Off on a Tangent 17.7 (part b)

Help needed in pre-colloquium build

We need a few students to help build the object shown below. This object (which I’m sure we will learn the name of during the colloquium) will be used in the colloquium on symmetry (details below). We will start the build at 2:00 PM on Tuesday, January 29 February 5 in the lobby outside the lecture halls on the first floor of VanderWerf. The build will probably last until around 4:00 PM. If you can’t come at the beginning, you are still welcomed to help when you can. As a bonus you can earn a colloquium credit for helping build!

Math Colloquium on Symmetry next week

  • Title: Symmetry: A mathematical approach using group theory and linear algebra
  • Speaker: Dr. David Reimann, Albion College
  • When/Where: 4 pm on Tue, Jan 29 Feb 5 in VanderWerf 102
Abstract: Symmetric patterns are used in many situations to decorate an object with a repeating motif that is translated, rotated, or reflected without changing size. We will see examples of several symmetry types and look at these from the vantage point of group theory. In particular, we will study rosette patterns, frieze patterns, wallpaper patterns, and patterns on the sphere. We will then see how we can create all these pattern types with a unified framework based on the vectors and matrices of linear algebra.

Off on a Tangent 17.7

Was that test too easy?

Did you ever take a class where you (and most everyone else in the class) received an A without really working that hard? Well that class was too easy. Or maybe you took a class that was a little out of your comfort zone and despite working really hard you ended up with a D. Sounds like that class was too hard.

Just like Goldilocks, you need a class that is just right. But what is just right?  According to researcher Robert Wilson, a test that is just right (or one that leads to optimal learning) is one in which you score 85%. He calls this the 85% rule for optimal learning. For more information on this, you can read the entire research article here or read a shorter report on the article in Scientific American here.

[Editor’s Note: The average score on my statistics quiz this week was 85% as was Prof. Cinzori’s Multi 2 quiz—just right!]

A most unexpected answer to a counting puzzle

Christian Forester alerted us to this video that gives a very surprising answer to a physics/math problem.

Problem of the Fortnight

In honor of the newly redefined kilogram, we give you the following problem to begin the semester.

Anna Berington, one of the 2018 Iditarod mushers, has five dogs — Abby, Betsy, Charlie, Danny, and Ebeneezer — who have peculiar dietary constraints. Each must consume a whole number of kilograms of food every day, and Betsy needs one more kilogram than Annie, Charlie needs one more kilogram than Betsy, Danny needs one more kilogram than Charlie, and Ebeneezer (the lead dog) needs one more kilogram than Danny.  The butcher gives Anna 12 packages of scraps whose weights are: 2, 2, 2, 2.5, 2.5, 3, 3, 3, 3, 3.5, 4, and 4.5 kg.  The butcher wrote “Ebeneezer” on one of the 2-kg packages and “Betsy” on one of the 3-kg packages, so Anna gave those packages to those dogs.

Given the Anna satisfies the peculiar dietary constraints of her dogs, as well as the butcher’s wishes for the two specially marked packages, which dog got the 3.5-kg package?

Write your solution (not just the answer) on a sheet of butcher paper and drop in the Problem of the Fortnight slot outside Professor Mark Pearson’s office (room 212 in The Werf) by 3:00 p.m. on Friday, January 25.  As always, be sure to include your name and the name(s) of your math professor(s) — e.g. Thu Nome, Professors Balto and Togo– on your solution.  Good luck and have fun!