An Aperiodic Monotile!

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You might have noticed Mr. Bezaire’s tattoo on his right forearm. It’s mathematical! (Shocker, I know). In Spring of 2023, mathematicians discovered a “new” shape. Not that the shape was necessarily new, but something new was proven about this particular shape. Read more about this shape in this article from the Guardian.

BADGING:

Read the article linked above and answer the following questions in your Badges’ Google Doc:

  1. Define the following two words: aperiodic and monotile (<– some links to help you there, since the article doesn’t do a great job defining each word). How does the combination of those two words describe what is unique about this shape?
  2. The article also calls this an “einstein” shape, even though it has nothing to do with famous scientist Albert Einstein. Why do they use that name?
  3. How many different shapes were in the first example of aperiodic tiling?
  4. In the article, mathematicians talk about how they “proved” that this is an aperiodic monotile. What might you imagine would be difficult about *proving* that a shape like this never repeats itself?
  5. In the math classroom, there are a set of twelve 3D-printed “hats”. Come by in a study hall, and put them together (sort of like a jigsaw puzzle). Take a picture of your design and include it in your Google Doc (HINT 1: Remember that for this to fill space, some of the tiles need to be reflected or “flipped” over, so if you’re stuck, try flipping a couple). (HINT 2: Use a picture from the article or the still image in the video above to see how to join the 12 tiles together).

Ancient War Tricks and Mathematics

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Quanta Magazine has an interesting article about how an ancient Chinese warfare technique is used in mathematics today, including making predictions for…comets? Check out the article here.

BADGING:

Read the article linked above.

Then, answer the following questions.

  1. One of the first scenarios in the article states: “In a morning drill you ask your soldiers to line up in rows of five. You note that you end up with three soldiers in the last row.” Make a list of the first 10 possible number of soldiers that could fit this arrangement.
  2. One of the next scenarios in the article states: “...then you have them re-form in rows of eight, which leaves seven in the last row.” Make a list of the first 10 possible number of soldiers that could fit this arrangement.
  3. The third scenario in the article states: “…and then rows of nine (soldiers), which leaves two (soldiers in the last row).” Make a list of the first 10 possible number of soldiers that could fit this arrangement.
  4. Explain how, once you found the first number shared by each of the three lists above, you could “jump ahead” to the next number shared by each of the three lists.
  5. Define the term “pairwise coprime“. Give an example of two numbers that are pairwise coprime.

The Perfect March Madness Bracket

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If you’ve ever filled out a March Madness bracket for the NCAA tournament, you probably realize that you aren’t super likely to pick all of the games perfectly. See how bad your chances are here.

BADGING:

Read the article linked above. Answer the following questions in a couple of sentences each.

  1. How do we arrive at the odds of 1-in -9.2 quintillion? Explain the mathematics that gives that large of an answer.
  2. One mathematician actually estimates that your odds are between 1-in-10 billion and 1-in-40 billion. Explain why he feels that you have these slightly better odds than the original 1-in-9.2 quintillion.
  3. Using the national accuracy of 66.7% when picking first-round games, and assuming we could continue that success rate over the course of the entire tournament, what are the odds of picking a perfect bracket?
  4. Over the past 8 years of bracket challenges, winners have averaged picking 49.8% of games correctly. Using that percentage and the techniques you saw used in the first three questions, what are the odds of a winner predicting a perfect bracket?

Thanks to Hugo W. for suggesting this badge!

Why Does Voting Take So Long? Math and Racism.

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There’s been a lot of attention paid to the amount of time it takes to vote in this 2020 Election recently. Turns out the main reasons are math and racism. WIRED can explain more.

BADGING:
Read the WIRED article linked above. Answer the following questions in a few sentences each.

  1. There are a number of variables (reasons) that can explain why some polling places have a long wait time. List some of them here, and give an explanation for one of them.
  2. There are a few variables (reasons) that researchers surprisingly discovered did NOT have any effect on the wait time or not. List them here, and for one of the reasons explain why it might be a surprising discovery.
  3. How could a better understanding of societal racism lead to decreased wait times in some voting locations?
  4. Visit THIS LINK (this was created by the mathematician mentioned in the WIRED article to help visualize wait times at polling locations). This year, Mr. Bezaire waited for exactly 1 hour to vote, between 2 and 3 pm in the afternoon. Play with the variables on this graph to come up with any scenario that makes this wait time possible. Explain the variables required to make this happen.

