# Math symposium introduces students to Ancient Chinese surveying

By Deandra Williamson

Point Park News Service

While standing on Mon Wharf, James Gualtieri and Drevin Galentine and a group of high school students calculated the height of Mt. Washington with an ancient Chinese surveying technique using sticks, strings, and a measuring tape.

The students created ratios and equations and were able to compute approximately the height of Mt. Washington.

Gualtieri and Galentine participated in a recent math symposium, which is an initiative of Point Park University and other high schools throughout the region to increase students’ interest in mathematics by allowing them to apply mathematics to real world situations.

“This is an event for regional high school students who have expressed interest in math and it’s our attempt at exposing them to some interesting math activities” Matt Pascal, a professor at Point Park University said.

The preliminary results of the Pennsylvania System of School Assessment Exams showed that students’ proficiency in math and reading declined in Pittsburgh Public Schools for the 2011-2012 school year.

According to the Pittsburgh Public Schools District, the percentage of district students proficient in math dropped 3.8 percentage points, from 66.2 percent to 62.4 percent.

The District also indicated that reading scores dropped by two points, from 60.8 percent proficiency to 58.8 percent.

According to the District, as a result of the drop in test scores, Pittsburgh Public Schools may not meet the state Department of Education’s Adequate Yearly Progress standards.

To boost interest in mathematics, thirty one students from nine high schools throughout western Pennsylvania participated in the math symposium at Point Park University.

Students, along with their teachers, were divided into groups and participated in the Sea Island Problem and a Geometry Scavenger Hunt.

The Sea Island Problem was based on the ancient Chinese surveying technique, which came from the book *The Sea Island Mathematical Manual*, written by Chinese Mathematician Liu Hui in 263 AD.

The book has practical surveying problems using geometry and it provides instructions on how to measure distances and heights with tall surveyor’s poles and horizontal bars fixed at right angles to them.

“It’s known as the first text with this technique in it,” Pascal said.

In the book the Pythagoras theorem is used to calculate, indirectly, the height of objects and distances to objects.

“It’s the basic. Fundamentally, that’s done in today’s surveying,” Pascal said.

Galentine, a student at McGuffey High School, loves math and it is one of his favorite subjects, so when his teacher told him that students who were interested in math will be taken to a symposium he was excited.

“Yea math, let’s go,” Galentine said.

According to Jacob Bittner, a Shaler Area High School student, the symposium began with a math equation, where everyone had to solve the problem by finding x. He found this to be pretty cool and even though he wasn’t able to find the correct height of Mt. Washington, he still enjoyed the experience.

“This is going to help a lot for me when I go back to my studies in class and further studies in math because we used a lot of different application problems for solving math problems and this is real life situations, which we apply to our everyday life,” Bittner said.

For the Geometry Scavenger Hunt, students walked around downtown and took photos of different geometrical shapes.

Cameron Breze, a student at Penn Trafford High School, explained that the scavenger hunt was pretty interesting.

“We went on a scavenger hunt for geometric shapes like triangles, spheres, parabolas, anything that we would find in everyday life that you can apply mathematics to,” Breze said.

For Katie Campbell, a student at Southside Area High School, the scavenger hunt taught her more information about some common shapes.

“Well, I knew they were around, but I didn’t know what they were called until now,” Campbell said.

Following the Sea Island Problem and the Geometry Scavenger Hunt, students went to the computer labs to finalize their calculations for the height of Mt. Washington and created a presentation about their activities.

According to Breze the height of Mt. Washington is approximately 370 feet.

Pascal, assistant professor in the Natural Science and Engineering Department at Point Park University, explained that there is a need for students in disciplines that use mathematics and with this symposium, he wants to expose the students to math activities because by the time some students reach college they choose a career that is unrelated to mathematics.

“By inviting high school students who are interested in mathematics now, maybe we can help them see a path,” Pascal said.

The students were given a diagram of a right angled triangle that was broken down into smaller triangles and they had to find an unknown side using the variables that were given. This diagram helped the students to calculate the height of Mt. Washington.

“These are similar triangles and the result that we used is that the sides of similar triangles are improportionate,” Pascal said.

Students had to make up ratios with the information given on the triangle and they had to create an equation to figure out the answer. They created two fractions.

“Vertical over horizontal, equals vertical over horizontal,” Pascal said.

To solve the problem on the diagram, the students had to find H, an unknown side of the right angled triangle.

According to Pascal, for the students to find H, they had to solve one of the equations to find A, another unknown side of the right angled triangle. The solution for A was then substituted to solve the problem for H.

“They are using geometry and similar triangles,” Pascal said.

According to Pascal, lasers are now used by surveyors to calculate height, which makes it much easier to do.

With this activity the students were exploring mathematics, as they gained more understanding about geometry and trigonometry.

“This is them using something that they either have intuitively or have learned in a math course at some point and putting it into practical use” Pascal said.

He explained that taking advanced courses was not a prerequisite for attending the symposium and if a student only knew a little geometry they were able to participate in the activities.

According to Darlene Marnich, chair of the Education Department, their first math symposium was successful and it will continue as an annual event for high school students.

Most of the students who attended the symposium enjoyed it and some may seek careers in mathematics.

“All these skills I’ve learned here can be useful in life. I hope to take a math oriented career,” Gualtieri, a student at Shaler Area High School said.

“These things are going to be useful later in math, later in careers because this is something you can use everyday to help you with everyday problems,” Shaler Area High School student, John Colarussa said.

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