INTRODUCTION LETTER from OLAP
ON YOUR MARK...GET SET...CALCULATE!
Most of this material has been written by SLCC
students and students from other nearby colleges
for OLAP's Mathematics and Science Day. This is our
first attempt at compiling information that is suitable
for college, high school, middle school, or junior high
students. More or less anyone who wants to understand a
little of the mathematics or science of OLAP. Much care
has been taken to make all of the exercises as accurate
as possible, but there are some inaccuracies. Please
forgive our oversights and please make any comments or
suggestions on problems so that we may write a better
book next time!
Our goal with this program is to make mathematics and
science more fun for everyone.
There is a potential for a contest. Each participant
group could submit one book on the day of the event. At
that time, say 2 p.m., we could have judges determine the
best book submitted. Due to the length of the book, the
judges may check randomly selected material. The winning
group could then be announced by the end of the day.
This book features activities for exercises prior to your
visit, during your trip to the park and at the park. We
have also left some blank pages for you to create new
problems or to take notes about your day.
Below find the list of individuals who wrote and worked on
this project and a note from one teacher who guided them!
HAVE FUN!
Loc Al Amuse, Chief Administrator
OLAP,
1234 Many Acre Place
Intown, Euforia 99999,
Telephone: 555 1212
Send comments to: OLAP, Mathematics Department
St. Louis Community College at Meramec
11333 Big Bend Blvd
St. Louis, MO 63122-5799
OLAP would like to acknowledge the time and effort
that many students put forth for this mathematics
and science day book, and extend a sincere thank you
to the following people! The authors, editor and
technical assistant are:
Dana Anschute,
Todd Bennett,
Damian Brindle,
Bill Bogenhagen,
Jonathan Burroughs,
Jason Campbell,
Amy Chromoga,
Christina Conteuo,
Jessica R. Copley,
Dwayne Crider,
Suzanne Crump,
Heather Dourron,
Ryan Dooley,
Deborah Esterman,
James Fornango,
Robert Gassett,
Kim Hoang,
Lana Hopkins,
Jared Jett,
Kevin KaLota,
Sean Kitchell,
Tim Klable,
Catherine Knoebel,
Mark Kopp,
Dennis Ku,
Ken Lazarz,
Scott Leisler,
Joshua Love,
Mary Mawhinney,
Susan Morse,
Diane Nelson,
Chris Parrish,
Christina Payne,
Lindsay Rockwell,
Andriel Rotzler,
Brian Saville,
Steve Stream,
Thong Tarm,
Stephanie Werton,
Chris Westerbeck,
Patrick Zoellner,
Bill Thayer, and
Dianne Pence
FORWARD TO OLAP's MATHEMATICS AND SCIENCE DAY by P. J.
I am pleased to introduce you to this years mathematics
and science day at OLAP. My students have learned a lot
of math and science in preparing this material for you.
I hope you will enjoy any challenge this book may provide
you. In fact, I hope you will send your mathematics and
science questions and ideas to OLAP early next fall for
next year's book.
Many concepts are provided, but students often worked
with the slope concept. Galileo's study of uniformly
accelerated motion using a "constant rate of change" of
speed certainly changed physics almost four hundred years
ago. He found that in free fall or motion down an incline,
the vertical position of an object is proportional to the
square of the time in motion. His parabola is a quadratic
function of time, a second degree polynomial!
Over three hundred years ago Newton found that Galileo's
constant acceleration was related to the force of gravity.
He devised a calculus approach that unified these slope
ideas. The OLAP rides you take celebrate the Galileo
polynomial relating distance to the square of time with
Newton's insightful constant.
Please attend my juggling show where I perform on stage.
I will explore fundamental concepts of math and science
that lead you to present day research about our human
physiology. Also, I wish to honor a scientist, P. J.
Beek and a mathematician by the name of Claude E. Shannon.
