|OFF ON A TANGENT
|A Fortnightly Electronic Newsletter from the Hope
College Department of Mathematics
|October 20, 2004
||Vol. 3, No. 4
Tomorrow's colloquium will
feature problems, puzzles, and pizza!
- 3:30 p.m. Thursday, October 21
Professor Emeritus John VanIwaarden will present puzzles and
problems for students to solve during tomorrow's colloquium. These will
be fun problems to work on and should stretch your mind a little.
To stretch your stomach a little, pizza will be served at the end of
the problem session. So come and enjoy working on some
interesting problems and eating some great pizza. This all starts
at 3:30 p.m. Thursday,
October 21 in VWF 104.
Since tomorrow's colloquium involves food (and we don't want you to
be too full to enjoy it) we will not
have tea time before the colloquium. Tea time will return, however,
before next week's colloquium at 1:30 p.m. in the reading room (VWF
Next week's colloquium will
feature Michigan Tech. professor
- 2:00 p.m. Friday, October 29
- VWF 102
from Michigan Technological University will present a colloquium on Friday next week at 2:00 p.m. (Note day and time
change.) She will talk about statistical genetics and will also
provide information about the graduate programs in the mathematical
sciences at Michigan Tech.
Today is the last day to sign
up for the Michigan Undergraduate
The Department of Mathematics at Central Michigan University will be
hosting the seventh annual Michigan Undergraduate Mathematics
Conference (MUMC) on Saturday, October 30, 2004 from 9:00 a.m. to 5:00
p.m. Hope College will be taking a group of students and
faculty. They will leave early in the day and return in the
There will be student presentations as well as presentations on
careers in mathematics, information about
mathematics graduate programs and REU programs. For those
interested in attending, the
deadline to sing up is today, October 20. Contact Prof. Darin
Stephenson if you are
interested in attending (he has a sign-up sheet outside
his office door, VWF 210). Visit the MUMC web page at
for more information about the conference.
Tomorrow is the last day to sign for the MATH Challenge
You have until tomorrow, Thursday, October 21, to sign up to take
the Michigan Autumn Take Home Challenge (or MATH Challenge). The
competition will take place on the Saturday morning November 6. Teams
of two or three students take a three-hour exam consisting of ten
interesting problems dealing with topics and concepts found in the
undergraduate mathematics curriculum.
For more information about this competition visit http://www.mcs.alma.edu/mathchallenge/.
If you are interested in competing, you need to sign up with Prof. John
Stoughton. You can sign up on the sign-up sheet on his door or
send him an e-mail at email@example.com.
Information session about the GRE is
scheduled for tomorrow
Taking the Graduate Record Exam (GRE) is a requirement for entrance
into many graduate schools. The Hope Pew Society and the Office
of Career Services are sponsoring an information session on the GRE.
Professor Charles Behensky of the Department of Psychology will discuss
the mechanics of the GRE, what students might do to prepare for the
exam, and answer questions. The session will be tomorrow, October
21, from 5:30 to 6:30 p.m. in 1000 Science Center.
For more information, go to the Career Service’s GRE web page: http://www.hope.edu/student/career/GRE.html.
The site provides more information on the GRE, including subject test
dates, and announces the availability of some practice test software.
Problem Solvers of the Fortnight
This fortnight nineteen of you proffered solutions to the somewhat
weightier problem of determining which of twelve coins was counterfeit
and whether the bogus one was heavier or lighter than the others.
Congratulations to Daniela Banu, Chris Johnson, Alex Larson, and Josh
Morse, who correctly determined that three weighings will decidedly
determine (without any luck) the counterfeit coin and whether it is
heavier or lighter than the others. For their weighty labors, our
problem solvers may claim their sweet rewards by dropping by Dr.
Problem of the
No coins this time. Just a neat problem!
The carousel on Windmill Island here in Holland has been around a
long time and is starting to show signs of wear. In fact, the deck of
the carousel has needed a paint job for a couple years now, but before
it could be painted, Herm VanderVeedenVanderMeen (the carousel master)
wanted to know exactly how
much paint would be needed to do the job. The problem was, though, he
couldn't figure out how to determine the area of the carousel deck,
which is an annular ring, because the motor and gears in the middle of
the merry-go-round prevented him from measuring the radii of the inner
and outer circles. If he could have measured those, his job would have
been easy! One day, he was talking to a group of Hope College students,
who had taken their parents to Windmill Island, and he told them about
his dilemma. One of the students, who had taken some really great math
courses at Hope, said to him, "I think I can help you out," and she
took his tape measure, walked over to the carousel and made a single
measurement along a straight line. Her measurement was 30 feet, and
after making a few quick calculations in her head, she told the man the
area of the carousel deck.
