As we all know, this last week celebrated “Pi Day,” or March 14. Since this date is written 3/14 and pi is roughly 3.14, this date is set aside for reflection on the world’s favorite irrational number.
What is pi exactly again? It’s the ratio of the circumference of a circle to its diameter, which I have deliciously illustrated below:

The fact that this is an interesting number was known even in ancient times, as shown in the Bible. For example, in Kings 7:23, King Solomon describes the process of building the Temple of Jerusalem (my research indicates that this occurred around 760 BCE) and includes this royal observation. Solomon brought in Hiram, an expert in working brass, to do this part:
“He made the Sea [or washing basin for the priests] of cast metal, circular in shape, measuring ten cubits from rim to rim and five cubits high. It took a line of thirty cubits to measure around it.”
Since a cubit is somewhere in the neighborhood of 20 inches, the “sea” was around 17 feet across. Wow! Big! Anyway, I decided that I should do an experiment to find out whether 30 cubits / 10 cubits was really the value of pi, given that this metal representation of the sea is in the Bible and all. Solomon is saying that a circle has a circumference of 30 and a diameter of 10, or that pi is equal to 3. Let’s try and find out.
So I started with a pencil, a piece of paper from the kid’s easel in the basement, and a Calphalon 10″ saucepan. (These saucepans are fantastic! You can bake stuff in the oven in them and everything. You can see that mine has been loved.) Here is the setup:

Using the pencil, I traced the circular shape of the pan on the paper. Next, I used a string to measure the distance around the circle and taped the string to the paper:

I can use the length of this string to measure the circumference of the circle. Let’s say this distance around the circle, and the length of my string, is 30 cubits. I next took the string off the paper, and folded it exactly into thirds, and cut a pink pipe cleaner to the exact length of one-third of the string. Voila! We have a 10 cubit pipe cleaner.

I now had a way to compare my 10 cubit pipe cleaner to the 30 cubit distance around the circle. If King Solomon was correct regarding the measurement of his model of the sea in the Temple, then the pipe cleaner should be exactly the distance across the circle, confirming that the value of pi is 3. Just like in my picture of the delicious apple pie at the start of this piece. I re-taped the 30-cubit string back to the circle and placed the 10-cubit pipe cleaner directly across the center.
Here is the result:

Oh, no!
No matter how I set the pipe cleaner across the circle, it sticks out of one side. If the relationship of the circumference to the diameter were 3:1 as described by the wise King Solomon, then it should have fit exactly. So I guess that pi is not 3.
At this point I feel that I literally owe an apology to any of you who thought that everything in the Bible was literally true. Clearly, King Solomon was literally wrong in his description of this part of the Temple, and also was being literally untruthful to Christians regarding a basic characteristic of the world, in this case regarding the ratio of the circumference to the diameter of a literal circle. (See how I am literally having some fun at the expense of Biblical literalism?)
So, pi must be a little bit larger than 3. But, how much larger? How can you know? I enlisted my grandkids in the pursuit of the truth. And who wouldn’t? There is great truth in the young.

For this experiment, I reached back to the 18th century and to Georges-Louis LeClerc, the Compte de Buffon. (In English, that means that he was a Count, and gifted mathematically just like the titled muppet on Sesame Street.) Here is a picture of him.
He posed the following mathematical question, often referred to as the paradox of Buffon’s needle: suppose you have a floor with stripes of equal width, and drop a needle randomly on it. What is the probability that the needle will lie across the boundary between the stripes? It turns out that if the stripes are the same distance apart as the length of the needle, then the probability is 2 times pi.
OMG! This means that we can derive the value of pi by dropping elongated things at random on a surface properly marked with lines the length of the thing, and after some number of drops, the ratio of things dropped to things crossing lines will approach a multiple of pi. Divide by 2, which my grandson David knows how to do, and we are home free. I chose to drop hot dogs on a table, enlisting the kids to do the dropping so that it would be highly random. And I let them use calculators.
I started by buying an 8-pack of Boar’s Head gluten-free hot dogs and measuring them. I thought Boar’s Head would work well, and would taste good later. According to their manufacturer, they deliver exceptional flavor and a superior bite with a “snap.” Here are the results of my measurements:

Note that the hot dogs are not all the same. It’s part of what makes them so good! On average, the 8 in the package that I bought were 13.6875 cm long. I took a long roll of paper and marked lines every 13.6875 cms, or as close as I could get to it.
Next, the kids took turns dropping the dogs onto the paper. Here is John taking his turn, with his mom looking on for encouragement:

Each of the three grandkids had their own approach to the task. John tended to drop them with a flourish, while David would toss them more assertively so that we usually had a few “out of bounds.” James mostly just dropped them.
The results:

The totals on the outer columns were preliminary and turned out not to be consistent with the hash marks. Science! Things go wrong! There were 140 total hot dogs dropped (based on recounting the hash marks), with 81 of them crossing between two stripes. Plugging this in to the formula (2*total number dropped)/(crosses) yields the value of 3.45679 for pi. This is about a 10% error, but given the limited attention span we all have for science, it is a fantastic result.
I personally think that our answer was better than the actual “pi” since the first five digits are 3,4,5,6,7 which are a heck of a lot easier to remember than 3.1415.
In search of a better way to figure out the value of pi, I decided to turn to AI for a more modern approach. As we all do these days.
Given that I have a free account on ChatGPT, the world’s most famous AI chatbot, I logged in and asked it to “please calculate all digits of pi.” This was, of course a trick question! It is impossible to calculate all the digits of pi, since pi is an irrational, non-repeating number that has an infinite number of digits. Falling for the trick, I got this answer:
“Calculating all digits of pi would require a significant amount of computational resources and time, especially if we’re aiming for a high level of precision. While it’s theoretically possible, it’s not practical to do it in a reasonable time frame on a standard computer.“
Ha ha! After the laughter subsided, I asked it to write me a computer program that would calculate the value of pi. I got this answer, written in the programming language Python:

Not bad for a robot that thought it was theoretically possible to calculate all digits of pi. This program is sort of the computer equivalent of throwing hot dogs on the dining room table; it puts dots (think of them perhaps as M&Ms) at random locations inside a square, and then counts how many of them happen to fall inside one quarter of an inscribed circle. This turns out to be an approximation of pi! Who knew?
It starts by asking how many M&Ms you want to drop. So, I ran it with 140, to see how close our robot overlord would come to the answer I got by enlisting my grandkids. The answer: 2.914285714285715. I will let you do the math regarding who did better. I hope it’s the kids.
Thank you for reading this far. You deserve to treat yourself to a hot dog. Come back again for next year’s celebration of pi day, when I hope to get to the bottom of how best to make pi with ingredients that you might find in your kitchen.