Scientific American profiled Dr. Shannon in January of
1990 indicating that he is to information theory as
Einstein is to physics. Professor Shannon devised an
equation that Scientific American called "The Unified
Field Theory of Juggling." The number of balls divided
by the number of hands equals the sum of flight time and
dwell time divided by the sum of empty hand time and dwell
time. The dwell time is the time a hand spends holding or
carrying the object being juggled. The path of a juggled
ball is short and slow enough to neglect air resistance.
It is a great example of Galileo's free fall motion.
The ball's flight path is a parabola. In Shannon's
equation, the flight time is completely described by
Galileo's polynomial. Yet Shannon's equation ties the
time knot of the physics of motion to the motions of the
juggler. Scientist P. J. Beek has begun to unravel the
complex human information processing occurring during
juggling activities. Beek's research has uncovered
interesting characteristics about human juggling motion.
His "Learning The Cascade Juggle: A Dynamical Systems
Analysis" may help entertain you and perhaps you may learn
to juggle at OLAP.
However, OLAP has learned how to juggle you in time and
space. On each OLAP ride, your position can be determined
by the seconds of time spent. The same equations of motion
governing the juggled ball determine your motion down each
slope. The constants in the equation may vary slightly but
Galileo, Newton, and OLAP are right in there with you. Now
it is up to you to help figure out how and how much they do
it!
My students are ahead of their time. Many mathematics
students are just beginning to do projects from their
course material. These students, see above list for some
of their names, went beyond the classroom projects into
producing projects for you. They have learned a lot more
about mathematical concepts such as: area or integration,
slope or differentiation, absolute value and inequalities
or coordinate positions, mapping or topology, and on and
on and on. They hope these questions will be seeds for
you and your mathematics and science teachers to grow
into a rich and rewarding new OLAP project book for next
year.
Some of the enclosed questions and ideas, if completed
before you go to OLAP this Mathematics and Science day
will increase your ability to do more complex activities.
Your ideas sent to OLAP shortly after your trip may help
other students learn based on your learning experience.
Make it your playground for math and science.
Have lots of fun and we will see you soon!
Yours, P. J.
Send comments to: OLAP, Mathematics Department
St. Louis Community College at Meramec
11333 Big Bend Blvd, St. Louis, MO 63122-5799
NOTES FOR THE LEADER OF AN OLAP TRIP
I. PRE-TRIP PREPARATION
1. You may want to do the doable problems from this
collection before the trip. The level of difficulty
changes on each question.
2. Other problems depend on estimations and measurements
at the park. Guessing answers and upper and/or lower
bounds for answers should be encouraged. Sometimes the
estimated value is what we are asking for.
3. Your "OLAP GRID MAP" of the park should be marked
with important points highlighted. Students should know
where to find you or leave a message for you. Students
should know where the First Aid station is located.
(-670, -20, 576)
4.
5.
II. ORGANIZATION SUGGESTIONS
1. Assign parties of people to engineering consulting
groups of two or three people. Example: Debby's group
might be called "DEBCO Consulting Engineers." This way
each person has some one to work with or someone to
consult for help if the need should arise. You may
want to mix levels of problem solvers and ask them to
help each other.
2. Arrange times and places during the day for
CHECK-IN with you. It is helpful if there is a bulletin
board (say at coordinates (0, 0, 570)) where people and
leaders can leave messages for one another. If you
choose to have people check in, set aside a large block
of time so that they are not forced to leave in the
middle of a long line. Don't forget to arrange a place
and time for groups to work on their contest books.
III. EQUIPMENT FOR THE PARK
1. Stopwatch: wristwatch type is great.
2. Three foot cloth ruler or sewing tape.
Centimeters on one side, inches on the other.
3. Calculators (Scientific recommended)
4. Video Tape Recorders and audio tape recorders.
IV. DAY'S SCHEDULE FOR YOUR GROUP
TIMES
PLACE
MATERIALS
Notes about writing projects and reports for your
group or leader should be anotated here.