Skating on Mathematically Thin Ice

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How thin can ice be before it breaks beneath you? Would you believe that mathematics can explain the answer? Watch the video above to learn more!

BADGING

Watch the video above and answer the following questions in a couple of sentences each.

  1. How is the thickness of the ice related to the sound that the ice makes? What “pitch” indicates that the ice is ready to break?
  2. List the three things that the mathematician observed about thin ice. Explain how each one is related to mathematics.
  3. What’s the name of the formula that relates the sound the ice makes to its thickness?
  4. What is his motivation for doing this dangerous activity?

Thanks to Jaymin P. for suggesting this badging opportunity!

The Math Behind the Sydney Opera House

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Interested in architecture? See some of the math behind the iconic Sydney Opera House in the video above.

BADGING:

Watch the video above. Answer the following questions in a couple of sentences each.

  1. Explain the difference between a catenary dome and a parabolic shell.
  2. Explain why a catenary dome was not useable for construction of the Sydney Opera House.
  3. Explain why a parabolic shell was not useable for construction of the Sydney Opera House.
  4. Explain why a sphere was acceptable for the construction of the Sydney Opera House.
  5. How is it possible for a sphere to produce different size domes if they’re all from the same shape and curvature?

From the NFL’s Big Data Bowl

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Alex Stern was a High School student volunteering at a nursing home when he heard about data analytics for the first time. Now, a few years later, he’s finishing college and presenting for NFL teams at the Big Data Bowl. Read about his story here.

BADGING:

Read the article linked above. Answer the following questions in a couple of sentences each.

  1. What was the context of the first model that Alex heard about when volunteering at the assisted living facility? What was the firm measuring about the assisted living facility?
  2. What was Alex’s undergraduate degree at the University of Virginia? What is he studying in graduate school (for his Master’s degree)?
  3. Explain Alex’s football algorithm and what it measured. Why might NFL teams find this information important?
  4. Alex learned a lot about communication when presenting to the Big Data Bowl. Why is it important for statisticians and data analysts to be good communicators?

Copywriting Every Possible Melody

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What would it take to own the copyright on every possible melody that could reasonably be created by humans? Watch the video above and find out!

BADGING:

Watch the above video and answer the following questions:

  1. The first computation they wanted to attempt was 8810. In a couple of sentences, explain where those values came from (what does each number represent) and why they ended up abandoning that plan.
  2. What mathematical calculation did they compute where the answer was 68.7 billion melodies? What did those values represent that led them to that answer?
  3. The computer programmers created these 68.7 billion melodies in 6 days. Before this, assuming music was being written in the traditional way, how long was it estimated to take before we “ran out of new music”?
  4. The creators of this project explain that they did not do this so they could force payment for any new melody. Explain who they are trying to support by embarking on this project.
  5. Write a paragraph expressing your opinion: Should people be able to “own” a melody? If there are a finite number of melodies available to humans, is it right for any one person to own one (or more) of them?

Thanks to Braun M. for suggesting this badge opportunity!

Geometric Baking

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A couple of bakers have adopted mathematics into the aesthetic design of their creations. You can see Dinara Kasko’s cakes here, and you can see Lauren Ko’s pies here.

BADGING:

Visit both of the links above and look at the artist’s creations.

Make a list of at least 7 mathematical/geometric concepts or ideas you see included in their creations. Pick at least one that you see in BOTH women’s creations.

Pick at least two culinary (food) terms that you weren’t familiar with from the descriptions, look up their definition, and explain what they mean.

Then, make a drawing for an idea you have for a mathematical cake or pie of your own in the style of either Dinara Kasko or Lauren Ko (your choice, just pick your favorite). Label your drawing with both the flavors/ingredients that you will include, and also the mathematical concepts that you plan to include in your creation. (NOTE: Instead of a drawing you’re welcome to actually bake something and include a photo of it!)

How NASA uses Origami

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Did you know that the ancient Japanese art of paper folding (origami) is mathematical in nature?  Did you know that NASA actually uses origami when designing spacecrafts?  Watch the video above to learn more!

BADGING:

Watch the video above.  In a short paragraph, summarize how NASA uses origami when designing spacecrafts.  Then, visit THIS PAGE of origami instructions to create any flower of your choice (if you don’t have suitable origami paper, Mr. Bezaire has some you can borrow).  Include a picture of this origami creation in your Badge Google Doc.  Then, write a second paragraph that describes different mathematical properties/ideas/concepts that you saw and experienced while making your origami creation.