Honoring Pi Day

Preface: This is a throwback from some years ago (circa 2012) when I was a Senior in high school, and was in honor of Pi Day. Enjoy!

π It is romantic, infinite, enigmatic, and yet so simple. It can be discovered by taking the area of a circle, and dividing that by the square of its radius. It has fooled may intellectual men and women throughout the ages, and still today. I will do a little manipulation of π (and hopefully not be committing mathematical heresy) with the advent of π day.

As many know π can be known as 3.14159265… Which would mean that the most accurate π day would have been on March 14, 1592. So, going off this, if π changed every year according to the date, what mathematical effects would this bring?

To illustrate this I will use one of the most basic uses of π, finding the area of a circle. For ease of understanding, our circle will have a radius of 1. Reach back to third grade and remember the formula for the area of a circle $$A=π r^2$$ Which means that if our radius ®=1, then the area will be π or 3.141592.

Now let’s have some fun.

If we modify π to change every year, π would equal 3.142012 this year and next year it would equal 3.142013 and so on for eternity. The repercussions of this would be that circles with a radius of 1, would be 0.00042 units$^2$ larger than the ‘true’ π day back in 1592. Even though this is a mere 0.013369018% increase in size and a 0.000001 unit increase per year, it could still be a pretty big deal (ok, not really). It would take 6,000 years, if this pattern is continued, for the ‘area’ of a circle to double (go from 1 unit$^2$ to 2 units$^2$). The year would be 7592, and every circle (where radius is equal to 1) that you would encounter would conceptually be twice the size… Crazy to think about.

But thankfully π is constant, or is it since it is infinite?

Happy π day.

-Cole