Hi! I’m Manda Brown, a software developer at Think Through Math, where I enjoy working with an amazing team to build great software. Although I love my job, occasionally everyone needs a change of pace, and I’m just returning to the office after a week-long vacation.

Last summer, my then 14-year-old daughter got a taste of bike camping over a weekend, and enjoyed it so much that she convinced us to make the trek from our home town of Pittsburgh, PA to Washington, DC. We took six days to do it, travelling 335 miles on the Great Allegheny Passage and the C&O Canal Towpath; bikes heavy with gear, food, and water. It was an amazing adventure! I’m so happy to have done it and to have been able to give that experience to my daughter. I’m also happy to be back home again, where I have a shower and a laptop.

Pedalling along the trail for hours a day leaves a lot of time for observation and contemplation. Beautiful forests sheltered the trail; it wound beside and around sinuous rivers, threaded through occasional towns, and eventually led us to the capital. Math was all around us; often the setting inspired thoughts about things like the fibonacci numbers apparent in natural growth of the plants, the diversity and population cycles of the creatures we glimpsed as we passed (or swatted when they took a bite), the complex and beautiful math that describes the swirling currents of water, or the stresses and forces at work to create and expose the varied rock formations sporadically embellishing the scenery. And the evidence of math informing human activity was everywhere from the canal and towpath itself, to the railroads, to the architecture that ranged from simple and functional to the ornate and grandiose.

We used math a lot too. There were very important questions to answer: where will we stop for snacks? Do we need to stop in town and acquire more calories and deliciousness? Should we refill our water now, or can we wait until the next opportunity? How long should we expect to be on the bike each day? Will we beat the thunderstorm edging ominously closer on the radar? (We didn’t.) We were constantly exercising simple math involving time and distance to help us manage our resources and energy.

But my favorite trail math is even simpler: subtracting one. My daughter and I wouldn’t really consider ourselves athletes; we like to ride our bikes, but this was by far the most challenging ride we’ve ever undertaken and it wasn’t always easy. Each mile marker was a small victory. And they added up to larger minus ones. One mile at a time until we got to the next stopping point. One stretch and water break at a time until we got to the next meal. One meal at a time until we got through the next day (at day 5, we were pretty happy with our progress; but stayed at a hostel with a bunch of amazing Appalachian Trail through-hikers whose time units were months!). One day at a time until we finished one trail, and then the other. And finally one challenge complete, the adventure over.

The best thing about that last one is that the minuend of the expression is infinite. So what’s next?