Christmas is a week away, temperatures have been hovering in the teens, and I'm writing about fun in the sun and something about using mathematics to tell time on the beach! Good gracious. You must be thinking how weird I am. Well maybe, but for those who have been following some of my other articles, you know then that I seek to show how mathematics"?yes even basic mathematics"?functions so universally throughout our everyday lives. Even the layman can use this beautiful tool do so many common and ordinary things! Perhaps while I sit here clacking at my keyboard, the chill running through my body forces me to hark back to the bright halcyon July and August days when I frolicked in the sand and listened attentively to the rhythmic crashing of the waves"?and of course, contemplated the hour of the day by observing the position of the sun in the sky. Now some might be thinking, "Wait. Navigators and sailors have used the stars and celestial bodies for time immemorial to do such things as tell time, pinpoint their position on the globe, tell their course of direction, and to make sundry other determinations."? I know this. Yet once again, while spending some time at the beach one day, I wanted to see whether I could, without any prior research or study in the field, nor prior knowledge of such, somehow devise a method of telling the time using the sun. Now why would any sane person wearing a watch on his wrist do this? Well for one, to see what it might have felt like before we had such conveniences as the wrist watch, and for two, to show that with a little thought and some basic knowledge, man is quite a formidable thinker! Passing this knowledge and experience on to you will serve the purpose of aligning your thoughts more with nature and to show you that you can do extraordinary things"?if only"?you start thinking a little. 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, "If 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. Using the assumption about the sun sweeping out equal arcs in equal time intervals, I then divided the semicircle into twelve equal segments to allow for the time period during which it would go from due east to due west position. Not having a compass or other instrument to segment the semicircle equally, I did my best to divide the 180 degrees in half into two equal ninety degree segments. I then divided the two ninety degree segments in half into two equal forty-five degree segments. Finally, I trisected (divided in three) each of the four forty-fivWeb-Site Savvy For Pet-Care Business Ownerse degree segments to obtain twelve equal fifteen degree segments. Having done this, I was left with thirteen radii (one more than the number of segments) or "spokes"?on my semicircle, starting with 6:00 AM and ending with 6:00 PM. Each of these radial spokes would represent an hour on the face of the semicircle. At last, I had my crude sundial. While basking in the sun, there I am looking up at this star and lining up its position with one of the spokes on my sundial. Ah, the sun is pointing right at the spoke corresponding to 1:00 PM. I look at my watch, and lo and behold, it's 1:05 PM! (Of course this has to be approximate because of the method used. You didn't think I could construct a perpetual motion Rolex in the sand, did you?) Yet after testing time and time again, this crude construct works consistently. To be able to tell time based on nothing other than a crude construct in the sand, and to be able to do this within plus or minus ten minutes of the actual time, is, I would think, quite a feat"?especially in this day of jaded excessiveness. Try it out and let me know your experience. Bear in mind, you might have to tweak the location of the spokes, or hour hands on the sundial depending on your exact location; however, using the basic assumptions made here, you should prove a marvel to your friends and family at the beach. And what a great way to spend real quality time with the kids on the sand. Until next time...... |
