|Off on a Tangent
|A Fortnightly Electronic Newsletter
from the Hope College
Department of Mathematics
|November 30, 2011||Vol. 10, No. 6
|Next week's colloquium will feature the actuarial field|
|Title: Actuaries – The Best Kept Secret in the
|Speakers: Ellen Bode, FSA, MAAA; Jenna Deenik ’03,
|Time: Tuesday, December 6
at 4:00 p.m.
|Place: VWF 104
|Math in the News: Eureka! The secrets of Archimedes are exposed!|
The Walters Art Museum in Baltimore is currently hosting the exhibit, Lost and Found: The Secrets of Archimedes. The exhibit centers around a book known as Archimedes Palimpsest. The book was produced by a scribe who copied the texts of Archimedes in the tenth century. (The original Archimedes papyri are lost.) In 1229, another scribe washed off Archimedes’ works and copied prayers over them. (The word “palimpsest” means writing over other writing.)
In 1907, a Danish scholar named John Ludwig Heiberg noticed the Archimedes text beneath the prayers, but there was much Heiberg could not decipher or even see with his magnifying glass. In 1998, the book resurfaced at a Christie’s auction and a mysterious private individual outbid the Greek government and the Greek Orthodox Church and purchased the Archimedes Palimpsest for just over $2,000,000. Soon afterward, the anonymous new owner entrusted it to the Walters Art Museum.
Museum workers spent twelve years unbinding the badly damaged book and producing digital images of the underlying Archimedes manuscript that were good enough for scholars to read. It is the only known version of many of Archimedes works.
of the Fortnight
||When the celebrated German mathematician
Karl Gauss (1777-1855) was nine years old, he was asked to add all the integers
from 1 through 100. He quickly added 1 and 100, 2 and 99, and so on for
50 pairs of numbers each adding in 101.
His answer was 50 · 101 = 5050.
Now ﬁnd the sum of all the digits in the integers from 1 through 1,000,000 (i.e. all the digits in those numbers, not the numbers themselves).
Congratulations to all our Problem Solvers of the Fornight -- Zac Lockhart, Nick Johnson, Evan Rugen, Patrick Malley, Eric Greve, Laine Heyboer, Michael Bowerman, Jencen Smith, David Dolfin, Elisa Shibley, Hunter Ford, Donald Kuick, Tim Cooke, Matt Johnson, Steve VanHoven, Harrison Clark, Lute Olson, Brant Bechtel, Lauren Warren, Tanner Gallant, Duncan Fairbanks, Eric Webb, Pete Stuckey, Morgan McCardel, Kaleb Skinner, Catie Gammon, Joshua Kammeraad, Jorden Demsey, Leah LaBarge, Lauren Aprill, Erin Strader, Eric Lunderberg, Emily Scott, Yubing Mao, Matt Eiles, Kelsey Cooper, Nicole Zeinstra, Eric O'Brien, Caitlin Kozack, Abigail Bohler, and Morgan Smith -- all of whom correctly determined that the sum of the digits in the first 1,000,000 integers was 27,000,001.
|Problem of the
||Imagine, if you will, you have three
boxes, one containing two black marbles, one containing two white marbles,
and one containing one black marble and one white marble. The boxes
were labeled for their contents---BB, WW and BW---but someone has switched
the labels so that every box is now incorrectly labeled. You are allowed
to take one marble at a time out of any box, without looking inside, and by
this process of sampling you are to determine the contents of all three boxes.
What is the smallest number of drawings needed to do this? Make
sure you give a thorough explanation of your answer.
Drop off your solution , along with a loaf of marble rye or a black and white cookie, in the Problem of the Fortnight slot outside Professor Pearson's office (VWF 212) by 3:00 p.m. on Friday, December 9. As always, be sure to include your name as well as the name(s) of your professor(s) -- e.g. David Puddy, Dr. Tim Whatley -- on your solution.
|Off on a