# 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:

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

# Tower of Hanoi moves plotted under a binary log plot

What you see here is the sequence of moves to solve the Towers of Hanoi puzzle. The sequence goes up to 2 to the power of the number of rings in your puzzle. The picture here is the sequence for 8 discs, so 256 moves. “If you plot log_2 (binary log), this shape (in red) would be under that log plot, except for the powers of 2 which would be exactly on the log plot!” Simon has noticed.

Simon’s earlier video about the math behind the Towers of Hanoi puzzle:

# Computers of the Future: How Far Do We Need to Go?

How many bits will computer operation memory have and how many do we need to have to link every single particle in the Universe to the internet? And how useful are quantum computers?

# Mom is 100111! And she is 33! And 124!

It’s my birthday today and Simon has calculated my age in bases 2-12, 16 and 20! In the video, he explains what my color is in hexadecimal (base 16), how can turn my age into 33 and why it’s cool to be the age of a Mersenne number (so that I start looking forward to turning 63). He also shows a cool way to generate Mersenne numbers, Fibonacci numbers and Lucas numbers. My birthday in all the bases up to 20 and my colour: In binary: In base 5: Simon’s present: a magic square adding up to 39 in all the rows and columns (and diagonals):   # Math touching programming

During his biweekly math lesson:

Mom, we are converting into binary numbers!  The same night Simon said to me: “Mom, you know how we have once talked about programming lessons?” We did discuss this approximately half a year ago when we started considering homeschooling seriously and back then Simon told me he really wanted to have private math lessons but no programming lessons. “Do you mean you’d like to start programming lessons now?” – I asked. He blushed and hid his face in the pillows. When he looked up again I saw a big toothless smile.