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Math Students Solve School’s Flag Problem

Hanover High Uses Geometry To Measure Proper Size, Height

Hanover High School junior Izzy Tuggle, left, gives a couple pulls on the cord to help Maintenance Supervisor  John Lammert, right, raise a new flag in Hanover, Monday, June 9, 2014. Warren Tucker's practical geometry class calculated the height of the flag pole using triangulation and, based on the rules for correct proportions between flag size and pole height from americanflags.org, found the proper sized flag to replace one that had been noted to be too be too small.
(Valley News - James M. Patterson)

Hanover High School junior Izzy Tuggle, left, gives a couple pulls on the cord to help Maintenance Supervisor John Lammert, right, raise a new flag in Hanover, Monday, June 9, 2014. Warren Tucker's practical geometry class calculated the height of the flag pole using triangulation and, based on the rules for correct proportions between flag size and pole height from americanflags.org, found the proper sized flag to replace one that had been noted to be too be too small. (Valley News - James M. Patterson) Purchase photo reprints »

Hanover — On a warm Monday afternoon, geometry teacher Warren Tucker gathered his class in front of Hanover High School’s World War II memorial to witness the raising of a new American flag after the old one was found to be undersized.

“For years, I’ve thought that the flag at the school was too small,” said Lynne Stahler, a member of the Friends of Hanover-Norwich Schools. “I decided to challenge the math department to determine how big the flag should be, and I told them I would pay to replace it when they did.”

Tucker teaches practical geometry at Hanover High School, and he saw this project as an opportunity to demonstrate to his students a real-life application of math. Although it was easy enough to measure the height of the flagpole’s base — a concrete World War II memorial — measuring the flagpole itself was difficult because of its height. So Tucker and his students figured out a solution.

“We couldn’t measure the pole, but we could measure the length of its shadow,” Rose Lippman, a 16-year-old Hanover High sophomore, said. “We also measured the height of a person and the length of their shadow.”

Measuring a person’s height and shadow, and connecting the two lines, creates a triangle. Since the students also had the measurement of the flagpole’s shadow, they could create a “similar triangle” by using ratio and proportion to find out the height of the flagpole, which turned out to be about 50-feet tall, including the memorial’s base.

“Comparing the two triangles got us a surprisingly accurate number,” Lippman said.

Once the class knew the height of the flagpole, they went online to figure out the correct size for the flag. As it turned out, the flag they were flying was too small — it was 4 feet by 6 feet, rather than the 6 feet by 10 feet specified by the National Flag Foundation as the correctly sized flag for that height.

“When the memorial was built, it’s possible that they forgot to take into account the height of the base, so they chose a flag that was too small,” Tucker said.

“I think it’s important to honor our country and our flag,” said Stahler, whose Friends group is dedicated to raising money and giving grants to teachers in the Dresden school district who apply for funding. “It should be flown in an appropriate way, and I wanted my local high school to reflect that. I also wanted to give the kids the chance to change it if it was incorrect, and I was particularly impressed that they figured it out.”

Michele Sacerdote, who is co-president of the Friends group, said, “It’s great to be able to have an opportunity for real world learning.”

The students took turns getting up on the ladder and pulling on the rope to raise the flag. Asa Peters, a 16-year-old junior, said, “It’s nice to have the right measurements after working on this problem.”

Izzy Tuggle, also a 16-year-old junior, added, “It’s good to have things in proportion.”

Ford Daley, who works in the atrium of the high school, said that the memorial is dedicated to alumni of the high school who had died during World War II. Their names are listed on the concrete base of the memorial.

“There’s a story behind each of these names,” Daley said.

Tucker said the flag size discussion “was a great little project.”

“We had a good day of discussion arguing about different aspects of the calculations we needed to make so that the height would be accurate,” Tucker said. “But there was no argument about coming outside.”

Lauren Bender can be reached at lbender@vnews.com or 603-727-3211.