Your Final Exam

POSTED BY , ON January 19, 2012, 23 COMMENTS

Several years ago, Hilary Thayer Hamann published a wonderful book called Categories On the Beauty of Physics. The book, which I highly recommend, beautifully blended accessible explanations of various physics topics with illuminating selections from literature and fine art. (Paintings from the Art Institute’s collection were used for the topics “momentum,” “orbit,” and “particle.”) Subsequent volumes covering other scientific disciplines were planned, but alas, there is still only one book in the series.

This great book came to mind one day as I was walking through Contemporary Drawings from the Irving Stenn Jr. Collection, an exhibition on view in galleries 124-127 until February 26. It is plain to see that many of the drawings in the exhibition relate to mathematics, including arithmetic, geometry, patterns, and codes. It struck me, though, just how many of the drawings might be used to literally describe or illustrate traditional math problems like we’ve all seen in school. Imagine the wonderful textbooks that might result from collaborations between educators, artists, and museum curators…

Just for fun, I wrote a few math problems for some of the drawings in the exhibition. These problems probably miss the point of the drawings and definitely fall short as a useful educational tool. But, for the one or two of you who relish getting extra math homework from art museum blogs: enjoy!

Just to make things interesting, the first person who submits a comment below with the correct answers to all three problems will receive a complimentary copy of the exhibition catalogue. So sharpen your pencils and get to work! You may begin.

#1: Based on Mel Bochner, Study for Double Solid Based on Cantor’s Paradox, 1966

A solid form is constructed out of small blocks. Each small block is a cube having dimensions 1 ism x 1 ism x 1 ism. (An “ism” is a made-up unit of measure).  There are no hollow cavities inside the form. The entire solid form, which is 15 ism tall, is cut along a plane of symmetry into two pieces, as shown above. What is the volume of each half of the solid form?

#2 Based on Robert Moskowitz, Red Cross, 1986

A cross-shaped tank holding 600 gallons of red paint sits in the middle of a large white room. For reasons that are not entirely clear, the tank suddenly begins to leak from all twelve of its vertical faces. If half of the faces each leak at a constant rate of 1 gallon every 3 minutes, and the other half of the faces each leak at a constant rate of 1 gallon every 6 minutes, how long will it take until the tank is half empty?

#3 Based on Robert Mangold, Circle In and Out of a Polygon 2, 1973

A regular hexagon is inscribed inside a circle, which is itself inscribed inside a square. An irregular hexagon is formed by half of the square and half of the inscribed hexagon, as shown above. If the radius of the circle is 1 unit, what is the area of this irregular hexagon?

EXTRA CREDIT: Write your own math problem based on a work in the Art Institute’s collection and submit it to If we get enough problems, we will post a few of our favorites. Problems can be easy, hard, serious, funny, or whatever. Be creative. Have fun.


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23 Responses to “Your Final Exam”

  1. 340 cubic isms; 2700 minutes or 45 hours; 5 square units?

  2. Darren Nicholson says:

    O.K., here goes:

    #1 – 2324 ism^3

    #2 – 200 minutes (or 3 1/3 hours)

    #3 – (3√3)/4 + 2 square units (or approximately 3.299 unit^2)

  3. Bart Seaman says:

    340 ism³, 100 minutes, 2 + ¾√3 unit²

  4. Steven says:

    760 cubic isms;

    720 min, or 12 h;

    2 + 0.75*sqrt(3) square units, or approximately 3.3 square units?

  5. Steven says:

    Wait wait wait wait wait no! My answer is 120 minutes, or 2 hours for the second one!

  6. chrisd says:

    I’ll send this link to my freshman who is taking advanced algebra and geometry. This makes my brain hurt.

  7. Stoney Belter says:

    I agree with the guy that got it right. I just had it first.

  8. 2990 ism
    600 min or 10 hours
    I didn’t even try the third one…

  9. Cassandra Swierenga says:

    #1 60 square isms
    #2 10 hours
    #3 3.5 square units

  10. Kai Mazurczyk says:

    Thanks for this fun exercise. I got the same answers as Bart: 340 ism3 each, 100 min, and 3.30 units2.

  11. HS says:

    Dang, Bart beat me to it.
    340 ism³, 100 minutes, 2 + ¾√3 unit²

  12. Crystl says:

    1) 340 cubic isms
    2) 100 minutes
    3) 3.125 square units

  13. Tamra says:

    Let’s see, here’s what I got:
    1. 340 isms^3
    2. 200 minutes or 3 hours 20 minutes
    3. 2+3/4√3 or 3.299 units^2

  14. Tamra says:

    If I could, I’d like to change my second answer to 100 minutes or 1 hour 40 minutes! I missed a portion of the question ^_^;;

  15. Troy says:

    We have a winner: Bart Seaman. Bart, send your mailing address to, and we’ll send you your prize.

    The answers:
    #1: 340 ism³
    #2: 100 minutes
    #3: 2 + ¾√3 unit²

    Let me know if anyone wants to see the solutions for any of the problems.

    We’d love to receive more math problems of your own creation, based on art in the museum’s collection. Please submit problems to and we’ll post our favorites.

  16. Teddy Bear says:

    1. 1020 isms
    2. 100 minutes
    3. 3.7 sq units

  17. Tamarack says:

    The second one is 200 minutes. Will we get answers?

  18. Audrey says:

    340 ism^3
    10 hours
    2 + square root(3)/2

  19. Audrey says:

    Oops! Change my second answer to 2 hours.

  20. Audrey says:

    Ok, one more time…

    340 ism^3
    100 minutes
    2 + square root(3)/2

    Final answer

  21. BillG says:

    352 cu ism

    10 hours


  22. BillG says:


  23. BillG says: