Real World Mathematics
10 Jan 2003
Have you ever sat in your math class asking yourself, "Why do I need to
learn trigonometry and calculus? Who uses trigonometry and calculus in the real
world?"
Civil engineering professors and students from the University of Hawaii
College of
Engineering visited McKinley High School and Kaimuki High School
to teach
upper division math students how civil engineers use trigonometry and calculus
to design and construct buildings, bridges, and other structures.

Dr. Robertson demonstrating the shake table.

At each high school, students were shown three exciting, handson civil
engineering demonstrations, where students got up close and personal with various
civil engineering equipment and testing tools.
In one of the demonstrations, civil engineering associate professor
Dr. Ian Robertson and civil engineering graduate student Alison Agapay demonstrated
how shake tables and determining a structure's natural frequency are used in the
building of a structure.
When designing and constructing a building, engineers have to consider
many factors. They have to figure out how a structure will respond to things like
earthquakes, wind, blasts, and extreme impacts. These events cause structures to
vibrate. If these vibrations happen to be the same as the natural vibration
frequency of the structure, the vibrations
can become very large and cause the structure to collapse. Using
mathematics, engineers can determine the frequency of a structure.
To demonstrate this Dr. Robertson had rods of various stiffness, height,
and mass on a computer controlled shake table. When a certain frequency is inputted
into the computer, only the rod that is attuned to that frequency will vibrate.
Change the frequency and another rod will vibrate.

A Kaimuki student using the surveying equipment.

Another demonstration dealt with surveying. You've probably seen
surveyors at
construction sites measuring various things, where one person is holding a
pole up and
another is looking through a piece of equipment from far away. The job of
surveyors is
to determine the height of things, distances, and slopes with their
equipment.
Graduate student Matt Fujioka gave presentations at McKinley High
School. Doctoral
candidate Lin Zhang, graduate student Kainoa Aki, and juniors Jason Chee
and Eric
Tashima gave surveying presentations at Kaimuki High School. Surveying
equipment
was brought in for the high school students to use. The tools of the
surveyor include a
theodolite, which is used to measure horizontal and vertical angles, and a
level, which measures elevations of the land relative to sea level. Trigonometry is a
big part of
surveying, since it deals with angles and altitudes.
At Kaimuki High School, Dr. Horst Brandes and at McKinley High School,
Randy
Akiona helped explain the forces of compression and tension using a
threetruss bridge.
Compression is the force that forms when two things are pushed together
and tension is
the force that is formed when something is pulled apart. Imagine pushing
a spring
together, it will try to get back to its original state, that's
compression. Now imagine
pulling that same spring apart, the force that wants to bring the spring
back to its original
state is called tension.

Randy Akiona working with McKinley students.

All structures have to take into consideration these forces of compression
and tension.
Students volunteered to construct the bridge and after they were done,
some of them
where able to cross it. They also learned when engineers design bridges
they also have to
think about factors like weight, load, and the wind. "It was interesting
because it was a
handson activity. We were able to see the structure being built and the
elements of
compression and tension playing their parts," McKinley student Diana Wan
said.
These demonstrations opened the eyes of many of these students to the
exciting world of
engineering. "After the presentations, I got a better understanding of
what engineers
really do," McKinley student Jessica Mau said. "I realize that engineers
thrive on
challenges and the love of their job makes it fun, yet serious. The
feeling of satisfaction
after the end product must really be rewarding."
