Contributing, Milestones, Murderous Maths, Museum Time, Physics, Trips

The Brachistochrone

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!

Exercise, Experiments, Notes on everyday life, Physics, Simon teaching, Together with sis, Trips

A lot of fluid dynamics at Technopolis

Today we celebrated my 40th birthday with a family trip to Technopolis, a mekka for science-minded kids in the Belgian town of Mechelen. (Technically, my real birthday is in two days from now, but I have messed with the arrow of time a little, to speed things up).
The entrance to the museum is adorned with a red lever that anyone can use to lift up a car!
Simon and Neva lifting up the car
The beautiful marble run and math and physics demo in one
Galton’s board and Gaussian distribution
Simon explaining the general relativity demo, which is part of the marble run
This was probably the winner among all the exhibits: a wall to climb with a mission (Simon figured it out rather quickly – one had to turn “mirrors” to change the direction of light (green projection) and have the light rays extinguish the targets.
Simon tried to explain this to other children, but they only seemed to want to climb. It was sad to see how no one cared to listen (well, except for Neva of course).
Simon was already familiar with this optical illusion. Later he saw another version of this on an Antwerp facade.
The logic gates were too easy.
the center of gravity
Huge catenaroids! Something Simon had already demonstrated to us at home, but now in XXL!
cof
And huge vortices! Another passion.
Hydrodynamic levitation! Hydrodynamic levitation!
Look! A standing wave!
And another standing wave!

Here Simon explains one more effect he has played with at home, the Magnus effect.