Hilarious, inspirational and loaded with cosmic coincidences, this was one of the best evenings ever! Many of our currently favourite themes were mentioned in the show (such as the controversy of Francis Galton, the BED/ Banana Equivalent Dose, sound wave visualizations, laser, drawing and playing with ellipses, Euler’s formula). Plus Simon got to meet his teachers from several favourite educational YouTube channels, Numberphile, StandUpMaths and Steve Mould.
Simon has tried Matt Parker’s multiplicative persistence challenge on Numberphile: by multiplying all the digits in a large number, looking for the number of steps it takes to bring that large number to a single digit. Are there numbers that require 12 steps (have the multiplicative persistence of 12)?
Simon has worked on this for two days, creating an interface in Wolfram Mathematica. He wrote the code to make the beautiful floral shapes above, they are actually graphs of how many steps three digit numbers take to get to single digit numbers (each ”flower” has the end result at its center).
What about the numbers with many more digits than three? Simon has tried writing code to look for the multiplicative persistence of really large numbers and also came up with some efficiencies, i.e. shortcuts in the search process. He did manage to find the persistence for 2^233 (the persistence was 2):
However after he applied one of his efficiencies to the code to be able to search through many numbers at once, the code didn’t run anymore. You can read Simon’s page about this project and see his code here:
277777788888899 is the smallest number with a persistence of 11.
The largest known is 77777733332222222222222222222:
This code works with a few efficiencies:
1. They’ve already checked up to 10^233, so we don’t have to check those again.
2. We can rearrange the digits, and the multiplication will be the same. So we don’t have to check any of the rearrangements of any of the numbers we’ve already checked.
3a. We should never put in a 0 (a digit of the number). Because then you would be multiplying by 0, which would result in 0 in 1 step!
3b. We should also never put in a 5 and an even number. Because, in the next step, the number would be divisible both by 5 and by 2, so it’s also divisible by 10. That would put a 0 in the answer, which we saw we should never do!
3c. With similar reasoning (assuming we want to find the smallest number of the type we want), we’ll see we should never put in:
– Two 5s
– A 5 and a 7
– When we put in a… (- means anything, the order doesn’t matter):
1,- , remove the 1
2,2, put 4 instead
2,3, put 6 instead
2,4, put 8 instead
3,3, put 9 instead
So, we can reduce the search space and time collossaly, with just some logic!
Inspired by Matt Parker’s video about the uniquely shaped building at 20 Fenchurch Street in London, Simon was very excited to visit this address. In the video below, made on the pavement in front of the skyscraper, Simon shows the geometric proof (he learned from Matt) of why the building’s shape used to let it set things on fire on extremely sunny days.
Wait a minute, is that Simon actually playing football? We never thought we would see that happen. All the credits go to Matt Parker. He is the one who got Simon interested in football, or rather – in the football as a geometrical object. Simon also gave us a lecture on the history of the football, its changing shape and aerodynamics.
Simon has been begging me to do this project together for days (fans of dodecahedrons that we are) and finally we made it – our own origami dodecoration! Simon learned this from a video by Matt Parker on Stand Up Math and looked up a dodecahedron graph on Google. In the video, Simon explains the main principles of how to make a dodecoration. The steps of how to fold your paper squares are below.
Make sure you have 30 origami paper squares, in 3 or 5 colours
Fold in two, valley fold down
Fold again, so that the cross section looks like the letter “M”
Make sure the bottom of the “M” is facing you, then fold like below. Repeat for all the 30 squares.
Now it’s time to start inserting the 30 pieces inside one another. The small triangular folds should fit together to make the vertices of the dodecahedron. Every vertex should be made up of three pieces of different colours.
The dodecahedron graphs (the plan to follow while building):
This experiment has been inspired by Matt Parker and his Stand Up Math channel.
As one of our Pi day activities, Simon attempted to calculate Pi by weighing a circle. In the video, you he first explains why this should work: the area of a circle with the radius r and the area of a square with a side of 2r can be expressed as Pi x r^2 and 4r^2 consecutively. This makes the ratio between the area of such a circle and the area of the square equal to Pi/4. In other words, Pi can be expressed as 4 times that ratio. But since both the circle and the square are made of the same material, their mass will also have the same ratio.
The result Simon got was pretty close, considering the low precision of our kitchen scales. As Simon’s math teacher correctly pointed out, the result would be much more precise if we had one thousand kids make their own circles and squares and weigh them, and then took the average of their outcomes.
This video has been inspired by the wonderful Matt Parker and his video on the Stand Up Math channel:
Yesterday was Pi day and we are still celebrating! Simon experiments with calculating Pi with a physical thing, a pendulum. For the experiment, he cut a cord one fourth of the local gravity value (9.8m/s^2), that is 245 cm. One full swing of the cord makes Pi (measured in seconds)! Simon measures the time the pendulum makes 10 swings and divides that number by 10, to get the average duration of a swing.
The values Simon got were pretty close! The closest he got (not in this video, but later that day) was 3,128 sec., which is exactly the same value that Matt Parker got! What is the chance of that?
The formula is t = 2Pi times square root of l over g (where l is the length of the cord and g the local gravity).
Starring the cute 3Blue1Brown Pi. Here is some extra footage, with the 3Blue1Brown Pi riding the pendulum:
What shape can roll well, other than a circle (wheel)? Two circles, attached together according to a formula involving a square root of two! Simon made these “wobbly circles” inspired by a Numberphile video where Matt Parker talks about how the ability to roll well (as in a wheel) is caused by the constant height of the center of mass (as opposed to a square wheel, whose center of mass goes zigzagging up and down). Wobbly wheels also have a stable height of their center of mass, hence they roll!
Simon also made a transparent version (with mom’s help):