Sequences converging to Phi and negative one over Phi. Both are the only solutions to the quadratic equation that Simon used earlier to prove that Phi is not a transcendental number.

# Tag Archives: pi

# Some more pictures of Simon’s everyday notes

Simon often drags his sketchbook to bed to “show me the beauty”, just before I would read a bedtime story to him and his sis. Last time he showed me a short proof of why there’re infinitely many primes. He assumed there were finitely many primes first… I think he learned that from James Grime:

Pi from Prime numbers:

Powers of 2:

# The irrationality of Pi and e

Simon has been watching a lot of Mathologer’s videos lately, mainly about Euler’s Number (e) and Pi. He is fascinated by the proofs Mathologer presented of why each number is irrational. “Mom, the proof that e is irrational actually doesn’t require any Calculus and the proof that Pi is irrational does! While you would expect it to be the other way around, right? Because e is about Calculus!”

Here are some of Simon’s notes, inspired by Mathologer. Some facts about e:

Notes about the proof that Pi is irrational:

Notes about the proof that e is irrational:

Simon watching the Mathologer channel:

# Calculating Pi by weighing circle and square

This experiment has been inspired by Matt Parker and his Stand Up Math channel.

As one of our Pi day activities, Simon attempted to calculate Pi by weighing a circle. In the video, you he first explains why this should work: the area of a circle with the radius r and the area of a square with a side of 2r can be expressed as Pi x r^2 and 4r^2 consecutively. This makes the ratio between the area of such a circle and the area of the square equal to Pi/4. In other words, Pi can be expressed as 4 times that ratio. But since both the circle and the square are made of the same material, their mass will also have the same ratio.

The result Simon got was pretty close, considering the low precision of our kitchen scales. As Simon’s math teacher correctly pointed out, the result would be much more precise if we had one thousand kids make their own circles and squares and weigh them, and then took the average of their outcomes.

# Calculating Pi with a Pendulum

This video has been inspired by the wonderful Matt Parker and his video on the Stand Up Math channel:

Yesterday was Pi day and we are still celebrating! Simon experiments with calculating Pi with a physical thing, a pendulum. For the experiment, he cut a cord one fourth of the local gravity value (9.8m/s^2), that is 245 cm. One full swing of the cord makes Pi (measured in seconds)! Simon measures the time the pendulum makes 10 swings and divides that number by 10, to get the average duration of a swing.

The values Simon got were pretty close! The closest he got (not in this video, but later that day) was 3,128 sec., which is exactly the same value that Matt Parker got! What is the chance of that?

The formula is t = 2Pi times square root of l over g (where l is the length of the cord and g the local gravity).

Starring the cute 3Blue1Brown Pi. Here is some extra footage, with the 3Blue1Brown Pi riding the pendulum:

# Happy Pi Day! Although a sad one this year due to Hawking’s death.

# Pi Day — Calculate pi in 3 ways (that I know of) · Issue #883 · CodingTrain/Rainbow-Topics · GitHub

Simon preparing for his favorite festive date tomorrow, Pi Day!! https://github.com/CodingTrain/Rainbow-Topics/issues/883

# Music of Pi in Processing

Simon wrote a program in Processing that plays the music of Pi. The idea to assign every integer a sound frequency belongs to the Numberphile channel, but Simon came up with the code. He plays the music for the first 41 digits of pi.

# Simon’s Function for Pi

Simon came up with a function that for bigger inputs approaches Pi. He has seen that the result of a function for infinity ∞ f(infinity) = Pi/4 in a Numberphile video and decided to express the same idea using χ (Chi).

# Infinite sum formulas

Simon writes:

Sorry the video was cut off, we’ve recorded this video from our phone, but the phone ran out of memory. Actually, if -1/4 = 3S, can you figure out what S is yourself?

Inspired by a Numberphile video, but Simon added the formulas himself.