# 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?

# 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!

# Geometric Baking

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.

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

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.

# A Song of Pi

A mathematician/musician has taken the infinite decimal digits of Pi and composed a song based on them.  Take a look and listen to the song here:

(This badge will likely go much smoother for you if you’re musically inclined or have some basic training in reading music.)

Watch the video above.

1.  First, reflect on what you think of the song.  Do you like it?  Is it pleasant to listen to?  In general, what are your feelings on using mathematics to help create a song?  Answer in a few sentences.
2. Pause the video at the 9 second mark and look at the scale he used to compose his song (A Harmonic Minor Scale).  Hypothesize in a sentence or two why he used this scale to compose his song rather than a “simpler” one (like, for example G Major).
3. Pick another irrational number besides Pi (Phi, e, the square root of two, etc.) Using the same scale and time signature (4/4) as the song above*, compose at least 8 bars of a song based on this irrational number.  You may print off sheet music here.
4. I need to hear this song.  You can record it, you can bring in an instrument and play it, or you can bring in the sheet music and I can play it on guitar (just give me a heads up so I can bring in a guitar that day).
5. Reflect on your new song in a couple of sentences. Do you like it?  Is it better or worse than the Pi song?  Has it changed the way you feel about math being used to create music?

* use a different scale and time signature if you really want to, but that seems more complicated and difficult than I am intending this to be.  But go for it if you want!  Likewise, you don’t have to worry about harmonies like you can hear in the original video, but if you’re capable and interested you are welcome to try!

This badge was suggested by USN Class of 2023 Colette.  Thanks, Colette!

# 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).

Watch the video and read the accompanying article.  Write a paragraph that explains the difference between the “traditional” way of making roasted potatoes and the “new, mathematical” way.  What changes were made and what is the advantage?  How did chefs determine that the new way was in fact “better”?

In a second paragraph, describe another food that you think might be improved using mathematics to aid in the preparation.  Describe a hypothesis you might have about how  that food might be improved using mathematics and why you think it would be an improvement.  Give a diagram if it helps your explanation.

# How Well Can You Remember Famous Logos?

STOP!  If you plan on finishing this badge, right now I want you to take a blank sheet of paper and draw any THREE (3) of the following company logos from memory (including color — not just black and white drawings unless the logo itself is black and white).  Don’t look them up, just draw what you can remember of any three of these logos:

Apple, Adidas, Burger King, Domino’s, 7-11, Foot Locker, Starbucks, Walmart, Target, IKEA.

People all over the country were asked to do this activity, and the results are interesting.  After you’ve drawn your logos from memory, click HERE to compare your drawings to everyone elses.

Draw the logos before reading the article, then look at the article.  You don’t have to read the whole thing — but read the introduction, then skip to the three sections that correspond to the three logos that you drew (You can use the icons near the top of the article to “jump” to that section”)

1.  How did you do?  Compare any mistakes you made to the most common mistakes made by other people.
2. Write a few sentences comparing common mistakes you noted between the three logos that you read about.  Do humans have any common tendencies?  Notice any patterns you see in the mistakes that people tended to make.  What were the easiest parts of each logo to remember?  Why do you think that is?
3. Read the Summary at the bottom of the page and “place yourself” on the table/chart that they showed.  Do you think you have a better- or worse-than average memory?
4. Take the interactive quiz underneath the summary  How did you do?  Better or worse than you expected?

# What Are The Most Likeable Prime Numbers?

So there’s this Twitter feed that tweets out the prime numbers…in order…on the hour…every hour.  Friend of Pre-Algebra.info David Butler analyzed the data from this Twitter feed to see which prime numbers were the most popular (via Likes and Re-Tweets).  See the results in his blog post.

`1.  Before you visit the blog post linked above, visit the Twitter feed that lists primes.  Out of the most recent 15 primes listed, which one is your “favorite”?  (You can decide how to interpret “favorite”.  Just decide which of the most recent 15 primes you like the best).

2.  Now visit Dr. Butler’s blog post where he analyzes the prime data.  Read the blog post and look at the data displays.  List at least four characteristics he noticed about the “most liked” primes, and give an example from the data to support each claim.

3.  Refer to your prime choice from question #1.  Does your choice fit any of the four categories from the second question?  Which ones?

4.  Hypothesize: Why do you think certain patterns or arrangements of primes are more “likeable” than others?  What might this have an impact on subjects like cryptography (internet passwords or even locker combinations)?

5.  Here’s a link to ten random ten-digit prime numbers?  Using what you’ve learned so far, which one do you think would be the “most liked”?  Explain your reasoning.

# Categorizing Flags

Via CityLab comes a bunch of infographics that examine how different flags around the world are constructed.  Pretty cool stuff!

Pick the United States and one other country (Your choice!  Maybe this is a country that you’ve visited, one where you have lived at one time in your life, one where a family member lives, or just one you are interested in for any reason).

Look through the infographics at the link above and answer the following questions about the flags for the USA and the other country that you chose.

1.  Do your countries’ flags (USA and the other one you chose) have any of the five most typical layouts?  If so, which ones?
2. Do your countries’ flags have any of the most typical colors included in them?  Which ones?
3. Research what the colors on your countries’ flags are used to represent. Are they the most typical meaning behind those colors, or a less-used meaning?
4. Do your countries’ flags include any of the five most common symbols?  Which ones?
5. How complex are your countries’ flags?  If they are more than just “Child’s Play”, what elements do you think made the flags more complicated?
6. Finally, imagine you were going to create a new country and had to design a flag.  Given what you learned about flag design from these infographics, how would you design your flag so that it was similar enough to other world flags (doesn’t feel like a huge outlier) but still different enough to be recognizable and unique (doesn’t feel like a copycat) ?  Draw/color a sketch of your new flag after you print out your answers to the previous five questions.