Today is Pi day. That most useful mathematical constant which relates the diameter of a circle to its circumference.
The ancient Greeks knew about it. They did have a slight problem, their number system didn't help them think in terms of non whole numbers. It wasn't as primitive as the Roman system which was little more then tally marks.
But they did understand ratios so they could approach it pretty well.
They attacked the problem in a great way. They would draw a circle and then draw a square inside. Finding the circumference of a square is easy, but it really isn't very close to the circumference of a circle. They knew that too, so they kept drawing polygons with more and more sides, like hexagons (6 sides) and octagons (8 sides) and so on.
Not only did they work from the inside but also the outside surrounding the circle with polygons with more and more sides. They were using the Limit Theorem which wasn't quantified until Newton and Leibnitz.
So after all that work they knew that pi was a little more then 3. We know it is 3.14159... which would have driven them crazy as its a irrational number, they liked the purity of whole numbers and even coined the term irrational number to ridicule the idea that numbers could be anything else.
Not that it stopped them from using it. They wanted to know how big the earth was. They understood that it was round. So they devised an experiment. Using two deep wells a known distance apart, they were able to calculate the circumference of the Earth with an error of something like a couple of hundred miles, which is amazing. Sure now we can measure it to less then centimeters but they didn't have near our technology.
Now it wouldn't be Pi day without a Pie recipe.
I really like Alton Brown's Pie dough
But our filling is a little different:
About four apples, Cameo or Granny Smith, sliced thin
3-4 Tbsp butter, softened
1/2 cup sugar
3-4 Tbsp cinnamon powder
In the pie shell layer the apples with some dabs of butter, and a sprinkling of sugar and cinnamon.