Professor Kate Poirier | D772 | Spring 2023

• $\pi$ day is 3/14
• Due date for this assignment: Monday, March 20

The number $\pi$ is one of the most famous numbers and appears all over mathematics. Since $\pi$ is approximately 3.14159, on March 14 at 1:59pm (3/14, 1:59) we observe $\pi$ day. Whenever we can, we celebrate by eating pie and doing some $\pi$ day activities. It’s not a national holiday, but it should be!

For this assignment, in honor of $\pi$ day you will learn something new (something you don’t already know) about the number $\pi$. Then you will write a short summary of what you have learned, and type your summary in the comments on this post. Make sure to include the source you used. You may include images in your comment if you like.

Contents

## Option 1

If you are available today (3/14) at 1:59pm, join this free virtual event as CityTech math professor Sandie Han guides us through a $\pi$ day activity. Sign up here. Include “live event” in your comment.

## Option 2

The YouTube channel Numberphile has tons of interesting videos about different elements of mathematics. Since $\pi$ is so important and so prevalent, they have a whole playlist devoted to $\pi$. Choose one of the videos to watch and summarize. Try to choose a video that one of your classmates hasn’t already chosen. Include the title of the video in your comment.

## Option 3

If you find another video or article that teaches you something new about $\pi$, you are welcome to summarize that one. Include a link to it in your comment.

1. Javier Bonilla

“Calculating Pi with Real Pies”

The video was focused on trying to calculate pi using real pies in a place where was drew the circumference and then put the more precisely the amount of pies in the figure and then count them and the result divided the circumference amount by the diameter amount of pies and surprisingly got a value near to 3.14.

2. Javier Garcia

How Pi was nearly changed to 3.2 – Numberphile

I never knew that Pi was going to be changed in 1897 century to 3.2 by Edward Goodwin. What is insane is that the story goes beyond that, meaning going to court, which led to the Indiana Pi Bill. What Edward was trying to do was square the circle, which was nearly impossible. I never knew anything behind the story of how Pi started or got to where it is, but the video really got me to research the person’s facts, and the announcer or host was right. https://www.youtube.com/watch?v=bFNjA9LOPsg&list=PL4870492ACBDC2E7C&index=4

3. Danny Mizhquiri

Option 2 – Pi is Beautiful – Numberphile

I am shocked and amazed at how capable the complexity of pi is in artistic work. Martin Krzywinski provides examples such as the pi poster where the digit is transformed into color dots, and also another poster where some dots are connected in adjacent digits which gives the meaning of randomness. Another example of the beauty of pi was the formation of the pi path. It is a circular form where numbers are placed from 0 to 9 and connected from 3,14 to etc which gives a shape structure of a star at the center to the edges. Then in his work on Random Numbers, there was discovered that pi had a sense of familiarity from the pattern of a randomly generated number to accidental similarity where he compared other famous mathematical numbers such as the golden ratio and e. Which is where he lines them up and finds the same digit. Then in his experiment, there was the fascinating similarity that pi,e, and the golden ratio have something in common, and can be transformed into a picture of a circular one where it gives a shape of a triangle and it never touches the center.

As such, despite pi randomness, there is a similarity, order, and beauty in the realm of Math.

4. Ken Mei

Option 2 – Mile of Pi – Numberphile

It was interesting to see the first million digits of pi. Brady printed out the first million digits of pi on a continuous mile long piece of paper and had it slowly unraveled on a runway. Through the process of unraveling the first million digits of pi it took 4 hours to reach the end. In the process of unraveling the digits of pi we were given various facts of pi. Some facts are after reaching 123 yards being long past the familiar bits of pi equals 3.1459. Brady mentions someone who memorized pi up the 67,890 decimal place which is the world record for memorizing pi and measures over 125 yards on the runway. He also mentioned a digit of pi, specifically the number 4 and for the next 157 digits it doesn’t contain a number 4. He states that it is the longest run in the first million digits that has one digit completely missing.

5. kevin

Option 2 – Numberphile – Pi and the sized of the universe.

After watching this video I learned a lot about pi. I first learned that taking the first 39 digits, that includes the 3. and 38 decimal places later to measure the circumference of the observable universe . That is crazy to me how only 39 digits from pi is needed todo that. That would be in the width of 1 hydrogen atom. When finding the diameter of the observable universe and multiplying it by pi, you get a more accurate reading for the diameter with pi, rather without it. I also learned in the 17th century a Dutch man name Ludolph Van Ceulen life work was working on pi. He was able to figure out 35 digits of pi. At that time they did not have decimals, he had to use fractions. Those 35 digits are also on his tombstone. I also learned that in the 19th century a guy had 707 digits of pie . But in the 1945 they found that the last 180 digits where wrong. around the 500 digits was suppose to be a 4 not a 5. I never knew any of this before. Its pretty cool knowing this now. When I was in high school my teacher always did something special for pi day, but I never learned this before.

