3/14: A Commemoration of “Pi”

March 14th is a date that ironically celebrates the math notion Pi (or π), but some of you may ask: “Why exactly 3/14”? Well, as many of you know, π is an irrational number that begins with the three numbers 3.14. So, since π’s first three numbers are 3.14, it only makes sense that the commemoration of the numerical symbol would be 3/14. While there won’t be much discussion about how the pies themselves are made, the mathematical aspects of the pies will be reviewed, but if you’d like to recreate these pies, the recipes will be at the bottom. So, to celebrate this valued symbol, let’s take a look at a few different pie recipes and their areas, circumferences, radii, and diameters! Also, let’s discuss the various formulas that go into calculating such a simple-looking symbol like π because calculating it may be more complicated than expected.

What is Pi (π)?:

Put simply, pi (or π) is C (circumference) / D (diameter). Now, you may be wondering what that exactly implicates, and well, the answer is more complicated than expected. Pi (π) has been studied across multiple different areas of the world, from the Middle East, Europe, China to the United States. Its studies show information revealing the true meaning of π but also a rich history of mathematics throughout time. A more shocking discovery in π’s research was the method of exhaustion, which explored the idea that if different shapes with multiple different sides (ex: pentagons, hexagons, and so on) were drawn inside of a circle, this would lead to an increasingly more accurate calculation of π. But, this obviously was not optimal since π repeats forever, and the highest value of any mathematician (Archimedes) was a 96 sided shape known as an enneacontakaihexagon. However, even this shape did not lead to an exact calculation of π. But, the main takeaway from thousands of years of research on π is that the symbol is more deceiving than it seems since it has infinite numbers calculations and continues indefinitely. Since a circle continues indefinitely, that means π will as well, which is why π constitutes an irrational number. While it may be common knowledge that circles have infinitely many sides, that’s not exactly the case, and that’s not the exact reason for π having infinitely many digits. A circle is essentially a type of polygon with infinitely many sides, but since you clearly can't tell these same sides from the circle itself, that means every point you take on a circle is aside. So, that means π will always be an irrational number that continues forever, containing infinite digits related to the “infinite” sides of a circle. But, what is the relevance of π? Well, that can be explained using actual, real-life pie...

Apple “Pi”:

This dessert is perfect for family or friendly get-togethers, it only takes a few elements to put together and make, but the more amusing part is how this pie, like the others, happens to be circular. This means we’ll be able to see the dimensional aspects that make up this pie using π to calculate them!

Radius: 4.5 in Surface Area: 63.617 in^2 or 20.25π^2

Diameter: 9 in Circumference: 28.274 in or 9π in

Original Photography by Christina Ossa

The “Pi” is not only sweet but contains rich dimensional elements! The radius of this “pi” is 4.5 inches, and the diameter is 9 inches, so from there, we can calculate the circumference and surface area. If you don’t remember, the formula for calculating circumference is either 2πr or πd (d standing for diameter), and for the purposes of this “pi,” we’ll be using both. Utilizing both formulas, we get that the circumference of this apple “pi” is about 28.274 inches or 9π inches. Now, we can use the radius of our “pi” here to calculate the area of it, which will let us know exactly how much filling can fit into our “pi.” Using the formula πr^2 to calculate the area of a circle (our “pi”), we can infer that the surface area will be about 63.617 in^2 or 20.25π in ^2. That means we would be able to fill this “pi” with 63.617 inches of filling, which could feed at least five or six people per about 12-13 inches! These calculations allow bakers to see the exact amount of filling appropriate for a pie dish. While many (including myself) would not calculate like this, it’s interesting to figure out step by step the dimensional, mathematical aspects of pie that include the use of π.

Blueberry and Pumpkin “Pi”:

This is a pie I’ve talked about before, and you would think that this pie would be the same size as the last one, but surprisingly it’s not. Pie pans can vary by a slim margin, a fact that not many bakers take into account since the essential part of a dish is mostly the ingredients. But that shouldn’t mean anyone should undermine the relevance of the pan! Also, since these pies were baked with the same pan (albeit at different times), their dimensions should be roughly the same, and we should be able to draw similar conclusions from calculating solely one!

Radius: 5 in Surface Area: 78.540 in^2 or 25π^2

Diameter: 10 in Circumference: 31.416 in or 10π in

Original Photography by Christina Ossa

The diameter of these “pi’s” turned out to be 10 inches instead of 9 inches. That would mean the radius would be 5 inches, and from here, we can use our circumference formulas! From the formulas, we would get that this “pi” has a circumference of about 31.416 inches or 10π inches, which gives us the exact value of the outside/crimping of this pie. Now, we would want to figure out how much this “pi” dish could be filled with apple filling, so we’d switch to our surface area formula (πr^2). Using the formula, we would end up with an area of about 78.540 in^2 or 25π in^2, telling us that this pie dish would feed at least 6-7 if they took 11-12 inches of pie per piece. This is helpful information since this delectable dessert could be served and shared amongst guests fairly, and we know the optimal dimensions for filling this pie. Also, this shows us how this pie dish is superior to our pie dish in the apple “pi” since it could supply more and, as a result, feed more people. Not only did the more profound and mathematical background to the “pi” help us figure out the optimal dish to use so that we could feed the maximum amount of people!

As you can see, the relevance of π in pies is more interesting and complex than it might appear on the surface. Even though circumference, surface area, diameter, radius, and π may not be the end all be all to baking a simple pie, it could give you insight into the physics of how baking truly works and explain the mathematical aspects of baking that allow a pie to be constituted as a pie. So, next time you think π is useless or has no real-world applications, think back to actual pies and how without π, there would be no pie!

Apple “Pi”:

Ingredients:

Crust:

Refer to either “Pi” article listed below!

Filling:

-5 lbs apples -1 cup brown sugar

-½ tsp salt -2 tsp ground cinnamon

-½ a lemon, squeezed -1 tbsp + ¾ tsp cornstarch

Glaze:

-3 tbsp water -1 tbsp + ¾ tsp cornstarch

-3 ½ tbsp unsalted butter

Directions:

• Peel and thinly slice apples into a large bowl

• Add brown sugar, salt, cinnamon, lemon, and the 1 tbsp and ¾ tsp cornstarch to the apples; make sure to combine the ingredients thoroughly into the apples (use your hands if you have to!)

• Add the apples to a colander and leave over the large bowl to drain the excess liquid for about 30-45 minutes

• Once drained, add the collected liquid to a medium-sized saucepan and add the apples back into the bowl

• Keep the saucepan over medium to medium-low heat until it begins thickening

• Once the mixture slightly thickens, add the remaining cornstarch to the water to make what’s called a slurry

• Once combined, add the slurry to the saucepan mixture and allow to thicken for 1-3 minutes; after thickened, add the butter and let melt

• After the “glaze” is done, allow it to cool for at least 15 minutes and begin prepping the crust or pre-made dough into a pie dish

• Add the glaze once cooled back into the apples, and once combined add this apple mixture evenly into the pie dish

• Place either a lattice or cover (slicing thin lines on top of the top piece of dough) on top of the apple mixture onto the pie dish (refer to blueberry or pumpkin pie recipes for detailed explanations!)

• Bake at 400°F for 40-45 minutes, let cool for at least 15-30 minutes, and enjoy!

Blueberry “Pi”:

Refer to this article!: https://www.vsnorthstar.com/articles/holiday-sweets

Pumpkin “Pi”:

Refer to this article!: https://www.vsnorthstar.com/articles/fresh-pumpkin-pie-vs.-canned-pumpkin-pie%3A-is-it-worth-the-time%3F-