So there I am on the beach looking at the cloudless azure sky and feeling somewhat bored, perhaps because the simplicity of beach life was just too overwhelming that particular day. I mean with all that sand between your toes, the constant beach chair repositioning to afford a better tan, the incessant requests from family and friends for water (having power of attorney over the beach cooler, I was de facto water boy), beach life can be somewhat enervating. Not to complain, mind you. Just that sometimes beach time makes you realize that there are petty annoyances no matter how good life can be. Hey, but what about the time thing?

Oh, yes pardon the diversion. So I was looking up at the sky, luxuriating in the warm caresses of the summer breezes that wisped intermittently by, and I challenged myself by saying, ?œIf you?™re so smart, find a way to tell time using the sun. After all, you?™re always preaching to students, friends, and family about how useful mathematics is and how it can be used in everyday life.??Thus I took the challenge and began quickly to make the usual assumptions, do some quick calculations, test the hypotheses...and...lo, I came up with something. I reasoned thus. Facing the water, I was looking due east. The sun rises in the east and sets in the west, dropping off the horizon.

From previous observations, I knew the approximate position of the sun at the end of the day, which for us, was about 5-5:30 PM, when we would undertake the arduous task of packing up and heading home. Using approximately 6:00 AM as rising time for the sun and its approximate due east position, I constructed, using my finger or a seashell, a circle?“–albeit crude?”in the sand. I reasoned that the sun should carve out approximately equal arcs in equal periods of time while traversing the sky from east to west, from rising, to its final setting position, before dropping off the horizon. I sliced the circle in half with a diameter, and this was done so that one end of the diameter would point to the sun?™s rising, or due east, position, and the other would point to the sun?™s setting, or due west, position.