Date: 4/1/96 at 20:58:1 From: Terry Perkins Subject: geometry assignment My son's 5th grade math assignment says to name objects in the real world that suggest geometric figures including lines and planes. The definitions of these two terms indicates infinite dimensions. The examples in the text (MacMillan) are the horizon for line and the ocean for plane. What are some other real world examples? Are we taking the infinite dimensions too literally? Is a desk top a plane? Even though your answer will not be received in time, we are still curious. Please help.
Date: 4/2/96 at 2:36:53 From: Doctor Jodi Subject: Re: geometry assignment Your question is a really good one. At my college, everyone studies Euclid's ELEMENTS - a great, ancient geometry book - in the freshman year. Classes invariably spend at least the first class, and sometimes the first WEEK discussing the existence of points and lines. The geometry of mathematics is much different from the "geometry" of our experience. In my opinion, such comparisons must be taken with a grain of salt:it is too easy to confuse experience and truth. For example, would you believe it if I told you that the shortest path betwen two objects isn't always a straight line? Or that "straight lines" don't always have to be straight? Of course, having an IDEA of what we're studying - being able to visualize it - is very important. But if we depend too much upon whatwe can see, we may find it difficult to talk about the geometry of four or even more dimensions. (Just for the record, visualizing the fourth dimension is a hot topic among research mathematicians.) Thanks for your question. I wonder what your son's class thinks about the similarity and differences between mathematical and "real" geometry... By the way--I'd say that points are one dimensional, lines two- dimensional, etc. I'd also say that they're infinitely small. A little bit different from your wording, but I think we mean the same thing... -Doctor Jodi, The Math Forum
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