# Alternating series, a crafty solution.

Simon learned this from an alternating series visualization by Think Twice.

# Area of a dodecagon without trigonometry

Simon learned this from a visual mathematics video by Think Twice.

# Simon’s Formula to Check Triangle Numbers

Simon spent the morning of December 5 pondering about how to test whether a number is a triangle number. “To test if something is a triangle number: double it, ask if it’s a multiple of its own square root. If that square root has a decimal, round it down”. This was his initial hypothesis, later discarded.

Another formula he came up with was if n is even, m is a triangle number. After we got back home, he quickly wrote some code to check it:

# Peg Solitaire

Simon proving his peg solitaire solution:

In a game of peg solitaire, if you win you must end up on one of these 5 points! This analysis was a little more difficult than with the pyramid. Because in the pyramid, I ended up with a symmetric picture whereas with this one I ended up with an asymmetric picture. So I had to do one more step of removing all of the x’s that break the symmetry:

# Divisibility by 3

Nice little trick for divisibility by 3

# More Puzzles from Maths Is Fun

In an earlier post, I have mentioned that for many games he programs Simon got his inspiration from the site Maths Is Fun. Perhaps I should add that at our home, Maths Is Fun has become an endless source of fun word problems, too! The problem below has been our favourite this week:

Some of the puzzles Simon likes to recreate with paper and scissors rather than program:

Simon and Neva have also especially liked the Tricky Puzzles section (puzzles containing jokes).

# 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.