This blog is about Simon, a young gifted mathematician and programmer, who had to move from Amsterdam to Antwerp to be able to study at the level that fits his talent, i.e. homeschool. Visit https://simontiger.com
When we arrived at the MathsJam last Tuesday, we heard a couple of people speak Russian. One of them turned out to be a well known Russian puzzle inventor Vladimir Krasnoukhov, who presented us with one colorful puzzle after another, seemingly producing them out of thin air. What a feast! Simon got extremely excited about several puzzles, especially one elegant three-piece figure (that turned out to have no possible solution, and that’s what Simon found particularly appealing) and a cube that required graph theory to solve it (Simon has tried solving the latter in Wolfram Mathematica after we got home, but hasn’t succeeded so far).
Vladimir told us he had been making puzzles for over 30 years and had more than 4 thousand puzzles at home. Humble and electricized with childlike enthusiasm, he explained every puzzle he gave to Simon, but without imposing questions or overbearing instructions. He didn’t even want a thank-you for all his generosity!
Vladimir also gave us two issues of the Russian kids science magazine Kvantik, with his articles published in them. One of the articles was an April fools joke about trying to construct a Penrose impossible triangle and asked to spot the step where the mistake was hidden:
Simon was very enthusiastic about trying to actually physically follow the steps, even though he realized it would get impossible at some point:
Simon loved our Easter weekend in Friesland, canoeing and taking boat rides together with his grandparents. He also did some experimenting with the splashing waves and learned how to use the waves to tell the Beaufort scale.
Today we have made beautiful rainbow chrystals! Polarized light iridizes sodium thiosulfate crystals, so we made the crystals in between two polarizing films and then observed them through the microscope. In the video, Simon also explains how polarizing film works.
From the scientific description at the MEL Science website: Sodium thiosulfate crystals contain five molecules of water per one unit of sodium thiosulfate Na2S2O3. Interestingly, when heated, the crystals release the water, while sodium thiosulfate dissolves in this water. This solution solidifies rapidly when cooling, forming beautiful crystals. If these crystals are put between polarizing films, they take on an iridescent sheen. This is because the polarizing films only let light with certain characteristics through, and this light in turn “iridizes” the otherwise-colorless sodium thiosulfate crystals.
We have wanted to do the Double-Slit experiment for a long time. Finally, last Friday, armed with a suitable box, we ventured outside. To our common disappointment, light just wouldn’t behave as a wave this time, even though we had no detectors to check which slit the photons actually passed through. What we observed inside the box looked like two perfect stripes. No interference.
Experiment failure aside, we were in for a pleasant surprise, too: the box suddenly turned into a huge camera obscura! This is a picture of me and the blue sky as seen from inside the box!
When we got home, and tried to look inside the box again in the dimmer light in the living room, we were finally rewarded with this beautiful interference pattern:
We can only guess why it didn’t work outside. The wrong angle of the light beams (the sun being high in the sky above our heads)? Or maybe the light wat too bright, too many photons got in? The slits being too wide? We’ll be repeating this experiment for sure.
This demo is inspired by a recent video on Steve Mould’s channel. It’s about creating a movable hole in soap film with a loop of cotton thread (the photo shows Simon sticking a pencil through such a hole). Once in the soap membrane, the cotton thread forms a perfect circle. It’s because the soap film tries to minimise its area and compress as much as it can. The only way that can happen is to maximise the area of the hole. And as we know, with a fixed perimeter, the biggest area that you can make with it is if you form that perimeter into a circle, Simon explains as I’m writing this.
Here is a fun math trick! Simon and Neva have made a 8 x 8 cm square (with an area of 64 cm²) and cut it into four pieces, turning the square into a puzzle. Using the same four pieces, they built a 5 x 13 cm rectangle. But wait a minute! 5 x 13 equals 65, so the area of the rectangle is one cm² larger than that of the square!
They also made a similar puzzle using bigger pieces. A 13 x 13 = 169 cm² square turned into a 8 x 21 = 168 cm² rectangle! So now the area of the rectangle is one cm² smaller than that of the square! What’s gong on?
You have probably recognized the numbers in this trick: 5, 8, 13, 21… Those are Fibonacci numbers! Simon explains, that with Fibonacci numbers, the effect of the rectangle area being greater or smaller than the square area is alternating. Fibonacci have a converging ration to φ (Phi), but not φ. The pieces only look like they are golden ratio bigger/ smaller. In reality, there is a little gap between the pieces in the first rectangle and a little overlap in the second.
Simon has been inspired by Mathologer to build this.
Just like last year, Pi Day activities are going to spill over to the next few days, I’m sure. Simon’s not yet done working on a Pi piano composition and there’s a Pi day MathsJam coming up! What you see above are some impressions of today, March 14, including Simon trying to approximate Pi the way ancient Greeks (Archimedes) did.