Simon’s self-made Onitama game set, real fun to play.
Simon has been pondering a lot about various ways to visualize or prove the quadratic formula.
He eventually came up with a 4-meter-long quiz sheet, slowly revealing the logic behind the quadratic formula as one solves the 9 problems one by one. Simon borrowed the actual problems from Brilliant.org but reworded some of them to match his personal style, writing all of them down in his beautiful handwriting on large sheets of paper taped together to form a road to the quadratic formula. The answers were hidden under crafty paper flaps. We had a lot of fun traveling down this rabbit hole as a family, Neva stuck around solving the tasks until half-way through.
Simon learned this from an alternating series visualization by Think Twice.
I want to mess with the Periodic Table to see what arrangements I can put it in.
This is called the Wide Arrangement. There are aso a few other arrangements, like the Left Step Wide (or Loop) arrangement, various 3D arrangements (like the ones where you make sure any consecutive numbers are next to each other and it looks like a layered cake).
Although it would be even nicer if we moved H and He over there where they obviously belong.
Simon learned this from a Minute Physics video.
Simon had a wonderful time at MathsJam Antwerp again. One of the problems was something he was already familiar with – the puzzle about hanging a painting using two pegs so that it would definitely fall if one removes any of the two pegs. He explained the way to solve this problem in an abstract way (turning pegs into strings, using knot theory and compiling the algorithm). Later the same evening, he developed a new algorithm to solve the same problem for three pegs and successfully demonstrated the result on his own shoe laces. His solution was the most efficient/ elegant in the group and his enthusiasm was very catchy, the audience said.
In the video below, Simon at first fails to apply his solution correctly, but succeeds upon the second attempt:
Inspired by the Card Flipping Proof by Numberphile, Simon created his own version of this proof. He made a solitaire game and proved why it would be impossible to solve with an even number of orange-side-up circles. He drew all the shapes in Microsoft Paint, printed them out and spent something like two hours cutting them out, but it was worth it!
If there’s an odd number of orange circles in the middle, then the end pieces are the same, both orange or both white. In both cases the total number of orange circles will also be odd. If there’s an even number of orange circles in the middle, then the ends have to be different (one orange, one white).
In the case of odd number of orange pieces, the ends have to match. In the case of an even number of orange pieces, you would have pieces that point the same way at both ends. “Now we’ve proven that to make this puzzle possible it has to have an odd number of orange pieces”, Simon says.
Why? Imagine a stick figure that always walks to the right, but always faces in the direction of the arrow (as in it can’t go backwards). It would flip every time it reaches an orange circle. Focusing on everything except the ends, if there are an odd number of orange circles, the puzzle pieces would face the other way. Which means that the end pieces are the same, and therefore the end circles are the same. If there are an even number of orange circles in the middle, the puzzle pieces would face the same way. Which means that the end pieces are different, and therefore the end circles are different.
Simon finds this sort of proof easy, but I felt like my brains are going to boil and dripple through my ears and nostrils. He patently exlained it to me several times and types the above explanation, too.