Simon saw this proof on the Numberphile channel.

# Category: Simon’s sketch book

# Physics Experiments: The Color Wheel and Mind Blending

Inspired by Physics Girl, here come a couple crafty color wheel experiments involving what Physics Girl calls “mind blending” (it may not be the real name) – mixing color wave lengths in your mind. Simon has already studied the way our brain perceives blended/ moving color before, in the several optical illusions he programmed. This time, however, he decided to observe how simple paint can produce the same effect.

CORRECTION by Simon: *You can’t actually even see the entire visible spectrum. You only see red, green and blue (I couldn’t think of that in the video)*.

The rotating green and red disk look more yellow in this extra 2 sec of footage taken by a different camera:

Simon prepared the props himself, with some help from his sister New (who painted one of the disks) and me (I helped cutting the hard cardboard). We couldn’t figure out a way to get the disks to spin fast and tried several options (like straws, pencils and even a dismantles giroscope). Eventually, we decided to use a small drill from a children’s woodworking set and it worked!

Making the fourth disk was the most difficult part as Simon wanted to divide the circle into 12 equal sectors. He came up with this elegant solution: he drew a hexagon and then bisected every angle (see below).

# Happy not back to school

Simon and Neva work on the math problem called ‘The Dollar Game’ late in the evening before the day school officially starts in Belgium and continue as soon as they wake up the following morning:

# Looking back at the vacation

Although vacation is a vague notion in our family, where days are devoted to doing favourite things 365 days a year. For Simon, that means that his days are filled to the brim with science experiments, practicing math and devouring books and videos on quantum mechanics, also when he is on vacation (away from home). The past three weeks in Southern France and Spanish Sitges also involved a lot of swimming and enjoying the outdoors of course, but science remains Simon’s top priority. He also felt like he had grown unaccustomed to the beach overkill (while at home, we only went to the beach something like once a week max) and couldn’t bear the sand sticking to his wet feet for a while. By the time we settled at our Spanish Airbnb he gradually got acclimatised to this continuous sensory ordeal though and I was happy to see him relax at the seashore, especially on the last day of our stay. He had spent about two hours in the water (experimenting with vortices, swimming after a ball and just playing silly), and Â didn’t even want to get the sand off his feet anymore. We just sat there on the beautiful retro beach in Sitges, hugging and watching the sea, in absolute tranquility. Simon had even forgotten that Daniel Shiffman’s live stream was due that evening!

Made a lot of “binary calculators” (above)

Helped little sis learn fractions

Introduced little sis to infinite fractions

Checked out his new lathe tools and tried sawing

Experimented a whole lot (with surface tension, forces, water and gases)

Yet another experiment

Followed tutorials by Physics Girl, Up and Atop, PBS Space Time, Veritasium, Reactions, PBS Infinite Series

Loved his new Larry Gonnick Calculus book and did quite a lot of… Calculus. It was quite funny when a restaurant owner noticed Simon differentiate at dinnertime and was very impressed. He trend out to be a former high school science teacher. Interesting how Simon’s giftedness is usually only openly appreciated by those who have some understanding of the subjects he elaborates upon. People with less understanding show less tolerance, like a guard at the French swimming pool who told us off and snatched Simon’s (clean) plastic plate away, not allowing Simon to carry out his beloved vortices experiment in the public pool (resulting in a huge meltdown and Simon being afraid the pool would close or change rules every day).

Launching propeller rockets on the beach

Simon’s first chemical equations. He first thought they worked like linear equations ðŸ™‚

More Physics Girl inspired experiments

Favourite one: burning matches in a glass results in all the water in a shallow plate getting sucked into the glass (water level rising). Has a physical and a chemical explanation!

Favourite evening activity

Loving the waves

# The Standard Model

Simon, let’s go to the beach, let’s get your shoes on! What’s that on your foot? – Oh, I was just building the Standard Model of Elementary Particles.

Simon is very fond of the new Physics book we are reading before bedtime, it’s called We Have No Idea and it’s about everything yet to be discovered.

# Some more memories from Friesland. Binary Calculator.

A couple more images from our trip to Friesland. Simon’s binary calculator:

Doing math at a restaurant where we were celebrating his friend’s birthday:

# The Leaning Tower of Lire

Also known as the Book-Stacking Problem. Simon had tried to build this tower at the Fries Museum where we visited a huge Escher exhibition (to the annoyance of the museum staff, to whom I had to explain that it was a serious math experiment and not just a kid dropping bricks), but it only worked with 4 blocks (possibly because the blocks were made of foam and weren’t rigid enough). He tried to stack the blocks on top of one another, shifting every next block first by one eighth, then by one sixth, next by one fourth, and next by one half – in the end, the top block would no longer be positioned above the bottom block.

He repeated the experiment at home, first doing some calculations and then using more rigid wooden blocks and managed to stack a tower of 6 blocks! (The top block still overlapped the bottom one by a bit though) :

# Simon’s proof that every Fibonacci number is a sum of its neighbouring Lucas numbers divided by 5

This has probably been proven before, but Simon likes to come up with his own proof. Here he uses proof by induction, that is a proof that proves that some property holds for all natural numbers.

# Simon’s proof that factorials are highly composite

“Mom, I’m just one step away from proving that every factorial is a highly composite number!”

# The Pi Strip

Simon made a measuring tool to check the diameter of round objects: by wrapping the strip around them, he reads the Pi times the centimeters value, which basically gives him the diameter (as the circumference equals Pi times the diameter).

And here he is, measuring the diameters of Neva’s and Dad’s necks: