Category Archives: Math History

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.

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.

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

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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.

BADGING:

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.

Thanks to Mr. Victoria for sharing this article as a badging opportunity!

W.E.B. DuBois at the World’s Fair

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W.E.B. DuBois, the first African American to earn a doctorate from Harvard University, attended the World’s Fair in 1900 in Paris with some amazingly beautiful graphs (“Data Visualizations”) that showed what life was like for black folks in America at the end of the 1800’s.  Read about them and see the striking images by clicking here.

BADGING:

Read the article linked above.

Pick any three of the graphs from below the article that DuBois displayed at the World’s Fair.  For each of the three graphs you choose, answer these questions:

  1. What is the title of the graph?
  2. What aesthetic or artistic choices (colors, layout, design, etc.) did DuBois make in creating this graph?
  3. How did those choices from the previous question add to the visual appeal of the data?  Why is this graph more effective than just listing the data as a table or a list of numbers?

Then, write a single paragraph that summarizes what you learned about what life was like for African Americans in the USA at the end of the 1800s (especially in the South).  What was DuBois trying to show the world by bringing these graphs to the World Fair?

Thanks to Jason Kissel via Chris Nho for suggesting this badging opportunity!

Number Gossip

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“Can you believe what 56 did?  It’s just so…odious!”

“Oh I know.  And 43 is so lucky, I can’t even stand it.”

You probably know a lot of properties of numbers like “even”, “odd”, “prime”, “square”…but there are so many more that you might have never heard of!  Head on over to Number Gossip to get the scoop!

BADGING:

Pick a favorite or interesting whole number.  It might be your uniform/jersey number for a sport you play, or your home address, or your lucky number, or something else entirely.  Enter it into the search field at Number Gossip.

  1.  List all of the “common properties” of your number that Number Gossip lists.  If any of those properties are unfamiliar to you, you should be able to click for an explanation.   Explain in a sentence next to each property why your number belongs to that property (Where applicable, give a specific reason for *your* number, not just a definition of the property).
  2. Pick one “rare property” (if your number has one; not all do) and do the same thing as in step 1.
  3. Pick one “unique property” (if your number has one; not all do) and do the same thing as in step 1.
  4. Search Number Gossip for the whole number directly before and after the number you chose.  How are the search results different?  How are they similar?  Write a few sentences comparing and contrasting, as well as your thoughts as to why they compare the way they do.

 

 

 

Mayan Mathematics

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Certain schools on the Yucatan Peninsula in Mexico are teaching native students the mathematics that was done by their ancient ancestors in the Mayan civilization.  Check it out in the video above.

BADGING:

Watch the video and pay attention to how the Mayans write their numbers and conduct simple arithmetic.  Answer the following questions.

  1.  How would you express the number 19 using the Mayan notation?
  2. In the video, the news reporter shows how to do the arithmetic 16 + 7.  Replicate that arithmetic using drawings.
  3. Now create a drawing/notation using the Mayan method to conduct the arithmetic 18 + 6.
  4. Explain at least three reasons why it is important for these children to be taught this method of arithmetic alongside the “typical” methods (like the way you learned to do addition, for example).

 

Who Cares If Math is Useful?

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The last time we saw Dr. Eugenia Cheng, she was on The Colbert Show cooking up some fun mathematical recipes.

This time, she’s on PBS talking about how the usefulness is math is…a burden?  What could she possibly mean?

Visit the video to hear what she’s talking about.

BADGING:

Watch the video linked above (less than 4 minutes).  Answer the following questions in a couple of paragraphs.

  1.  Why does Dr. Cheng feel that we should let go of the idea that math is “useful”?
  2. What are some adjectives Dr. Cheng uses instead of “useful”?
  3. Dr. Cheng gives a number of examples of math that wasn’t “useful” until centuries after it was discovered.  Describe a couple of those examples (internet cryptography, viruses, soccer balls, etc.).
  4. How does Dr. Cheng suggest we “break the cycle” of how students (particularly elementary students) view mathematics?

 

 

A Mathematical Analysis of the Electoral College

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You may have heard that there’s a Presidential Election this year?

As this is one of the most hotly contested and emotional political races in recent memory, every facet of the election is going to be under scrutiny.  One such facet is the Electoral College.

Mathematician John Allen Paulos wrote an opinion piece back before the 2012 Presidential Election for ABC News criticizing the Electoral College system.  He posits that a candidate could conceivably lose the popular election 70,000,000 to 11 but still win the presidency.

Is that possible?  Does this carry even more weight in 2016 than it did in 2012?  Read on and see:  http://abcnews.go.com/Technology/mitt-romney-barack-obama-win-eleven-votes-electoral/story?id=16470327

BADGING:

Read the article.  Explain how a candidate could logically receive only 11 votes but still win the presidency.  Write a paragraph explaining your feelings on the Electoral College (Do you think it is fair?  Should we do it differently?).  Then research one other free, democratic country and determine how their national leader is elected.  (Example:  Prime Minister of Britain, Japan, Canada, Australia, etc.)

Gambling & Mathematics

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Many people know that mathematicians have used their knowledge of numbers as an advantage when gambling (For example: http://www.sonypictures.com/movies/21/)

What we might not know is that a LOT of new mathematical knowledge was developed as a result of gambling or “games of chance”.

Check out the Guardian article here:  https://www.theguardian.com/science/alexs-adventures-in-numberland/2016/may/05/seven-lucky-ways-that-gambling-changed-maths

BADGING:

Read the above article.  Each of the 7 bullet points lists a mathematician (or two) that contributed to this new knowledge.  Pick any three of the mathematicians listed.  Summarize (from the article) what they did to promote a new mathematical understanding based on their “hobby” of gambling.  Then research each mathematician online (Wikipedia is fine) and add a sentence or two (per mathematician) about what else they are known for (in mathematics or outside of mathematics).