Henry Nass loves numbers, especially prime numbers. He’s also an advocate for teaching math skills, and he keeps finding creative ways of calling attention to the numbers around us in hopes of kindling more interest in the study of mathematics.
Nass may have found an intersection that appeals to land surveyors. He contacted POB to talk about his observation that a number of latitudes and longitudes are prime numbers and that the intersection of some of these primes fall within the landmass of the continental United States.
Have Your Pi and Eat It
First, a little background. Nass says efforts by the American Mathematical Society to establish Pi Day for schools to promote mathematics have fallen a bit flat. The idea of using the date March 14, which corresponds to the mathematical constant Pi (3.14), have basically become an excuse to have a pizza party. While the intentions are good, he’d like to see the effort expanded, and he thinks an appreciation of prime numbers is one of the ways to go.
There’s an interesting link for land surveyors. Nass discusses the Sieve of Eratosthenes, named for the Greek astronomer and geographer who, in the third century BCE, measured the circumference of the earth. Eratosthenes developed a tool which generates prime numbers — basically a grid system which allows the exclusion of non-prime numbers, leaving only prime numbers in place.
A number of years ago, when the year 2000 and the dawn of the 21st century were getting a lot of attention, Nass observed that the first prime number year of the 21st century would be 2003 (followed by 2011 and, of course, eventually 2017). He took that a few steps further and identified some dates within 2003, which were also represented by prime numbers, and he proposed to his city councilman that the City of New York adopt a resolution commemorating these prime number dates.
Living On the Grid
Nass didn’t say what started him looking at a map of the United States and visualizing the “prime locations” represented at the intersection of a prime-number latitude and a prime-number longitude. Perhaps someone mentioned the Prime Meridian in Greenwich, or he was contemplating Eratosthenes’ early geospatial endeavors, but either way, he made the leap.
When Nass called POB, he had in mind student field trips to locate the exact spots where these primes intersect. It sounded like a good opportunity to develop some awareness of land surveying and an excuse to get involved with schools, so POB decided to help Nass spread the word.
One advantage of the prime location exercise is that it is not tied to a single, specific day, so events can be scheduled at any time. Since 2017 is a “prime year,” it provides an opportunity to begin the conversation, but it’s not even dependent on getting done in a prime year.
There are quite a number of learning opportunities that can branch out from there that involve the land surveying profession. They can be scaled to fit the level of teaching and the subject — mathematics, geography, history, etc. And, let’s face it, the profession is struggling for ways to gain some visibility with young people with the right interests and skills in math and other subjects to get them to look at land surveying as a career.
One of the first steps is an outreach effort. Armed with some ideas of how professional land surveyors can contribute to the learning process and specific topics, get to know some teachers. At the same time, get them up to speed on land surveying and geospatial professions and help them understand how they can bring some of the real-world experience and application of the theories they teach into the classroom. Here are a few thoughts. These can be suggested as part of a lesson plan for math or science teachers, and the teachers can take it from there.
Ideally, anyone located near enough to one of the points represented by the intersection of two primes can turn it into a field trip. The opportunity for a land surveyor to go into the field with a class and demonstrate the tools and techniques to find and mark the point should be obvious. Where there is no such point near enough, the tools and methods can still be demonstrated while the location of the point becomes a map exercise.
Here’s how the prime location idea Nass has can support a lesson plan. It should be easy to see where the math teacher starts and the land surveyor joins in:
- Identify what is a prime number.
- List prime numbers between 20 and 50 (corresponding to latitudes). Then extend that list to 140 to cover longitudes.
- Pinpoint on a map the rectangle extending from 20 to 50 N latitudes and 60 to 140 W longitudes (corresponding to the location of the continental United States).
- Identify the latitudes within the rectangle that are primes.
- Identify the longitudes within the rectangle that are primes.
- Find the intersections of two primes on the map and identify the location and nearest city.
Discussions leading up to the exercise can include the development of modern mapping using the lat/long coordinate system. This is a good opportunity to introduce the practice of surveying and highlight the Point of Beginning, and various principal meridians that followed and their importance in land management and surveying. From there, it’s just a matter of demonstrating how to get to that sub-centimeter measurement that starts a boundary survey. Discussions can go in any number of directions, depending on what the class is studying. If the teacher(s) gain a good understanding of what you do and how you do it, they should be able to lead the way in developing a lesson plan that puts math and science into practical terms using a land surveyor’s experience to make it real. Some cool equipment and technology certainly helps.
When POB looked at the future of surveying last June (A Shortage of Surveyors?), some of the state associations were being recognized for their efforts to promote the profession and recruit new, young talent. One of the most striking images was a photo provided by the North Dakota Society of Professional Land Surveyors showing a young boy sitting at the wheel of an ATV that was part of a career day display at a local shopping mall. So, the gear can definitely work.
While Nass was focusing on the intersection of prime coordinates, there’s an intersection many teachers struggle with — showing students how the lessons they are teaching have practical application. Land surveying lives at that intersection.