When my children were little, we celebrated advent by singing Christmas carols around a lit advent wreath. Afterwards, I served a treat. My son, four years old at the time, didn't quite have the knack of advent. He requested songs like “Old MacDonald Had a Farm." Once he'd had his fill of songs, he punctuated our singing with “Gimme pie!" Every time I think of Pi Day, the cry “Gimme pi!" rings in my ears.

Last Friday, I completely missed out on Pi Day. A friend invited us over for some chicken pot pie and caramel pumpkin pie. I left school after the nature walk and spent the rest of the day and night in bed with a bad head cold. But, that's okay. The Pi Day that really counts is next year, specifically 3/14/15 9:26:53 a.m.

What is pi? Pi is a ratio of a circle's circumference (C) and diameter (d): π = C/d.

Most people say that it's a number used to find the area of a circle. Pi is more than that!

First, it's constant. By constant, I mean it's a number that's true for every circle in existence. Regardless of the size of the circle, pi is always pi. It never varies. It never changes.

Second, it's non-terminating. By non-terminating, I mean it's without end. Pi just goes on and on and on, one digit after another with no end in sight.

Third, it's non-repeating. By non-repeating, I mean that, although it goes on forever, pi never repeats a pattern of digits. No matter how far you take pi, you'll never see it repeat itself in the sequence of digits.

Fourth, it's irrational. By irrational, I mean that you cannot calculate pi by dividing one integer by another. The ratio 22/7 isn't pi. It's an approximation of pi that makes number crunching easier if you've lost your calculator.

I love the paradoxes of pi.

Pi is constant and yet it never repeats.

Pi is irrational, but it's also a ratio.

Here is what I like most about pi. Some infinite series converge to pi.

Huh?

This is an infinite series.

π = 3 + 4/(2 x 3 x 4) - 4/(4 x 5 x 6) + 4/(6 x 7 x 8) - 4/(8 x 9 x 10) + 4/(10 x 11 x 12) - + ...

Do you see how the pattern works: the sign of the term alternates between positive (+) and negative (-). The number 4 is always in the numerator (the top part of the fraction), so the next term will subtract 4 over something. The denominator takes the third number of the product in the denominator of the last term (12) and multiplies it by the next two consecutive integers: 13 and 14. Thus, the next term will be: - 4/(12 x 13 x 14).

If you go term by term, you can see how this series gets close to pi as you add more terms.

First Term:

π ≈ 3

Second Term:

π ≈ 3 + 4/(2 x 3 x 4) = 3 + ¹⁄₆ = 3 ¹⁄₆= 3.1666...

Third Term:

π ≈ 3 ¹⁄₆ - 4/(4 x 5 x 6) = 3 ¹⁄₆ - ¹⁄₃₀ = 3 ²⁄₁₅ = 3.1333...

Fourth Term:

π ≈ 3 ²⁄₁₅ + 4/(6 x 7 x 8) = 3 ²⁄₁₅ + ¹⁄₈₄ = 3 ⁶¹⁄₄₂₀ = 3.14523809523809....

I created a spreadsheet to make these calculations because they're tedious.

At the 1st term, the series converges to the ones place of pi: 3.166666666...

At the 2nd term, the series converges to the tenths place of pi: 3.133333333...

At the 6th term, the series converges to the hundredths place of pi : 3.14271284271...

At the 9th term, the series converges to the thousandths place of pi: 3.141254823...

At the 33rd term, the series converges to the ten-thousandths place of pi: 3.141585704...

At the 46th term, the series converges to the hundred-thousandths place of pi: 3.141595220...

At the 89th term, the series converges to the millionths place of pi: 3.141592299...

At the 175th term, the series converges to the ten-millionths place of pi: 3.141592606...

At the 412th term, the series converges to the hundred-millionths place of pi: 3.141592657...

At the 849th term, the series converges to the billionths place of pi: 3.141592653...

Do you see why Pi Day 2015 is a big deal?

