Mow Your Lawn Using Math

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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.

BADGING:

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

  1. Explain the difference between “geometry” and “topology.”
  2. How does the concept of “less error” factor into the most efficient way to mow a rectangular lawn?
  3. 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?

 

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.

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!

Using Math to Cast Space Jam 2

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Some mathematicians at 538 examined the original cast of the Monstars in the movie Space Jam to see if they could estimate the closest comparable players in today’s NBA.  See who they chose for the new Monstars team!

BADGING:

Watch the video linked above.  Answer each of the questions in a few complete sentences each.

  1.  What does the acronym CARMELO stand for?  Explain in your own words what the CARMELO projections are trying to accomplish.
  2.  Look at each of the graphs that compare the original player with the new player  from the modern NBA (pictured below).  Which new cast member appears most similar to the original member they are replacing?
  3.  Look at each of the graphs that compare the original player with the new player  from the modern NBA (pictured below).  Which new cast member appears most different to the original member they are replacing?

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4.  Fred VanVleet is 9 inches taller than Muggsy Bogues was in the original Space Jam movie.  Explain how they can have the exact same rating on the “height” metric in their comparison graphs.

5.  Pick one of the statistics listed in the comparison graphs that you aren’t sure of its meaning.  Look it up in the basketball-reference glossary and explain what the statistic measures in your own words.

Who is the REAL star of “Friends”?

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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.

BADGING:

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!

 

Women are better than men at free throws

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The results of a 30-year study show that women NCAA basketball players shoot free throws more consistently than male NCAA basketball players.  See the findings here.

BADGING:

Before reading the article, make at least three hypotheses that you think might be the reason women tend to be “better” at free throws than men in the NCAA.

Then read the article linked above.

Below your hypotheses, write a paragraph explaining what the study found.  What appears to be the major factor in the women’s free throw consistency?  Compare this finding to your hypotheses.

Write a second paragraph stating another athletic comparison that you would like to see studied (for example, “Who makes free throws more consistently, left-handers or right-handers?”).  It doesn’t have to be a basketball comparison.  Explain why you think this comparison could be valuable to athletes and coaches.

Thanks to Bradley Warfield for suggesting this badge!

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!