Off on a Tangent
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
  November 29, 2010 Vol. 9, No. 7 
http://www.math.hope.edu/newsletter.html


We will take a look at student research in this week's colloquium

Title:  Student Research Reports
Speaker: Hope Students
Time:  Tuesday, November 30 at 4:00 p.m.
Place:  VWF 104

Abstract: In this colloquium (the last of the semester) we will hear about the experiences and results of two groups of undergraduate research students in mathematics.  Matt Eiles, Robert Nash and Dan Waldo will present "The Mathematics of Falling Sand Grains" and Jessalyn Bolkema will present "Non-Real Zeros of Derivatives."

This will be a great opportunity to hear about interesting new results in mathematics and see the types of projects you could be working on this summer as part of the summer research program in Mathematics at Hope College. Come and support your classmates!

 

Welcome Dane Wallace Edwards-Parker!

Prof. Stephanie Edwards has another reason to be thankful this year with the arrival of her fourth child, Dane Wallace Edwards-Parker.  Dane was born Monday, Nov. 22, at 11:12 p.m and weighed in at 7 pounds and 9 oz. and was 19 1/2 inches long.  Both baby and mom were released from the hospital in time to celebrate a special Thanksgiving at home.  Also welcoming Dane home were his sisters, Maya and Bella, big brother, Eli, and their father Darren Parker.



Math in the News:  The Mathematics of H-O-R-S-E

Should you try and easy shot or should you shoot backwards from half court? You may have asked yourself this type of question when you are playing HORSE with your friends.  Ben Blatt of the Harvard Sports Collective has looked into these types of questions and has developed a probability-based model that determined the best strategy to win the popular basketball game.

In order to improve in this game, you should not only practice some interesting shots, but should also run the numbers.  For more information and a breakdown of some of the probabilities, visit an article from The Wall Street Journal here.


Problem Solvers of the Fortnight


We had the following problem in our last newsletter: October 10, 2010 garnered a lot of attention because of its representation as a calendar date by 10/10/10.  Suppose instead that we represented month, day, and year in base 12.  Thus in base 12, December would be indicated by 10 because 10twelve = 12 in base 10.

Determine which year(s), if any, during the 21st century will have a 10/10/10 date, where each "10" is base 12 representation.  In particular, this 10/10/10 date would represent December 12 of a year (or years) for which base 12 representation of the year that ends in the digits 10.
The following students gave a correct solution of 2028:  Emily Nock, Lyndsey Shembarger, Terra Fox, Alex Perkins, Scott DeClaire, Gregg Elhart, Danielle Goodman, David Dolfin, Kendra Donze, Dale Shepherd, Kiley Spirito, Jo Forst, Joshua Kammeraad, Tanner Gallant, Curtis Drozo, Lauren Warren, Amanda Black, Megan Ludwig, Katherine Brune, Rachel Elzinga, Derek Blok, Thomas Endean, Danelle Koetje, Samantha Steffens (who wrote the solution on a dodecahedron!), Cornelius Smits, Kim Slotman, Anna Filcik, Eric Hallquist, Joel Brogan, Robyn Dewey, Luke Platte, James Bour, Jeff Shade, Ben Bockstege, Michael Bowerman, Nick Hazekamp, Craig Toren, Conner Hosner,  Guillermo Rangel, and Eric Zeinstra (another solution writtien on a dodecahedron!).


Problem of the Fortnight


Suppose a cubic polynomial with leading coefficient of one and with inflection point at the origin passes through (c,0) and (a,b), where a>c>0.  A translated copy of the cubic has its inflection point at (a,b) and passes through the origin.  Show that twice the area between the two cubic polynomial curves equals a4.

Write a complete solution (not just an answer) on a 2011 Nissan Cube and drop it off in (or park it by) the Official Problem of the Fortnight Slot outside VWF 212 by 3:00 pm on Wednesday, December 8.  As always, be sure to include your name, the name(s) of your professor(s), and your math class(es) -- e.g. Polly Nomial, Dr. Q. Bick, Math 123 -- on your solution. 


A life without adventure is likely to be unsatisfying, but a life in which adventure is allowed to take whatever form it will is sure to be short.

Bertrand Russell

Off on a Tangent