More Numberphile-inspired stuff! 

More Numberphile-inspired stuff! Simon has been studying Mersenne Primes (2^n – 1) and their relation to perfect numbers via the Numberphile channel and heard Matt Parker say no one has proved that there are no odd perfect numbers (that perfect numbers are always even). In the video below, Simon tries to prove why all perfect numbers are even. Here is Simon’s proof: When calculating the factors of a perfect number you start at 1 and you keep doubling, but when you reach one above a Mersenne prime, you switch to the Mersenne prime, and then keep doubling again. Once you double 1, you get 2, so 2 is ALWAYS a factor of any perfect number, which makes them all even (by definition, an even number is one divisible by 2):

 

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More topics Simon learned about from the Numberphile channel included:

The Stern-Brochot Sequence:

Stern-Brochot Sequence 16 Jan 2018

Prime Factors:

Prime Factors 16 Jan 2018

Checking Mersenne Primes using the Lucas-Lehmer Sequence. Simon’s destop could only calculate this far:

Checking Mersenne Primes 16 Jan 2018

The 10958 problem. Natural numbers from 0 to 11111 are written in terms of 1 to 9 in two different ways. The first one in increasing order of 1
to 9, and the second one in decreasing order. This is done by using the operations of addition, multiplication, subtraction, potentiation,
and division. In both the situations there are no missing numbers, except one, i.e., 10958 in the increasing case (Source). The foto below comes from the source paper, not typed by Simon, but is something he studied carefully:

10958 Problem 17 Jan 2018

Simon’s notes on the 10958 problem:

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The Magic Square (adding up the numbers on the sides, diagonals or corners always results in the number you picked; works for numbers between 21 and 65):

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Simon also got his little sis interested in the Magic Suare:

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And, of course, the Square-Sum problem, that we’ve already talked about in the previous post.

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Simon’s 3D version of the Square-Sum problem:

Square-Sum Problem 3D 17 Jan 2018

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The Square-Sum Problem

Simon has become a full-blown Numberphile fan over the past couple of days. He had already watched two Matt Parker videos before, but it’s this week that he got seriously hooked on the channel, and it all started from the Square-Sum Problem video!

Simon recorded and edited two videos of his own (in OBS) trying to solve the Square-Sum Problem, manually and using JavaScript code:

 

 

Live Stream #6. (Mostly) Chapter 2 of Living Code: Forces.

Simon’s latest live stream on Thursday, January 11 was a blast! For the first time in his programming career he actually had quite a few viewers – largely thanks to Daniel Shiffman, who posted an announcement about Simon’s live session in his Twitter:

During the session, Simon recorded 6 tutorials:

  • a bonus video about vectors,
  • a video about forces in general,
  • a video about mass,
  • a video about the Friction Force,
  • a video about Air Resistance
  • and a video about Gravitational Attraction.

All as part of his “Living Code” Course. The lessons in the course are loosely based on Daniel Shiffman’s book “The Nature of Code“, but focus on JavaScript.

Simon was worried in the beginning, because he had forgotten to prepare for the stream and had no choice but do the theory (on physical forces) on the fly. It was wonderful to see how the competent viewers gave him a helping hand every now and then and generally encouraged him in the live chat. He even got a real Q&A session in the end, something he had always dreamed of:

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Magic around New Year’s Eve

This magical time of the year, Simon’s craziest, most daring dreams come true! First, his guru from the New York University Daniel Shiffman sends Simon his book and the words he writes there are the most beautiful words anyone has ever told him. Then, on the last day of the awesome year 2017, Simon’s other hero, the glamorous knight of AI Siraj Raval materialises in our living room, directly from YouTube! Happy New Year full of miracles and discoveries everyone!

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Daniel Shiffman’s book “The Nature of Code” that Simon had already largely read online and now also reads before bed. It also comforted him recently when he was in pain, he cuddled up of the sofa with this big friendly tome on his lap.

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Daniel Shiffman signed the book for Simon:

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Siraj Raval stepped out of the YouTube screen straight into our Antwerp apartment on December 31. Simon has been following Siraj’s channel for months, learning about the types of neural networks and the math behind machine learning. It is thanks to Siraj’s explanations that Simon has been able to build his first neural nets :

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Stardust

Looking at the Moon and the Orion nebula from a roof top together with a true friend

The telescopes were brought to the panorama floor of the museum “het MAS” by the Urania observatory staff and volunteers, including Robert Matheus – a very special someone who has already done so much for us in the past.

Simon into Simon’s eyes, is it like a mirror reflected by a mirror? (Simon’s best friend is also called Simon).

Simon writes CodePen blog on for-loops

Simon has authored a comprehensive post about For-Loops (in JavaScript ES5 and ES6) in the CodePen blog, nice for anyone learning about loops syntax:

https://codepen.io/simontiger/post/for-loops

Simon’s update: I now also have a post about While-Loops: https://codepen.io/simontiger/post/while-loops

Simon’s Fibonacci function and Fibonacci counter in p5.js

Simon came up with this Fibonacci function while taking a walk downtown:

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f(0) = 0

f(1) = 1

f(n) = f(n-1)+f(n-2)

When we got home, he used the function to build a Fibonacci counter in p5.js:

You can play with Simon’s Fibonacci counter online at: https://alpha.editor.p5js.org/simontiger/sketches/Skhr3o8Gf

The idea about the Fibonacci function struck Simon when he was looking down at the cobbles under his feet. “Look, Mom! It’s a golden rectangle!”, he shouted:

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He had read that golden ratio has a direct connection to the Fibonacci sequence. The same evening, he took out his compasses to draw a golden rectangle (this time not his own invention, but following the steps from his Murderous Math book):

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If you turn the page, the smaller rectangle is a golden rectangle as well, and if you slice a square off of it, the remaining rectangle will also have the golden proportions. You can continue doing this infinitely. The sizes of the rectangles will exactly correspond to the numbers in the Fibonacci sequence, which makes these drawings an illustration to the sequence.

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The next day, Simon showed his function to his math teacher. Below are the Fibonacci sequence numbers he got through his selfmade JavaScript program. After a certain number, the computer started taking too long to compute the following number in the sequence (several seconds per number), but didn’t crash.

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Tetris in Processing continued

Inspired by a Meth Meth Method Tetris video, Simon has come back to his Tetris project in Processing, something he started a long while ago and never finished. At the moment, the primary difficulty he experiences is having the pieces accumulate at the bottom of the grid and not vanish immediately once hit by other pieces. Work in progress.