Hobbies And Interests
Angles
The ancient Greek mathematician Eratosthenes saw that when the sun was directly overhead in Syene (modern Aswan), a city in Egypt, it cast a shadow in Alexandria, a port city due north. Eratosthenes measured the distance from Syene to Alexandria, and the angle of the shadow in Alexandria when it was high noon in both places. The only devices he needed, essentially, were measuring rods and sticks in the ground (or he may have dispensed with the sticks and looked straight down water wells to calculate the sun's angle). The rest is trigonometry: The slice of the circle represented by the angle is proportional to the whole 360-degree circle (Eratosthenes knew the world was round), so the distance between Syene and Alexandria has the same proportion to the total circumference.
GPS
A modern variation on Eratosthenes' experiment uses the Global Positioning System, the satellites that orbit the Earth and send signals from which we can calculate our position. One person finds his position on Earth using a handheld GPS device. His assistant walks east or west, doesn't matter, along the same line of latitude, those imaginary lines girdling the Earth. After the satellites tell the assistant he has traveled exactly 1 second of latitude, the distance between the researchers is measured. Since there are 60 seconds of latitude in every minute of latitude, 60 minutes in each degree and 360 degrees in a circle, multiply those numbers together, then multiply by the measured distance to get the circumference.
Polaris
Worried about sunburn, or GPS batteries dead? Measure latitude at night from two east-west points using a compass, a quadrant and Polaris, the brightest star in Ursa Minor. A quadrant is a quarter-circle marked off in degrees, with a plumb line to keep it steady. You'll need a similarly equipped helper to take the second measurement at the same time, but the math works the same way it did for Eratosthenes, who looked down rather than up.
Sunset
Wear a bathing suit for this one. You'll be planking at the seashore, with an unobstructed view of the sunset. (Sunglasses are also recommended.) Use a yardstick to measure the height of your eyes above the ground. When the sun reaches the horizon, start a stopwatch, then stand up; the sun is back above the horizon again. Time how long it takes the sun to hit the waves again. Measure your new eye height above the ground. The time it takes the sun to set is proportional to the day, 24 hours (or 86,400 seconds), the same way the angle of movement is proportional to 360 degrees. That angular displacement, and the height difference, are plugged into an imaginary right triangle running to the center of the Earth. That triangle's long side gives you the Earth's radius. Double the radius to get the diameter, which you multiply by pi, 3.14 rounded off, to calculate circumference.