6. benyusufov

“Buffon’s Needle and the Surprising Importance of Pi,” a video from Numberphile’s Pi playlist that I found particularly interesting, is titled “Buffon’s Needle and the Surprising Importance of Pi.” Brady Haran, a mathematician, explains the concept of Buffon’s Needle, a thought experiment proposed in the 18th century by Georges-Louis Leclerc, Comte de Buffon. Dropping a needle of a specific length onto a floor marked with parallel lines spaced apart is the experiment. One can estimate the value of pi by counting the number of times the needle crosses a line and using probability calculations. Harun uses a computer program to simulate this experiment and compares the results to the theoretical value of pi. He also demonstrates how Buffon’s Needle can be used to calculate pi.

7. Jocelyn Nacimba

Option 2 – Numberphile – Sounds of pi

This video references the digits of pi to music. Professor Phillip Moriatry explains how pi can be used to play the c major scale because sine the scale doesn’t have any sharps or flats, the melody corresponds to the digits. The video also talks about Feynman Point. The Feynman point is a sequence of six 9s that begins at the 762nd decimal place of the decimal representation of π. It is named after physicist Richard Feynman, who once stated during a lecture he would like to memorize the digits of π until that point, so he could recite them and quip “nine nine nine nine nine nine and so on”, suggesting, in a tongue-in-cheek manner, that π is rational. I never knew these facts before because I always thought that pi is a random number that never ends and only used for mathematical applications but now know that pi is special and has various applications.

8. Luijen Payano

Option 2 – Numberphile – Sounds of Pi

I learned that pi when converted into sound can sound musical. There isnt a repetition but if played slowly it almost sounds like something. There is also a “Feyman Point” in pie in the 762 point of pie there is six 9’s in a row.

9. JTruong27

Pi and Four Fingers – Numberphile

In the video, it talks about how in The Simpsons, the characters only have four fingers on each hand. In an episode, Apu is questioned about how good his memory is, and tells the court that he can count to the 40,000 digit of Pi. He states that it is 1, but that is the decimal variant of pi and not the base 8 version. We use base 10 and decimals because we have 10 fingers. In the video it talks about prior ways of calculating pi, such as using the using polygons with increasing sides and their perimeters to make an estimation for pi. The simpsons writers then talked to David Bailey, an expert on pi on what the 40,000 digit was. He sent them a paper consisting of 40,000 digits of pi.

Option 2

Pr and Bouncing Balls — Numberphile

In this video, the video is essentially about rolling balls with different sizes into each other as the bigger ball hits the little ball in into the wall the little ball will bounce of the wall and hit back into the big ball. Now how does this relate to pi, well in the video Numberphile used pi to record how many hits would it take for the little ball to actually know the big ball in the opposite direction. In this video the mass of the big ball will be M= (16 x 100^n)m where m represents the mass of the little ball. So, if these conditions are met then the number of collisions the little ball would need to have to make the bigger ball go in the opposite direction is the first N plus 1 digits of pi. So if n=0 it will take three collisions because pi is 3.14 so 0+3=3 therefore it will take the little ball three collisions. This was very fascinating because you would never think that pi would have any relevance to this at all. I thought it was more into physics but pi could actually be used in a mathematical instance to solve how many collisions a little ball has to make to turn around an incoming ball will a greater mass of M= (16 x 100^n)m.

11. Opemipo Odugbemi

It is incredible how you can calculate Pie from pie(yeah eatable pie). 264 and two-thirds pie lined up on the circumference and Diameter of a circle 84 and 1/3. Divide the 264 and 2/3 by 84 and 1/3 you have 3.13834. Round it up and You have 3.14. I’m blown away!! Yeah I was shocked too.

12. Atta Tariq

Happy Pi day. I just read this article and learned new things about pi. Pi is the ratio of the circumference of any circle to the diameter of that circle. Pi day falls on the same day as Albert Einstein’s birthday. Pi has been known for thousand of years and used by ancient civilizations like the Babylonians and Egyptians. Pi has been calculated to over 31 trillion digits. It is also used to create art, music and even poetry. Overall, the article provides a fascinating glimpse into the history, significance, and applications of pi.

