Hello maths fans! I am Dr Tom Crawford and this is the 226th Carnival of Mathematics from the Aperiodical…

Whilst this post is published in April, submissions have been open for the past month, which means an inundation of Pi Day related content, beginning with a new world record.

We now know the infamous constant to 105 trillion digits thanks to US computer storage company Solidigm. The calculation took 75 days and required 1 million gigabytes of data. If you were to write all of the digits in a line using size 10 font it would stretch from Earth to a point somewhere between Uranus and Neptune. Oh, and in case you were asking, the 105 trillionth digit is 6. You can find more information on the calculation here.

The biennial Pi calculation from Matt Parker at Stand Up Maths saw the biggest hand calculation in over a century. Matt and his army of volunteers were able to calculate Pi as approximately equal to 3.14159265358979323846264338327950288419716939937510582097494459230
781640628620899862803482534211706798214808651328230664709384460955
058223176.

It’s not quite 105 trillion, but a solid effort nonetheless! Watch the full video below.

Twitter (are we still calling it that?) user John Beach has been in touch to share his article on Ancient Egyptian uses of Pi, and how they were able to approximate the volume of a sphere as 11/21 of the volume of a cube with a side length equal to the sphere’s diameter. Neat stuff for sure, and a great follow-on from my recent trip to Egypt where I visited Karnak Temple to see actual carvings of Ancient Egyptian numbers. You can find John’s post and my video below.

Speaking of YouTube videos, I took a more creative approach to defining Pi by baking a Pi-shaped pie where all of the ingredients are in multiples of Pi (that’s a lot of pie). You can watch me in action courtesy of the ‘Tom Rocks Maths’ cooking channel below.

And now that we are sufficiently hungry for pie, let’s move on to look at some fun facts about the number of the carnival: 226.

• 226 is a deficient number, which means the sum of its proper divisors (116) is less than the number itself
• It would take you around 53 seconds to count from 1 to 226
• 226 is a member of Aronson’s sequence, an integer sequence defined by the English sentence “T is the first, fourth, eleventh, sixteenth, … letter in this sentence.”
• The London bus route from Ealing Broadway to Golders Green station is numbered 226
• 226 is the maximum number of different permutation patterns that can occur within a single 9-element permutation
• 226 is a happy number

So, what’s a happy number? A happy number is a number which eventually reaches 1 when replaced by the sum of the squares of each digit. For 226 the sequence is as follows:

226
2² + 2² + 6² = 4 + 4 + 36 = 44
4² + 4² = 16 + 16 = 32
3² + 2² = 9 + 4 = 13
1² + 3² = 1 + 9 = 10
1² + 0² = 1 + 0 = 1

The tree below shows all happy numbers up to 100. How many more are there between 101 and 226?

And on that happy note, we move onto the non-pi-day related submissions to this month’s carnival…

John Cook has formulated a simple approximation for the amount of ‘sag’ in a cable with an error of less than 1%. The formula reads:

g² = (s − x)(s + x/2).

where x is half the distance between the two end points, and s is the length of the cable. A handy shortcut for engineers, and those of us trying to solve tech company interview questions… More information on John’s blog here.

Andrew Elliot has rebuilt the website ‘is that a big number?’ which will respond with helpful comparisons to the value you enter. I tried it with 226 and was presented with the following fun facts:

• Smaller than: Estimated world population of Pygmy Hog (250 individuals)
• Bigger than: Number of bones in the human body (206 ) 

Play around with it for yourself here.

Continuing with the theme of ‘play’, Fractal Kitty has created a version of the popular game ‘2048’ using Fibonacci numbers. Tiles will combine whenever the sum is a Fibonacci number and the game ends when the board fills up and there are no more valid moves. It took me a lot longer than I’m willing to admit to get to the following score…

You can play for yourself here.

From a long time to an ‘infinitely long’ maze in the form of Cantors labyrinth. Ioanna Georgiou is the latest guest on the Infinitely Irrational podcast discussing all things Cantor and infinities. Listen below.

35: Cantor's Paradox: A Journey through the Rabbit Hole of Sets – Infinitely Irrational: A Math Podcast

Ioanna Georgiou, mathematics educator and author of “Mathematical Adventures!” and “Peculiar Deaths of Famous Mathematicians”, finishes up the discussion on Georg Cantor! In this episode, we'll attempt to answer the following questions: Should you count sheep or letters to get to sleep? Can you have infinite infinities? What do either of these have to do with math?  Connect with Ioanna at her website https://ioannageorgiou.com/ or on one of her social channels: IG: @yoayeo.maths

1. 35: Cantor's Paradox: A Journey through the Rabbit Hole of Sets 23:53
2. 34. Cantor's Labyrinth: Navigating the Maze of Infinite Numbers 28:46
3. 33. Cantor: An Infinite Odyssey 38:49
4. 32: Charles Dodgson: Curiouser and Curiouser 28:25
5. 31: Charles Dodgson: It Sounds Uncommon Nonsense 25:15

And if you want more Ioanna (and let’s be honest, who doesn’t) you can watch some short clips from her PubSci talk on “Maths, Murder and Storytelling” here.

Finally, we end with one of my favourite pages on the internet: Reddit’s ‘they did the math’. With the total solar eclipse happening across North America next week (Monday April 8^th) the following post caught my attention:

Reading the comments, it turns out that this was attempted in the 1970’s with a Concorde flying at 2250 km/h for 80 minutes. There’s a great video explaining the attempt below, which includes some neat maths to maximise the time spent flying in totality.

And that brings us nicely to a close for the 226^th Carnival of Mathematics. This post contains 226^1.267 words and 226^1.604 characters (and you thought we were done).

The next carnival will be hosted by Colleen at Mathematics, Learning and Technology – see you there!