Geometry Joys, Math and Computer Science Everywhere, Math Tricks, Murderous Maths, Notes on everyday life, Simon teaching, Simon's sketch book

Sums of consecutive numbers

While waiting to pick his little sister up from a ballet class, Simon explaining general algebraic formulas to calculate the sums of consecutive numbers. He derives the formulas from drawing the numbers as dots forming certain geometric chapes.
consecutive integers
consecutive odd integers
chemistry, Experiments, Together with sis

MEL Chemistry Experiments: Foil Etching, Magnetizing Magnesium, Metal Contest

In the Foil Etching experiment we had copper burn a whole in the aluminium foil.

This is the reactivity chart from the MEL science website, as you see aluminium is a lot more reactive than copper

As you can see, aluminum Al is much more reactive than copper Cu, but nothing happens when aluminum foil comes into contact with the copper sulfate CuSO4 solution! How come? Unfortunately, it’s all a bit more complicated than it first looks. Being quite an active metal, aluminum Al  reacts with oxygen O2 in the air, forming a very strong film of aluminum oxide Al2O3 on its surface . This film protects the metal from reacting any further.

When you add some sodium chloride NaCl, a vigorous reaction starts as Cl ions are able to compromise the otherwise-strong Al2O3 shield. Once Cu2+ is face-to-face with the aluminum Al itself and not its Al2O3 shield, the reaction can proceed, and quite spectacularly!

the hole in aluminium foil as active aluminium atoms have fled

In the next experiment, we obtained a magnetic substance from two non-magnetic ones, magnesium Mg and iron sulfate FeSO4, via a simple chemical reaction! The Fe2+ from the FeSO4 solution turned into metallic iron Fe on the surface of the magnesium particles, so we ended up with magnesium shavings covered with a thin layer of iron! The picture below shows how the magnesium shavings actually hold a heavy neodymium magnet in the air!

a heavy magnet hanging on the bottom of a glass beaker thanks to electromagnetism

And lastly, we did what MEL Chemistry calls a “Metal Contest”, because here too, three metals (zink, copper and tin) were competing in reactivity. “If you arrange metals from more active to less active, you’ll see that zinc Zn is a more adventurous fellow than tin Sn and copper Cu. That’s why, when you put a zinc rod into a solution containing, say, copper ions Cu2+, the latter are happy to settle inside the comfortable cloud of electrons, forming metallic copper Cu on the surface of the rod. Zn ions Zn2+, in turn, go swimming in the solution. The reaction with the tin chloride SnCl2 solution is essentially the same”, MEL Science website explains.

copper and tin on the surface of the zink rods


Modular Arithmetic visualized with Wheel Math

Simon learned this method from a MajorPrep video and was completely obsessed about it for a good couple of weeks, challenging everyone in our inner circle to factorize numbers using the wheels.

Simon’s proof for the 7 section circle. The remainders lie in the smallest circle (for example, the section where all the numbers are divisible by 7 have a zero in the inside circle, and in the section to the right you can see 1 in the inside i.e. all the numbers in this section mod 7 equal 1)
12 sections
5 sections
Experiments, Geography, Milestones, Physics, Together with sis, Trips

CERN Open Days September 14 – 15, 2019

The most important experience was actually simply to see how huge the Large Hadron Collider is. We totally didn’t expect the site of every experiment on the 27km ring to resemble an industrial town in its own right, scattered miles across a desert-like terrain with the Mont Blanc and the Jura mountains as the scenic back drop. It was a challenge to walk between the activities we had carefully planned in advance only to find out that some of the were full or required an hour of waiting in line. But the kids have withstood these challenges heroically and were rewarded with a few unforgettable impressions.

In front of the CMS experiment
A schematic of the LHC
It all begins with simple hydrogen protons…
the waiting
Magnet levitation above superconductive material used at CERN to create strong magnetic field to bend the path of the particles
Cloud chamber: we have actually seen energetic charged particles leave traces in the alcohol vapor in real time, in the form of a trail of ionized gas! What we saw were mainly alpha particles and electrons, we were told, judging by the character of the trail they left. Cloud chamber detectors used to play an important role in experimental physics, this is how the positron was discovered! Simon was a bit sad he didn’t get to actually build a cloud chamber as part of a workshop (they didn’t allow anyone younger than 12 to do the workshop), but he was lucky to get a personal tour at another site, where a couple of cloud chambers were available for exploration.
Our wonderful guide computer scientist George Salukvadze showing us around at DUNE, the Deep Underground Neutrino Experiment. George told us the detectors they are building will be employed at Fermilab in the U.S. Among other things, George has done the programming for the live website (screen with liquid Argon).
Playing the particle identity game
Geography, history, Milestones, Murderous Maths, Museum Time, Notes on everyday life, Physics, Together with sis, Trips

Surrounded by the equations that changed the world

At the main entrance to CERN there is an impressive smooth curve of a memorial to the world’s most important equations and scientific discoveries:

Simon pointing to the Fourier transform function
Computer Science, Murderous Maths, Simon's sketch book

The most efficient base

I’ve discovered that base 3 is the most efficient base (not base 2). Actually the most efficient base is e, and 3 is the closest to e (the proof requires Calculus).

South Korea has published a complete design of a ternary computer in July 2019! So this is actually cutting edge material here!

(Inefficiency is calculated by multiplying the number of digits by the base number).

Simon has also showed me a trick to translate any number into binary using a grid:

using acorns instead of pebbles

and a card trick based on quickly translating a number into binary in his head:

Group, In the Media, Milestones, Murderous Maths, Notes on everyday life, Set the beautiful mind free

The Netherlands Chase Away Extreme Talent

This summer, aged 9, Simon @simontigerh was named a World Science Scholar and joined a two-year program for the world’s most exceptional young math talents, as the youngest among the 75 students selected in 2018 and 2019. See the official press release for more info:

Simon’s passion for science and his unique way to see the world have blossomed again once we have pulled him out of school, where he was becoming increasingly unhappy and was considered a problem student. The only way to set his mind free and allow him to follow the path that suits him best, the path of self-directed learning, was to leave Simon’s native Amsterdam and The Netherlands, where school attendance is compulsory.

I am sharing this at the time when educational freedom and parental rights in The Netherlands are in serious danger to become limited even further. It is bittersweet to celebrate Simon’s beautiful journey and at the same time see how The Netherlands are chasing away extreme talent as we are aware of more stories similar to that of Simon’s.

art, Crafty, Geometry Joys, Math and Computer Science Everywhere, Math Riddles, Murderous Maths, Notes on everyday life, Simon makes gamez, Simon teaching, Simon's sketch book, Together with sis

Math puzzles: Is it Possible?

Simon has been fascinated by these possible-impossible puzzles (that he picked up from the MajorPrep channel) for a couple of days. He prepared many paper visuals so that Dad and I could try solving them. This morning he produced this beautiful piece of design:

Simon showing one of the puzzles to another parent while waiting for Neva during her hockey training
Simon’s original drawing of the doors puzzle. The solution of the puzzle is based on graph theory and the Eulerian trail rule that the number of nodes with an odd degree should be either 0 or 2 to be able to draw a shape without lifting your pencil. The number of rooms with an odd number of doors in the puzzle is 4 (including the space surrounding the rectangle), that’s why it’s impossible to close all the doors by walking though each of them only once.
Simon explaining odd degree nodes