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

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:

Community Projects, Computer Science, Group, Milestones, Murderous Maths, Notes on everyday life

Simon introducing himself for the World Science Scholars program

This is Simon’s introductory video for the World Science Scholars program (initiative of The World Science Festival). In May this year, Simon has been chosen as one of the 30 young students worldwide, joining the 2019 cohort for exceptional talents in mathematics. Most of the other students are 14 to 17 years old, age was not a factor in the selection process. To help the students and their future mentors to get to know one another, every World Science Scholar was asked to record an introductory video, no longer than 3 minutes, answering a few questions such as what is the biggest misconception about math, what your favourite branches of math and science are and who among the living mathematicians you’d like to meet.

Throughout the program, the students are given access to over a dozen unique interdisciplinary online courses and have the option to complete an applied math project, alone or as a team, consulting real experts in the field of their project. Simon has already started the first course module, on Special Relativity by Professor Brian Greene. The course has been specifically recorded for the World Science Scholars and reflects the program’s ethos: it’s self-paced, no grades, it relies on beautiful animations and visualizations, it’s full of subtle humour, is dynamic, thought-provoking and quite advanced (exactly in TheĀ Goldilocks Zone for Simon, as far as I could judge), yet broken up into easy-to-digest pieces. It’s difficult to predict how Simon’s path as a World Science Scholar will unfold (I’m afraid of making any predictions as he is extremely autodidact), but so far we have been very pleased with the nature of this program and it seems to match our non-coercive, self-directed learning style. I have especially liked one of the course’s main postulates: “Simultaneity is in the eye of the beholder”.

Simon watching Brian Greene’s Special Relativity course
Studying light clocks
Light clocks. Does the moving light clock tick slower?
Simon thinking about the question: Does the moving light clock tick slower?