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Pi day (π day) comes every year, but this year’s pi day is special and there won’t be another one like it for a hundred years. If you write pi to two decimal places, you have π=3.14, and you can read that as March 14. But if you write it out to four decimal places you have π=3.1415. That’s March 14th, 2015 and that happens only once every hundred years!
Some of you reading this don’t feel the excited need for an exclamation point at the end of that previous sentence. We’re sorry about that. We realize that you have to have a certain affection for mathematics and a love for pi in particular to get excited about seeing it carried it out to four places in decimal notation and on your calendar.
Though pi may not be exactly loveable, it’s definitely special. There are certain numbers that keep turning up again and again, and some of them are so omnipresent that mathematicians, wanting to save time and space, have used symbols to represent them. Pi, as we say it, or π, as we write it in mathematics, is certainly the most famous. Among mathematicians, e is almost as famous as π, but if you gave up on math when you left high school you may still remember something about π while you haven’t heard a thing about e. But let’s put e aside and get back to pi.
In mathspeak, pi is an irrational number — not to imply that 3.14159 is a particularly wacky numeral, but simply that you cannot get it by dividing a number by another number. Or, to speak mathematically, it isn’t the ratio of two numbers and, hence, it’s irrational. So, it’s not equal to 22/7, which many students pick up in high school.
You can calculate pi by drawing a regular hexagon inside and outside a circle, and you can use the sides of the hexagon as the base of triangles whose vertex is at the center of the circle. It’s simple enough to calculate the areas of the triangles and hence the hexagons, and you know that the area of the circle is bigger than the inside hexagon and smaller than the outside hexagon. Archimedes did that and kept doubling the number of sides until he had a 96-sided polygon. Then he was able to show that pi was bigger than 223/71 and smaller than 22/7. And that’s where 22/7 comes from.
Our pi is transcendental. That sounds more unusual and ecstatic than it is. Again, in mathspeak, a transcendental number is not algebraic, which is to say that it’s not a root of a non-zero polynomial equation with rational coefficients. (Satisfied?) Most real numbers are transcendental, but if we start discussing what we mean by that previous sentence we won’t enjoy much of the day.
Pi — everyone knows you know this — is the number you get when you divide the circumference of a circle by it’s diameter.What’s interesting — or amazing, if you’re in the mood — is that when you compare the diameter and circumference and try to divide the circumference by the diameter, you get a number which is clearly just a little bit bigger than three, but it’s impossible to discover exactly how much bigger. Or look at it this way, you can divide the diameter into little equal pieces with nothing left over, or you can divide the circumference into little equal pieces with nothing left over, but you’ll never find a size of equal little pieces that that will work on the circumference and on the diameter, too, with nothing left over. Far better to eat your Pi pie.