Tom Rocks Maths intern Isaac Wood introduces the most amazing formula for pi - involving prime numbers and multiples of 4 - and shows you how to prove it.
The proof is broken down into several steps. We begin by proving 'Mini Result 1' which gives the sum of an infinite geometric series. Next, we prove a result about the infinite limit of a sum of powers - this is 'Mini Result 2'. We then set up the geometry of the problem and using results about similar triangles and Pythagoras' Theorem, obtain a formula for the approximation of the arc length which is equal to pi divided by 4. This is known as the 'Leibniz Formula for Pi'. Finally, using prime numbers and the fundamental theorem of arithmetic, we deduce the amazing result: Pi divided by four is equal to the product of each prime number divided by its closest multiple of 4.
Timestamps for individual sections:
Mini Result 1: 0:40
Mini Result 2: 2:24
Leibniz Pi Formula: 7:59
Final Proof: 17:01
Produced by Isaac Wood with assistance from Dr Tom Crawford at the University of Oxford.
Isaac is a second year undergraduate student at the University of Cambridge studying Mathematics. Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall: www.seh.ox.ac....
For more maths content check out Tom's website tomrocksmaths....
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
/ tomrocksmaths
/ tomrocksmaths
/ tomrocksmaths
Get your Tom Rocks Maths merchandise here:
beautifulequat...
Негізгі бет Amazing Pi Formula - Prime Numbers and Multiples of 4
Пікірлер: 54