). Have fun! 🌒✨
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Charles Hermite – patron of all the things I love in mathematics: Number Theory and Floor function.
Maybe he didn’t find this identity, but he surely generalized it! I used his identity in one of my articles, so I basically owe him my whole life. Thanks Charles!
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