Happy Pi Day

I'm probably not going to bake a pi-themed pie today. Or any pie. So above is a screen capture from Google images.
On an earlier Pi-Day post, I calculated some useful pie-making numbers using π -- you probably remember them from basic math class: first the basic calculations. The area of a circle is π (approximately 3.14) times the radius squared. Therefore:

• 8 inch round pans have diameter 8, radius 4 so they have 3.14 x 4 x 4 = 50 square inches of area
• 9 inch round = 63.5 sq. in.
• 10 inch round = 87.5 sq. in.

Square pans have the following areas:

• 8 inch square = 64 sq. in.
• 9 inch square = 81 sq. in.
• 9 by 13 inch = 117 sq. in.

If you pour in filling to the same depth, the amount of pie filling or cake batter you need is the same when you fill pans of the same area, assuming that the round pans have straight, not sloping sides. Sloping sides add a bit of unpredictability. These are useful results:

• An 8 inch square and a 9 inch round are virtually identical in their need for filling or batter.
• A 9 inch square and a 10 inch round are less than 10% apart.
• Two 8 inch squares are very close to a 9 x 13 inch rectangle.
• NOT equivalent: a 10 inch pie with sloping sides probably holds close to twice as much filling as an 8 inch pie.

UPDATE: the most extreme pie movie I've ever seen: