An introduction to pi and radians

The summer algebra and trigonometry course is a first encounter with radians for many if not almost all of my students. I like to start out on the lawn with a big circle.

Starting at the generator, Madona held a line with a radius of 44 feet, Suzanne walked behind her with the surveyor's wheel. At 90° the wheel had measured 70 feet or about 1.59 radians.

Afilina was the center of the circle, Patty and Herder on the right.

Coming up to 180° in the morning class. The weather was sunny, already hot, but cooperative. The grass was still wet, but not overly so. At 180° the arclength was 144 and for 3.27 radians (against 3.14 theoretic).

Madona passes David out near 180°.


Coming down to 270° the arclength was 218 feet or 4.95 radians. The surveyor's wheel measures feet, in algebra and trigonometry leaving measurements in feet is easier.

Reading the measurement on the wheel.

Headed back to 0 radians.

Zero radians. 298 feet. 6.77 radians as measured.

In the afternoon section I backed the center off from the generator until the rope was at the rope's full length of 50 feet. Rayleen was on the surveyor's wheel, an arclength of 79 feet took her to pi over two radians, which was 79/50 = 1.58 radians out on the lawn. The radius came within decimeters of the pillars.

Redson was circle center.

A fifty meter radius dropped the walkers onto the slope of the water hazard. There is barely a scant one hundred feet between the generator and the culvert. How Redson managed to wind up at the right spot to clear both the building and the culvert escapes my hindsight comprehension.

The full circle would have an arclength of 320 feet for an estimate of two pi of 6.40. That is only 2% above 6.28, not bad for wandering around the lawn.


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