Pi on a clothesline near the equator

In MS 101 Algebra and Trigonometry I opened the chapter on angles and radians by introducing a dimensionless measure of angles out on the lawn. I put Seagal at the center and then had Tammy walk the surveyor's wheel around Seagal at the end of a 44 foot long piece of clothesline. I probably should have given the line to someone else to keep the line taut as this would prove problematic out between pi over two and pi radians. Every ninety degrees I took a measurement and placed a student. Hansha was at zero next to the A building generator. Moving counter-clockwise, Patricia was a quarter turn, Maggie opposite Hansha, and Shellany at three-quarters of the circle.

Circle complete, Seagal on center, Natasha and Hansha at zero, Tammy holding the wheel, Patricia up at pi over two. Note that Natasha now has the line.

With Hansha at zero, Patricia was 68 feet worth of arc length away. Divided by 44 yielded the dimensionless 1.55 radians. Maggie was at 145 feet around the circle, 3.30 radians. Shellany 216 feet, 4.91 radians. The full circle was 295 feet, 6.70 dimensionless radians. 

Natasha with the line

There is more line, but not enough space on the front line to use the full line. Moving north would not help significantly: the hill to the east is problematic, the terminalia to the north is also limiting. Still, the concept can be well demonstrated that angles need not have units if they are specified as arc length divided by radius.

A Google pan of the three shots stitched together with some artifacts.


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