Wynwood Walls in Miami, one of the stops on the friends’ America in a Day trip. (Wilfredo Lee/AP)

For all you kids twiddling your thumbs in math class, wondering when you’ll ever use this stuff in real life, a pair of George Mason University students have two-squared words for you: America in a Day.

Math majors Laura Maldonado, a junior, and Kathleen McLean, a senior, devised math models to help them plot day trips to cities across the country. Their calculations have led them to Miami and Seattle, where they squeezed a whirlwind of sightseeing into one calendar day. Next up: Boston.

“We used a real-world network model,” said Kathleen, who plans to pursue an advanced degree in engineering. “It’s not like, ‘Jimmy goes to the market to get a watermelon.’ ”

Added Laura, who hopes to teach high school math after graduation, “Don’t let the idea of a mathematical model scare you.”

The longtime friends hatched the idea of America in a Day at the start of spring break last March. Neither had vacation plans, so they punched in some numbers and fiddled with a handful of navigational points. Four hours later, they had two plane tickets to Miami.

George Mason University students Kathleen McLean, left, and Laura Maldonado devised math models to help plot day trips to U.S. cities. (Kathleen McLean)

“Miami was the cheapest,” Kathleen said. “We mapped out how many places we could go to. ”

At the recent Science and Engineering Festival in Washington, they presented the sample problem that inspired their ad­ven­ture in math and travel: “You have one day to go to Miami. Arrive at 9 a.m. and need to leave the airport, go to Bayside Marketplace, the Miami Design District, and Wynwood Walls all before 12. How can we do this?”

They called upon geometry and optimization for the answer.

“Technically, each time we map out our travels we have created a small linear programming problem and are trying to solve a network model,” they posted on their blog.

As cash-strapped students, they set a budget of $250, including airfare. (They raised the limit for the Seattle trip.) They compared the cost and expediency of different modes of transportation, such as bus, taxi, bikes and legs. They scoured Yelp for restaurant reviews and prices. For activities (some free), they perused Instagram and travel blogs.

To maximize their on-the-ground time, they chose flights that departed early in the morning and returned late at night. To avoid wasteful transits, they determined the shortest distance between sites and diagrammed their route — a scalene triangle hitching a ride on an acute triangle. They arranged the stops on Google Maps, the red points floating over the city streets like tiny hot-air balloons. Because they are always back home for bedtime, they don’t need to worry about lodging. They cat-nap on the plane.

For Miami, the friends said Operation One Day was 95 percent successful. The 5 percent mistake: Kathleen and Laura rode to the rental shop to return the bikes only to discover that the store was closed. The duo pedaled a mile to another outpost — also shuttered. Their flight left in two hours. They rang up the parents for advice. The solution was to lock up the two-wheelers outside the shop and leave a message. They still have the keys.

On their blog, the travelers document their trips and share tips. For the Seattle Art Museum, they suggest visiting during a free admission day. In Miami, they recommend Cafe Charlotte, which serves tasty tequenos, or fried cheese sticks, as well as complimentary bread. They advise flying midweek, when fares are usually lower.

The America in a Day concept isn’t staying in America. Their professor, Jennifer Suh, will share the approach with South Korean teachers, who may incorporate Korea in a Day into their curriculum. The friends may also expand to international destinations. If they do, they will have another math puzzle to crack: creating a model for Foreign Cities in Two Days.

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