The question is, What measurement did she make (and how did she use
it to calculate the area of the carousel deck), and what is the area of
the carousel deck?
Write your solution on the back of a pair of World Series tickets
(old ticket stubs from Windmill Island will suffice if you have
difficulties procuring World Series tickets), and drop them in the
Problem of the Fortnight slot outside Dr. Pearson's office (VWF 212) by
3:00 p.m. on Friday, October 29.
|Got a Math Question?
Ask Elvis ...
... email him at firstname.lastname@example.org
Note: Student names have been changed for identity protection.
How were/are the values for the known transcendentals such as Pi and e
found? Obviously, I can draw a circle and measure circumference and
radius to get a decent estimate, but we know these numbers to the
millionth decimal. How is this accuracy accomplished and confirmed?
In awe of Mathematics, "Kyle Williams"
Thanks for writing -- that's a GREAT question! I've come across
those transcendental numbers many times in my studies of calculus and
wondered the same thing. I didn't know the answer offhand (or
offpaw, as the case may be), so I had to do a little digging. I
asked around the department, and Dr. Cinzori transcended the call of
duty with his answer. He writes:
currently known to over 1,240,000,000,000 decimal digits. Amazingly,
the basic formula used to calculate pi to this accuracy was discovered
around 1800 by a teen-aged Carl Gauss. Gauss' algorithm is quite
straightforward; it uses only addition, subtraction, multiplication,
division, and square roots. The algorithm is recursive which means that
it begins from an initial guess, applies a formula to produce an
output, and then uses that output as the next input to the formula.
Doing this repeatedly produces a sequence of numbers that converge to
pi. Gauss' algorithm is fast (it converges quadratically) because it
more than doubles the number of correct digits with each iteration.
Starting with the initial guess 3.14, it only takes 38 iterations to
produce over one trillion digits. You can see Gauss' algorithm at
algorithm is so simple, it is easy to code and check for accuracy. Even
so, a record is not officially established until it is checked by an
independent party using a different algorithm, of which there are many.
Many mathematicians have produced fast algorithms for pi. Most famous
are Gauss (1777-1855) and Ramanujan (1887-1920), but during the past 20
years great progress (including a quartically convergent algorithm) has
been made by Peter and Jonathan Borwein and Simon Plouffe.
If you are
interested in learning more, check out the book Pi Unleashed by Jorg
Christoph Haenel available in VanWylen Library. The book includes a CD
with many different routines for calculating pi. The homepage of
Yasumasa Kanada, the current record holder for calculating digits of
Prof. Kanada has calculated over
one trillion digits of pi. You can also check out Peter Borwein's
Thanks again for the great question, "Kyle"!
Mathography: Srinivasa Aiyangar
The story of Ramanujan reads almost like a
fable. Born in his grandmother's house in Erode, a small town
about 400 km southwest of Madras, India, Ramanujan contracted smallpox
at the tender age of two but survived the disease whose death rates
have historically been as high as 30%. (The last case of smallpox
in the U.S. occurred in 1949, and smallpox was eradicated from the
world only in 1977.)
In school, Ramanujan proved himself an able
scholar in all subjects, but he was particularly entranced by
mathematics and in high school picked up a copy of G.S. Carr's book,
"Synopsis of elementary results in pure mathematics," a book that
contained only theorems, formulas and short proofs and was out-of-date,
having been published in 1856. From this book, Ramanujan taught
himself mathematics, providing proofs where none were given and
deriving the book's formulas for himself.
In 1906 Ramanujan went
to Pachaiyappa's College to prepare for admission to the University of
Madras, but he failed all his examinations, except for mathematics, and
thus was denied admission to the university. But he continued his
research in mathematics, with only Carr's outdated book to guide him,
and in 1913 sent a letter to G.H. Hardy, professor of mathematics at
Oxford, that contained some of the results Ramanujan had
obtained. Impressed by Ramanujan, Hardy invited him to Oxford in
1914. Apart from his mathematical fellowship with Hardy and his
colleague, Littlewood, Ramanujan was miserable: he had no friends
outside his mathematical colleagues, finding food that agreed with his
diet was extremely difficult, and doctors feared that when he fell
seriously ill in 1917 he would die. By 1918 Ramanujan's health
improved, but his homesickness did not. In 1919 he set sail once
again for India, but his health problems returned and he died the
following year at the age of 32.
His mathematical legacy is
recorded in the many notebooks he left behind at his death, but because
of the idiosyncratic style of writing mathematics that Ramanujan
learned from Carr's book, many of the results he recorded in his
notebooks seem to come out of thin air. Nevertheless, Ramanujan
made significant contributions to many areas of mathematics, including
infinite series (see above on computation of pi). He was one of
India's greatest mathematical geniuses.