Does anybody mow their own lawns anymore? Mr. Bezaire does
Well, maybe now he can use math to cut it more efficiently. Popular Mechanics has the details here.
Read the article linked above. Answer the following questions in a few sentences each:
- Explain the difference between “geometry” and “topology.”
- How does the concept of “less error” factor into the most efficient way to mow a rectangular lawn?
- If you have a “weird lawn”, explain briefly why you should start in an area with an odd number of connections to other areas. What does this have to do with the Prussian city of Königsberg?
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:
- Describe the “sum of three cubes” problem (aka a “Diophantine equation”).
- 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?
- Why are 33 and 42 “special cases” when it comes to Diophantine equations?
- Explain how long it took computers to finally find a Diophantine solution to 33 and 42.
- 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!
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.
Then read the article linked above.
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!
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!
Read the article linked above.
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!
UPDATE: This video has been removed. This badge is unavailable for now. Will update later if it becomes available somewhere else.
The Beatles famously shared songwriting credits for all of their songs; throughout history, it’s been gradually revealed whether or not John Lennon or Paul McCartney wrote each famous Beatles song. However, there’s one song that they were never able to agree on. Hear how mathematicians have determined who actually wrote The Beatles’ hit “In My Life”.
Listen to the song above. Then you should read this NPR article and/or listen to the interview (top left of page).
Write a brief paragraph summary explaining in your own words how mathematicians determined the authorship of “In My Life”. Write a second paragraph hypothesizing: Where else might this statistical method be used? Think not just in music, but in the written word as well. How might historians and archaeologists use this method in other instances?
Finally check out this post, wherein the author used a technique similar to “Bags of Words” to see if a machine could read recipes and create new ones. The results are…interesting.
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.
- Explain (from the video) her comparison of liking magic tricks to understanding how nature works. What did she mean by this?
- What are fairy circles, and how does mathematics play a role in how termites help to create them?
- What does Dr. Tarnita hope that “patterns” and “symmetry” will help teach them about the ecosystem in the African savannah?
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.
Gerrymandering is the term for when political borders (shapes of districts, etc.) are set so that one political party/group gains an advantage. It’s widespread, but there are some cases in the court system now trying to address the issue — and mathematicians are helping. From The Nib comes a comic the describes mathematicians’ roles when it comes to Gerrymandering. Check it out!
Read the comic linked above. Answer the following questions in a couple of sentences each.
- Using the cartoon of red/blue houses, explain how gerrymandering can take an evenly split vote between two parties and make it a “majority win” for one of the parties.
- Courts have rules against districts in the past for racially-based gerrymandering. But why have the court systems been mostly powerless to rule on partisan gerrymandering cases to this point?
- Mathematicians are tackling the unresolved question of how “compact” districts can be and how to define that compact-ness. What are two ways that “compact” can be defined mathematically?
- In your own words, describe what is meant by “negative curvature”. Why is this a red flag for districts?
- How are mathematicians using “maps that could have been” as a way to frame the gerrymandering discussion?
From the original article at Quanta, see the video above for Dr. Rebecca Goldin’s explanation for why mathematics helps the world to make sense.
Watch the above video. Answer the following questions in a couple of paragraphs.
We define the term literacy as the ability to read and write (and understand what you read and write). Using that as a basis, what do you think Dr. Goldin means by the term quantitative literacy?
Why does Dr. Goldin think quantitative literacy is so important? What can individuals who are quantitatively literate accomplish?
In her Quanta interview (towards the bottom), they discuss her work with an organization called STATS. Explain what STATS is hoping to accomplish, and how it is related to her views on quantitative literacy that you described earlier. (You don’t have to read the entire article — you may — but you can skip ahead to where they discuss her work with STATS).
Ever wonder how noise-cancelling headphones work? Is it just more insulation than other headphones? Or is there more to it than that?
Turns out it is mathematical. And we have one Joseph Fourier (1768-1830) to thank for the equation that makes noise-cancelling headphones work. Check it out here: https://www.wired.com/2011/05/st_equation_noisecanceled/ (via WIRED)
Read the brief article linked above.
Print off this picture of a sound wave:
Use the information from the article to answer these questions on the page where you printed off the above sound wave:
- Under the picture of the sound wave you printed off, draw another wave that would be higher-pitched sound than the one you printed off. (NOTE: When the article mentions “frequency”, it is referencing the wavelength).
- Underneath that picture, draw another picture of a sound that would be quieter than the one you printed off.
- Explain in your own words how the article describes how an engine roar is “like an ocean in a storm”.
- In your own words, explain what noise-cancelling headphones do in order to reduce outside noise.