This needs to be said carefully, but pi is technically a ratio.  More below, but first:  a ratio is a comparison of two quantities, as in ‘the ratio of boys to girls in that class is 5 to 4.’   Such a comparison (using the example) is often written 5:4, or sometimes 5/4.  And that can be viewed as the fraction number 5/4 or 1.25.

Ratios and numbers are pretty much interchangeable (all numbers can be written as ratios, but not quite all ratios can be written as numbers*), so this is usually not a problem.  But, in the case of pi (and other places), it tends to obscure things.

SO: Take anything that can be viewed as a perfect circle:  a wedding ring, a manhole cover, a circular pizza pan – you name it.  It will always be the case, no matter how large or small, that the distance around that circle (circumference) is a little over 3 times the distance across the circle (diameter).  That is, their ratio is a little more than 3 to 1.  This has been known since before the time of Christ.

So this particular ratio [of circumference to diameter] is approximately 3/1 then, but not quite.  (Though the ancient Babylonians used that approximation – see Pi Triva Quiz ).  The ratio is almost 22/7, but not quite.  And, it is nearly 3.14 -or even 3.1416*but not quite.

For centuries, math types struggled to find the exact value of this ratio. (Archimedes, who lived over 200 years before Christ*, proved it was between 22/7 [3.1428 . .] and 223/71 [3.1408 . .] – a remarkable feat!).  In the 1700s, it gradually became popular and standard to use (as a shortcut) the Greek letter π (pi) to denote/name the ratio, and thus make things easier (the value of notation!).  So, when one hears ‘pi is almost 22/7, but not exactly’, they mean (whether or not they realize it) the equivalent ‘ratio’ sentence in the paragraph above.

Finally -also in the 18th century- Johann Lambert proved that the ratio we call pi will NEVER be able to be exactly calculated or represented.  (In math terms, pi is irrational.)  Thus you find more and more precise values being calculated (see Pi Trivia Quiz) with new records all the time, though we know it will never be exact.

By the way, using the vocabulary and symbol above, you can now see where the ‘mysterious’ formula for the circumference (C) of a circle comes from!  The equation – or formula – so many have memorized, namely C = π * d means precisely the same as ‘the circumference of any circle is a little more than 3 times the diameter.’  If you know one, you can find the other.

Isn’t mathematics wonderful?  🙂


* Examples, among others: Ratios comparing three quantites can’t be written as numbers. (The ratio of sophomores, juniors and seniors on the starting team is 2:5:4, e.g.).  And comparisons involving 0 can be tricky.  (The ratio of Missourians to Texans in the club is 7:0, say.  7/0 is not defined as a number.)
* Or even 3.1415926535 🙂
* And is still considered by most to be one of the 3 greatest mathematicians of all time (alongside Newton and Gauss)!