What a blissful atmosphere at Maths Jam Antwerp yesterday, full of respect, encouragement and acceptance. It’s an international monthly meet-up taking place every second to last Tuesday of the month, simultaneously at many locations in the world, three hours of maths fun! This was Simon’s first time. He solved two difficult geometry problems and showed some of his current work to the math enthusiasts who attended. Was hopping and giggling all the way home.
Simon has crafted his own tiny slide rule that he carries around rolled up in an elastic band and calls his “toy”. The two strips of paper aligned together in certain ways can give answers to multiplication and division problems. Simon distributed the numbers on them according to a logarithmic scale.
Simon and Neva make a 3D projection of a Hypertetrahedron – one of the regular solids in 4D – using straws. Simon looks up the formula for the center of the tetrahedron (radius of its circumscribed sphere) to measure the sides of the inside straws. To cut the exact length of the inside straws, he constructs a segment with the length of square root of six, divides it by 4 and multiplies the result by the original length of the straws.
Please also see our next and even cooler project – a 3D projection of a Hyperoctahedron:
The Hyperoctahedron came out to look very nice and four-dimensional. “It lands on the floor very nicely”, Simon says throwing it around – it is a very stable shape, made up of 16 tetrahedrons. Simon had to work out the centre of the triangle for this projection, which is easy to do for equilateral triangles.
The making of the Hyperoctahedron:
Measuring the center of the equilateral triangle:
Cutting the straws so that their length equals the distance between the vertex and the centre of the triangle:
The Hyperoctahedron is ready:
“I’m holding a four-dimensional shape in my hands!”
And Simon learned that a Mobius ring is a knot, too.
Inspired by the videos by Matt Parker
and James Grime:
Simon also made the Borromean rings:
And cubes (which Simon now uses to practice juggling!)
Simon has developed his version of the Magic Cards, this time in Base 3. He invented this system completely on his own and actually created a program in Processing (Java), using ternary function, to make the cards! The the code for creating the five cards in Processing and exporting the images as png files is available on Simon’s page on GitHub: https://github.com/simon-tiger/browns-criterion-base3
To play the game, have someone think of a number between 0 and 242 and let that person look for his/her number on every card and tell you which colour it is on every card. Every card stands for a power of 3: 81, 27, 9, 3, and 1. There are three grids of numbers on every card, a blue grid (representing the zeros in base 3), a red grid (representing the ones in base 3), and a green grid (representing the twos in base 3). After your friend has found his/her number on all the five cards, you can go ahead and add all the results up to guess the number. Alternatively, if you find working with base 3 too difficult, just sum up all the red numbers in the top left corners (on all the cards where your friend’s number was red), then double all the red numbers in the top left corners (on all the cards where your friend’s number was green) and add all of those together to guess the number.
Simon started out by actually trying to draw the magic cards:
But quickly realised he’s better off writing a computer program to fill in the grids. When the program (pretty tough to write) was finally ready, he tried to print a card out and… ran out of ink on our home printer. Next, we rushed to the print shop, as it was about to close.
“Mom, I can calculate why it says 17 million colours! It’s 256 cubed!” (255 for Red, Green and Blue plus one for alpha).
Simon previously developed a magic card system for Prime Numbers and wrote a Java program that guessed the numbers using powers of two.
Simon showing math magic tricks at Easter celebrations with extended family and Dad’s colleagues:
Here is another interesting puzzle Simon learned from the SingingBanana math channel, about two drugs undergoing testing in the course of two days. The fish drug cured 63 out of 90 people (70%) on the first day and 4 out of 10 people (40%) on the second day. The second drug cured 8 out of 10 people (80%) on the first day and 45 out of 90 people (50%) on the second day. Which drug is more efficient?