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
Simon believes that he has found a mistake in one of the installations at the Technopolis science museum. Or at least that the background description of the exhibit lacks a crucial piece of info. The exhibit that allows to simultaneously roll three equal-weight balls down three differently shaped tracks, with the start and the end at identical height in all the three tracks, supposes that the ball in the steepest track reaches the end the quickest. The explanation on the exhibit says that it is because that ball accelerates the most. Simon has noticed, however, that the middle track highly resembles a cycloid and says a cycloid is known to be the fastest descent, also called the Brachistochrone Curve in mathematics and physics.
In Simon’s own words:
You need the track to be steep, because then it will accelerate more – that’s right. But it also has to be quite a short track, otherwise it takes long to get from A to B – which is not in the explanation. It’s not the steepest track, it’s the balance between the shortest track and the steepest track.
Galileo Galilei thought that it is the arc of a circle. But then, Johan Bernoulli took over, and proved that the cycloid is the fastest.
We’ve also made some slow motion footage of us using the exhibit (you can see that the cycloid is slightly faster, but as far as I can tell, it’s not precision-made, so it wasn’t the fastest track every time): https://www.youtube.com/watch?v=5Brub0FnpmQ
I hope that you could mention the brachistochrone/ cycloid in your exhibit explanation. I don’t think you can include the proof, because for such a general audience, it can’t fit on a single postcard!
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.
Caught Simon’s reaction to Wednesday’s breaking news on video: the first-ever image of a black hole published, made by the Event Horizon Telescope project team. Simon explains why, if you stood next to the black hole, you would be able to see the back of your own head.
Simon loved this video by Veritasium about how the image of the black hole was made (he had watched this one day prior to the actual publication of the black hole image).
Yesterday, wee also watched this beautiful TEDx contribution by Katie Bouman (one of the leading figures behind the algorithm that helped stitch the M87 black hole image data together). The video is from three years ago, when the project was just getting started. Katie is such an inspiration: a computer scientist helping astrophysicists!
We have tried using an LED backwards: not get it to shine by letting an electric current pass through it but produce electricity by shining light on an LED (this is how solar panels work). It’s important to use a sensitive LED for this experiment, and as we have observed, it also seems to be important to use light photons of the same frequency as the colour of the LED (red laser didn’t work on a white LED, but it may have to do with the fact that red light is weaker than white light anyway, i.e. has a lower frequency). The picture below shows us measuring the voltage of the current produced by the LED.
We’ve have learned this and a a lot more from Steve Mould’s video on How diodes, LEDs and solar panels work: Photovoltaic cells and LEDs are both made of diodes. Diodes are designed to allow electricity to flow in one direction only but the way we make them (out of semiconductors) means that can absorb and emit light.
In the video, Steve shows how the semiconductor atoms share elctrons. Semiconductors are crystal structures of atoms are replaced by the atoms of neighboring elements, for example a structure where some silicon (Si) atoms are replaced by phosphorus (P) or boron (B) atoms, thus providing for free electrons inside the structure (N-type conductor) or for free “holes” unoccupied by electrons (P-type conductor). A diode is basically two semiconductors pushed together. With enough voltage, the electrones are able to jump from the N-type semiconductor across the depletion zone and into the P-type semiconductor, emitting light (photons) as they fill the holes and go from a high energy state into the low energy state.
If you shine a light at a diode, you can kick some electrons from their shells and thus create free electrons and holes that will move (because of the electric field in the depletion zone) and generate voltage.
Simon showed us this amazing hing with a fidget spinner. It’s called stroboscopic effect. It’s a visual phenomenon that occurs when continuous motion is represented by a series of short or instantaneous samples (like camera shots), distinct from a continuous view.
In the video below, Simon also demonstrates the rolling shutter effect with the same fidget spinner and camera.
Mesmerised by the 3D printed gears on Numberphile: “If you move two of these, the third one appears to be hovering in mid-air!”, Simon made a similar construction of his own – 6 straws forming 3 gears.
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.