Real World Mathematics

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, hands-on 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 three-truss 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 hands-on 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."


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