Technolandy

Day 124 (of 2024/25) pi π day! 314

Pi is a fascinating number (a delightful topic to get sidetracked in History of Math 11) but too often it is a good example of how we look at the surface of math beauty without diving deep enough into the “y” (pun intended).

Most people know Pi as 3.14 – and love to make the connection to getting a slice of Pie on March 14 (third month, 14th day – and yes, I’m posting this at 1:59.26 to be as precise to honouring the number as I can.

Then people tend to notice it as having some mathematical connections – and the UBC Pizza place called itself PiRsquaared  – because it can be used to show why whether a piece of ribbon is looped around the earth or around a tennis ball, to get it one meter off the surface, in either case you need to add the same amount of material (our brain can’t really comprehend why another 100cm-ish of ribbon will raise either amount off the surface by the same amount because while it is easy to visualize a tennis ball being wrapped around, the earth is much…much bigger than we like to admit). 

But pi is more than ‘just part of a formula’ – or a couple of formulas…

It is a mathematical constant. And there aren’t too many of those – it still bugs me when people say that math is nice to assess because it is either right or wrong… to me that’s like assessing a poem simply by checking if it is in iambic pentameter with a rhyming scheme. Or a painting because it uses the primary colours. Or spelling because it follows commonwealth or ‘merican rules. 

At it’s ’simplest’ Pi is the ratio π of a circle’s circumference to its diameter (the length around the circle : length across the circle) Because circles are ‘perfect squares’ (360 corners make it have no corners) it doesn’t matter the size… the ratio is always the same – thus a ‘constant number’. 

But… it’s a tricky math beast, because the division part has no end number… if you divide 3 by 2, you get 1.5 It gets trickier if you divide 17 by 3 = 5.6666666 – it repeats with the same number… but Pi has an ever changing sequence after the decimal point. It’s delightful – and a fun challenge to see how far you can memorize it – I’m awful, my oldest girl had it memorized way too far – the trick is to get the first few digits right and then just add a sequence of numbers with confidence! Pause after a bit and then get back into rhythm!

It sticks out as a little annoying because we, as humans, like to find and secure patterns – and Pi is irrational… there is no pattern

But…

It is useful when dealing with circles, or spheres, or curves. The vastness of space, and even the spiral of DNA all need a bit of an understanding of Pi – while best known in trigonometry and geometry (my biggest math weakness… I had to abandon the otherwise amazing book Geometry by Paul Lockhart (of mathematicians lament fame – if you haven’t read it: https://worrydream.com/refs/Lockhart_2002_-_A_Mathematician’s_Lament.pdf but his books Arithmetic and Geometry are likewise inspiring and amazing ~ but the geometry left me in the dust… But pi as a constant helps deal with a variety of complex mathings… and some fun ones: https://youtu.be/HEfHFsfGXjs?si=Nsxg68IrVLMmY2T7 (didn’t see that pattern coming!)

So while we might enjoy having some “pie” for PiDay – it is important to realize that this little number (infinitely large nonetheless) shows up in a variety of ways: from calculating the area, volume, and circumference of a variety of shapes, used in calculations to design bridges, buildings, and satellite/navigation systems! There are cultural moments as Pi has been fascinating people for thousands of years (maybe tens of thousands??)

And as a puzzle, people love exploring it – Pi was solved to 500 digits at the start of the 20th century, and as of this blog there have been around 105 trillion digits! That’s a lot of solving in the last 5% of its ‘life’. Though some, like me, are hoping/waiting for 1415… to start a repeating pattern! That would either be funny… or ironic… or a cruel trick of the universe!

Hot apple pie for me today!