π ≈ 3.141592653

3/14/15 9:26:53 a.m.

You might find a picture of this process interesting. The chart shows how the series dances above and below pi until it converges according to what the naked eye sees.

Last Friday, I completely missed out on Pi Day. A friend invited us over for some chicken pot pie and caramel pumpkin pie. I left school after the nature walk and spent the rest of the day and night in bed with a bad head cold. But, that's okay. The Pi Day that really counts is next year, specifically 3/14/15 9:26:53 a.m.

What is pi? Pi is a ratio of a circle's circumference (C) and diameter (d): π = C/d.

Most people say that it's a number used to find the area of a circle. Pi is more than that!

First, it's constant. By constant, I mean it's a number that's true for every circle in existence. Regardless of the size of the circle, pi is always pi. It never varies. It never changes.

Second, it's non-terminating. By non-terminating, I mean it's without end. Pi just goes on and on and on, one digit after another with no end in sight.

Third, it's non-repeating. By non-repeating, I mean that, although it goes on forever, pi never repeats a pattern of digits. No matter how far you take pi, you'll never see it repeat itself in the sequence of digits.

Fourth, it's irrational. By irrational, I mean that you cannot calculate pi by dividing one integer by another. The ratio 22/7 isn't pi. It's an approximation of pi that makes number crunching easier if you've lost your calculator.

I love the paradoxes of pi.

Pi is constant and yet it never repeats.

Pi is irrational, but it's also a ratio.

Here is what I like most about pi. Some infinite series converge to pi.

Huh?

This is an infinite series.

π = 3 + 4/(2 x 3 x 4) - 4/(4 x 5 x 6) + 4/(6 x 7 x 8) - 4/(8 x 9 x 10) + 4/(10 x 11 x 12) - + ...

Do you see how the pattern works: the sign of the term alternates between positive (+) and negative (-). The number 4 is always in the numerator (the top part of the fraction), so the next term will subtract 4 over something. The denominator takes the third number of the product in the denominator of the last term (12) and multiplies it by the next two consecutive integers: 13 and 14. Thus, the next term will be: - 4/(12 x 13 x 14).

If you go term by term, you can see how this series gets close to pi as you add more terms.

First Term:

π ≈ 3

Second Term:

π ≈ 3 + 4/(2 x 3 x 4) = 3 + ¹⁄₆ = 3 ¹⁄₆= 3.1666...

Third Term:

π ≈ 3 ¹⁄₆ - 4/(4 x 5 x 6) = 3 ¹⁄₆ - ¹⁄₃₀ = 3 ²⁄₁₅ = 3.1333...

Fourth Term:

π ≈ 3 ²⁄₁₅ + 4/(6 x 7 x 8) = 3 ²⁄₁₅ + ¹⁄₈₄ = 3 ⁶¹⁄₄₂₀ = 3.14523809523809....

I created a spreadsheet to make these calculations because they're tedious.

At the 1st term, the series converges to the ones place of pi: 3.166666666...

At the 2nd term, the series converges to the tenths place of pi: 3.133333333...

At the 6th term, the series converges to the hundredths place of pi : 3.14271284271...

At the 9th term, the series converges to the thousandths place of pi: 3.141254823...

At the 33rd term, the series converges to the ten-thousandths place of pi: 3.141585704...

At the 46th term, the series converges to the hundred-thousandths place of pi: 3.141595220...

At the 89th term, the series converges to the millionths place of pi: 3.141592299...

At the 175th term, the series converges to the ten-millionths place of pi: 3.141592606...

At the 412th term, the series converges to the hundred-millionths place of pi: 3.141592657...

At the 849th term, the series converges to the billionths place of pi: 3.141592653...

Do you see why Pi Day 2015 is a big deal?

π ≈ 3.141592653

3/14/15 9:26:53 a.m.

You might find a picture of this process interesting. The chart shows how the series dances above and below pi until it converges according to what the naked eye sees.