Crafty, Math and Computer Science Everywhere, Math Riddles, motor skills, Murderous Maths, Simon makes gamez, Simon teaching, Simon's sketch book

Proof Visualization. Warning: Mind-boggling!

Inspired by the Card Flipping Proof by Numberphile, Simon created his own version of this proof. He made a solitaire game and proved why it would be impossible to solve with an even number of orange-side-up circles. He drew all the shapes in Microsoft Paint, printed them out and spent something like two hours cutting them out, but it was worth it!

The colourful pieces in the lower row are a “key” to solve the solitaire puzzle. The objective is to remove all the circles. One can only remove a circle if it’s orange side up. Once a circle is removed, its neighbouring circles have to be flipped. Using the key, start with the yellow pieces, and move in the direction of the “grater than” sign (from smallest to largest).

If there’s an odd number of orange circles in the middle, then the end pieces are the same, both orange or both white. In both cases the total number of orange circles will also be odd. If there’s an even number of orange circles in the middle, then the ends have to be different (one orange, one white).

In the case of odd number of orange pieces, the ends have to match. In the case of an even number of orange pieces, you would have pieces that point the same way at both ends. “Now we’ve proven that to make this puzzle possible it has to have an odd number of orange pieces”, Simon says.

Why? Imagine a stick figure that always walks to the right, but always faces in the direction of the arrow (as in it can’t go backwards). It would flip every time it reaches an orange circle. Focusing on everything except the ends, if there are an odd number of orange circles, the puzzle pieces would face the other way. Which means that the end pieces are the same, and therefore the end circles are the same. If there are an even number of orange circles in the middle, the puzzle pieces would face the same way. Which means that the end pieces are different, and therefore the end circles are different.

Simon finds this sort of proof easy, but I felt like my brains are going to boil and dripple through my ears and nostrils. He patently exlained it to me several times and types the above explanation, too.

Crafty, Experiments, motor skills, Physics, Together with sis

Some Physics Demos with Geomag

Rotating a merry-go-round with a “magic wand”
One beautiful thing about Simon’s recent return to Geomag is that, as it turned out, he is now capable of building all the tricky constructions on his own, without any help from the grown-ups
An example of a Gaussian Gun, a magnetic chain reaction to launch a steel ball at high speed. As soon as the rolling ball hits the magnet, another ball in the opposite side is launched.
Computer Science, Crafty, Electricity, Electronics, Engineering, Logic, Milestones, motor skills, Simon teaching

Simon building an 8-bit Computer from scratch. Parts 1 & 2.

Parts 1 and 2 in Simon’s new series showing him attempting to build an 8-bit computer from scratch, using the materials from Ben Eater’s Complete 8-bit breadboard computer kit bundle.

Simon is learning this from Ben Eater’s playlist about how to build an 8-bit computer.

In Part 1, Simon builds the clock for the computer
In Part 2, Simon builds the A register (more registers to follow).
these little black things are an inverter (6 in one pack), AND gate and OR gate (4 AND and OR gates in one pack)
this schematic represents the clock of the future 8-bit computer
Simon and Neva thought the register with its LED lights resembled a birthday cake
Crafty, Geometry Joys, motor skills, Murderous Maths, Simon teaching, Simon's sketch book

A Square Triangle?

Simon explains what Gaussian formula is to check a shape’s curvature and shows how to make a triangle with three 90° angles. Or is it a square, since it’s a shape with all sides equal and all angles at 90°? He also says a few words about the curvature of the Universe we live in.

Almost everything he shares in this video Simon has learned from Cliff Stoll on Numberphile:
https://www.youtube.com/watch?v=n7GYYerlQWs
https://www.youtube.com/watch?v=gi-TBlh44gY

Crafty, Geometry Joys, motor skills, Murderous Maths, Notes on everyday life, Simon's sketch book

A Knot Theory Puzzle

Simon has shown us a curious puzzle: if you hang a poster on a string using two pins, what is the way to arrange the string so that the poster definitely falls once you remove any pin? The math behind the trick involves Knot Theory. Simon has learned the trick from this video by Jade, the creator of the science and phlosophy Up an Atom channel that Simon loves.

It’s relatively easy to solve the puzzle for one particular pin. The picture below shows the solution for removing the right pin:

But the puzzle asks us to think of a configuration that makes the poster fall once ANY pin is removed, doesn’t matter which! And that’s way more difficult. Simon said that we should simplify the problem by removing the poster altogether and replacing the pins with two small loops of string.

What Simon did next was show us the math behind the trick, trying to come up with such a combination of the three loops that would stay connected but, if you remove any of the three, the rest of the construction would fall apart. “Wait, that sound familiar! We’ve actually turned the problem into Borromean rings!”

The letters x and y stand for the ways to intertwine the strings, with x wrapping around 1 and y wrapping around 3. The regular x and y are clockwise (x or y) and the inverse x and y are anticlockwise (x^-1 or y^-1). Obviously, a sequence of clockwise-anticlockwise of the same string should be avoided as it unties itself.
the moment of truth!
performing in front of our guests the day after (in Dutch)
the solution
chemistry, Exercise, Experiments, Good Reads, Milestones, motor skills, Murderous Maths, Notes on everyday life, Physics, Simon makes gamez, Simon's sketch book, Together with sis, Trips

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  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!

dsc_06646749091631384876171.jpgMade a lot of “binary calculators” (above)

dsc_08098571406704053720752.jpgHelped little sis learn fractions

dsc_07972979319674618445058.jpgIntroduced little sis to infinite fractions

dsc_06271192208290101593530.jpgChecked out his new lathe tools and tried sawing

dsc_06877459075749954970581.jpgExperimented a whole lot (with surface tension, forces, water and gases)

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dsc_07585635002843708540665.jpgYet another experiment

dsc_08371515643779040846973.jpgFollowed tutorials by Physics Girl, Up and Atop, PBS Space Time, Veritasium, Reactions, PBS Infinite Series

 

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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).

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dsc_09612735924853232773240.jpgLaunching propeller rockets on the beach

dsc_09071976964664774880504.jpgSimon’s first chemical equations. He first thought they worked like linear equations 🙂

dsc_08943237920924875579728.jpgMore Physics Girl inspired experiments

dsc_09108778766156185324596.jpgFavourite 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!

dsc_08732805749892983265193.jpgFavourite evening activity

dsc_09114093660143972351481.jpgLoving the waves