And it turned out to be a that little path next to the Royal Observatory in Greenwich, not the Prime Meridian line. The 0° meridian is what the GPS uses for global navigation, the discrepancy results from the fact that the Prime Meridian was originally measured without taking it into consideration that the Earth isn’t a perfect smooth ball (if the measurements are made inside the UK, as it it was originally done, this does’t lead to as much discrepancy as when vaster areas are included).
Hilarious, inspirational and loaded with cosmic coincidences, this was one of the best evenings ever! Many of our currently favourite themes were mentioned in the show (such as the controversy of Francis Galton, the BED/ Banana Equivalent Dose, sound wave visualizations, laser, drawing and playing with ellipses, Euler’s formula). Plus Simon got to meet his teachers from several favourite educational YouTube channels, Numberphile, StandUpMaths and Steve Mould.
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.
The (only) most elegant proof I’ve seen so far is in this 3Blue1Brown video: https://www.youtube.com/watch?v=Cld0p3a43fU
There’s also a VSauce1 video, where they made a mechanical version of this (like Technopolis): https://www.youtube.com/watch?v=skvnj67YGmw
Wikipedia Page: https://en.wikipedia.org/wiki/Brachistochrone_curve
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!
Here Simon explains one more effect he has played with at home, the Magnus effect.
Sunday at the beach, Simon was reenacting the 5 doors and a cat puzzle (he had learned this puzzle from the Mind Your Decisions channel). The puzzle is about guessing behind which door the cat is hiding in as few guesses as possible, while the cat is allowed to move one door further after every wrong guess.
“Here’s a fun fact!” Simon said all of a sudden. “If you add up all the grains of sand on all the beaches all over the world, you are going to get several quintillion sand grains or several times 10^18!” He then proceeded to try to calculate how many sand grains there might be at the beach around us…
In the evening, while having a meal by the sea, Simon challenged Dad with a Brilliant.org problem he particularly liked:
Simon’s explanation sheet (The general formulas are written by Simon, the numbers underneath the table are his Dad’s, who just couldn’t believe Simon’s counterintuitive solution at first and wanted check the concrete sums. He later accepted his defeat):
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.
An amazing visit to the Red Star Line Museum this weekend! It’s a museum telling the moving story of the exodus from Europe at the turn of the 20th century. Red Star Line was a private passenger liner company that brought over 2 million Europeans to America. Simon enjoyed following the story of a 9 year old girl Basia Cohen who fled the violence and hunger in Ukraine in 1919 (well, maybe it was not the story that actually triggered his interest but the exciting quest involving looking for a suitcase in every hall of the museum and completing the tasks hidden inside the suitcase).