Monogons and Digons - Polygons with Fewer Than 3 Sides
Date: 01/24/2006 at 13:22:38 From: Jay Subject: monogon and digon polygons ??? What do monogon and digon polygons look like? One of my students obtained the list of polygons from your site and asked me about those two polygons. Frankly, I do not know. I have always thought a polygon had to contain "at least 3 sides". I teach 7th grade math and would like to have an explanation for my students about those two shapes. Thanks!
Date: 01/24/2006 at 14:10:46 From: Doctor Peterson Subject: Re: monogon and digon polygons ??? Hi, Jay. If you search our site for "digon", you'll find this, which explains it a bit: One- and Two-sided Polygons http://mathforum.org/library/drmath/view/54142.html The idea is that, although real polygons in the usual sense can't have one or two sides, we reserve those names for cases where we extend the definition of polygon and CAN have monogons or digons. One example, mentioned there, is in spherical geometry, where "straight lines" are great circles, so a polygon is bounded by parts of great circles. Then the nothern hemisphere is a monogon (taking any one point on the equator as the one vertex); and the region bounded by two longitude lines (say, from the prime meridian to the meridian through New York) is a digon, with vertices at the poles. Another example is in topology, where we don't pay attention to whether "lines" are straight in the first place, but just look at the way they connect. If the "sides" are allowed to bend, it's easy to draw a monogon or digon. It's interesting to realize that the basic definitions kids learn are often stretched and twisted in higher math, as we try out "what if" questions like these: what if we aren't drawing on a plane? What if we don't require sides to be straight? In each case, some properties remain valid, while others change, and we discover new features of well-known ideas like "polygons". Math is a lot more dynamic than most students ever get to see, and this is just a taste! If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Date: 01/24/2006 at 14:29:44 From: Jay Subject: Thank you (monogon and digon polygons ???) Hi Dr. Peterson, Thank you very much for the very quick and detailed explanation. I am very impressed! I tell my students to visit your site often and have it bookmarked on my classroom computers. This is a perfect example of why I feel so confident making that recommendation to them. Respectfully, Jay
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