13. Rubab Tariq

Option 3 :

Happy Pi Day

This enigmatic number without end was given the Greek letter in 1706 by self-taught British mathematician William Jones, probably because it is the first letter of the Greek phrases for perimeter and periphery. Leonhard Euler, a Swiss mathematician, subsequently made usage of the sign more common, but it wasn’t widely used until 1934. Pi has a cult following that includes plenty of nerdy tattoos and even has its own national holiday due to the fact that it appears everywhere, including arcs, pendulums, and interplanetary navigation in addition to circles. See how you may observe National Pi Day by reading on. National Pi Day was formally proclaimed by the US Congress in 2009, although its (certainly not “square”) origins may be traced to 1988 and a guy by the name of Larry “The Prince of ” Shaw.

https://science.howstuffworks.com/math-concepts/pi.htm

14. Juan Giraldo

Pi and Buffon’s Matches – Numberphile

This video was very interesting to watch. At first, what the guy was saying was making no sense, but after he proceeded with the demonstration, everything became much clearer. Basically, we take a flat surface where we draw lines and we make sure the gap between each line is 2 matches long. Then, we use a bunch of needles or matches and spread them randomly on the floor. After they’re spread, whatever match is crossing a line, gets removed from the surface. Finally, we divide the matches we took out over the total quantity. After that, we can go further if we want where we take intergrals which will allow us to find the probability for the matches to cross the line.

15. charlie

Option 3

The video “3 Ways Pi Can Explain Practically Everything” taught me that Einstein also used Pi in order to prove his theory that anything with momentum and energy can curve space and time around it. This was interesting because the video then stated that anything with circles or spheres will use Pi. I never put much thought of how much Pi is used not only in math but in the real world in order to find many things. You can even find the circumference of the universe!

16. Michael Krisno

Option 2

Pi and the size of the universe

In the video the speaker explained we only need the 39 digits of pi to accurately measure the circumference of the observable universe. He explained that even though that 10 trillion digits of pi have been calculated with supercomputers, he argued that only a handful of digits is required for accurate practical engineering. I think it’s very interesting to me because like a lot of people I think that precision engineering would require very precise usage of pi, probably to several hundred digits. I assumed people keep calculating the infinite numbers of to get an accurate measurement for calculations using pi. The video informed me that the calculating the several trillion digits of pi is to test the computing power of a computer or algorithm.

17. Damian Kyle Brathwaite

Option 3: “Pi Day: 7 interesting facts about the most famous number in mathematics”

In this article I learn many new interesting facts that I have never heard before. For example, Pi is a mathematical constant that is believed to contain all possible combinations of digits, including every conceivable string of numbers and letters, making it all-encompassing. Although it has not been proven, it is theoretically possible that any given string of digits can be found within the infinite sequence of pi’s digits. Also, another really cool fact is The Babylonians and Egyptians used different approximations for pi, while the Bible describes dimensions that suggest a value of 3. These were all some facts that I was unaware of until now. I hope you learned something new like I did!

18. Maharin Khondoker

Option 3

In the video by Numberphile, I learned that pi is a mathematical constant that represents the ratio of a circle’s circumference to its diameter. The video explores the history of pi and shows how it is used in various areas of mathematics and science, such as geometry and calculus. The video also explains several methods for calculating pi, including Archimedes’ method and Buffon’s needle experiment. Additionally, the video explains that pi is a transcendental number, meaning it cannot be expressed as the solution to any algebraic equation. The video concludes with some fun facts about pi and the cultural fascination that people have with it. Overall, the video provides an entertaining and informative introduction to pi and its many interesting properties.

19. Kate Poirier

[latexpage]

Excellent $\pi$ day finds, everyone! As you’ve seen, $\pi$ pops up all over mathematics, even in places one might not expect it to. Here’s one more short video that you might like that shows how $\pi$ (unexpectedly) appears as the sum of a familiar infinite series (as in Calculus II): https://www.youtube.com/watch?v=YBNvta_p2xQ

20. Evan Anthony Cedeno

Option 3 – Find your own article/video? Summarize it here! 😀

One really fascinating thing about Pi, it is (apparently) all encompassing! Pi is thought to have every string of digits that are known or will ever be known, being that Pi has an infinite number of digits!

This essentially means that almost everything we base of a circumference while useful and functional, is technically inaccurate? But I mean, a circle is still a circle sooo, does it matter?

Option 2

Video: Calculating Pi with Real Pies – Numberphile

The objective of this video was well…..calculating Pi with …. pies. I obviously choose this video cause I hungry. Moving on, the way this worked is that they place pies along the circumference and diameter of the circle measuring a circumference of 264.66 pies and a diameter of 84.33 pies. To get Pi you have to divide the circumference by diameter which will equate to 3.13834 approximately 3.14.