# Skating on Mathematically Thin Ice

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!

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

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

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

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.

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

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!

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!

# How NASA uses Origami

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!

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.

# How Half-a-Million Home PC’s Finally Cracked an “Unsolvable” Math Problem

Many people’s home computers sit idly during the day when homeowners are away at work or school.  Did you know that some organizations allow you to connect your computer to a mainframe so that they can “borrow” bits of your operating power to work on difficult problems?  The Charity Engine is one, and it helped to solve one of history’s great unsolved math problems.

Watch the the first 5 minutes of the Numberphile video embedded above, and then read this brief Popular Mechanics article.

Answer the following questions in a few sentences each:

1.  Describe the “sum of three cubes” problem (aka a “Diophantine equation”).
2.  Explain why some numbers (like 4 or 5) will never be written as a sum of three cubes.  What mathematical property do these numbers share that makes them unwritable in this way?
3. Why are 33 and 42 “special cases” when it comes to Diophantine equations?
4. Explain how long it took computers to finally find a Diophantine solution to 33 and 42.
5. Find any two Diophantine solutions/equations that weren’t shared in the video or the article.

# Who is the REAL star of “Friends”?

A data scientist studied the transcripts for every episode of the hit TV show Friends to try and determine who the real “star” of the show is.  Which Friend is the show really about? Read the article to find out more.

Assuming you are familiar with the show Friends (why are you doing this badge otherwise?!  There are plenty of others that might interest you more!), write a short paragraph explaining which Friend you think is the main character of the show.  Explain your reasons for making that choice.

In a second paragraph, explain the data scientist’s reasoning for making his choice.  Include the five categories (graph headings) that he studied and how they helped him to arrive at his conclusion.

Then, in a final paragraph, state a data point that you think the data scientist should have also included to help make his decision.  What other information do you think could help decide who the most important character is on Friends?  Do you think including this information would change the results of the study?

Thanks to Jason Kissel for suggesting this badge!

# The Mathematics of the Black Panther

As part of Chalkdust Magazine‘s celebration of Black Mathematician Month 2018, Dr. Nira Chamberlain discusses one of Shuri’s creations in Marvel’s Black Panther movie; T’challa’s suit, which supposedly disperses energy from impact blows and absorbs the shock to minimize damage.  Is this mathematically possible?  Read on to find out!

In a paragraph, describe what would have to be true about a suit that disperses kinetic energy in the way that Black Panther’s suit does in the movie.  A suit like that hasn’t been invented yet, but a mathematical model has been made.  Describe in your own words what characteristics that suit would have in order to make the energy dispersal possible.

In a second paragraph, think of some movie tech that doesn’t yet exist (choose a favorite movie that contains some sci-fi or futuristic element to it).  If you were to make a theoretical model of that tech, what type of mathematical and scientific questions would you have to address before attempting to build a prototype?  For T’challa’s suit, mathematicians had to determine how to disperse the shock of impact.  What would have to be mathematically feasible for different movie tech?  Be sure to tell me what movie and what tech you’re discussing!

# Fairy Circles and the Mathematics of Nature

Mathematician Dr. Corina Tarnita studies the mathematics of nature and biology, including things called “fairy circles”.  Watch the video above and read more about her work here (via Quanta).

Watch the video and read her interview at the link above.  Answer the following questions in a couple of complete sentences each.

1.  Explain (from the video) her comparison of liking magic tricks to understanding how nature works.  What did she mean by this?
2. What are fairy circles, and how does mathematics play a role in how termites help to create them?
3. What does Dr. Tarnita hope that “patterns” and “symmetry” will help teach them about the ecosystem in the African savannah?

# The Math Of Roasted Potatoes

Chefs in Great Britain have used “maths” to determine the best way to cook roasted potatoes.  See the magic formula here (courtesy of the Sun).