Who Ate All the Pi?

Posted by Collin Ward on 12th Feb 2020

We were all taught to use pi at school. But not everyone was taught – or not everyone remembers – where pi comes from. When you understand where pi comes from, it's easier to use.

Pi is simply a ratio. If you divide the Circumference by the Diameter you will get pi.

Turn that around and if you multiply:

Let’s prove this. And let’s use an easy number to help.

Set the diameter at 10 cm (that’s dead easy to multiply with.) We know what pi is because the calculator tells us: 3.142

Pi (3.14) x Diameter (10) = 31.42

If this is right, when we do the other equation we SHOULD get back to pi.

31. 42 ÷ 10 = 3.142 Hooray!

Shopping for Pizza.

Let’s get serious now. Pizza. Sometimes it is hard to work out when it is better to buy one large pizza OR two small pizzas.

Let’s imagine a large pizza of 10” – we know the age old equation for the area of the circle is

π x 52

π x 25 = 78.5 inches2

So, surely, if we buy two 5” pizzas we should get the same amount of pizza, right?

Well, half the diameter is 5”, making the radius 2.5.

That means a 5” pizza has an area of 19.6 inches2

If you buy two 5 inch pizzas you’ll get 39.2 inches2 which is kind of rubbish, as it’s only about half the amount of a single 10” pizza. That’s why the smaller pizza’s are a complete rip-off when you look at the prices. You’d need to buy 4 of them to match a large pizza. and you often find them in “Buy One Get One Free” special offers.

However, if it's the special filled crust of the pizza you love, you’re going to be more interested by the circumference. Your 10” pizza, we know already, gives your 31.42 inches of crust. Two 5” pizzas would give you the same amount of Crust, but a higher ratio of Crust. And if you get to use the advantage of a sale price to buy the 4 pizzas you need to match the same surface area of 10" pizza, you’d end up with 125.682” (yes, double) the crust.

And if you like the crust, then the smaller pizza is a must.

The same goes for using pi to decide with pie to buy.

That should make those junk mail pizza menus a little more amusing.