Fourth Grade Geometry Questions
Date: 24 Apr 1995 23:08:40 -0400 From: B Eggers Subject: Geometry Question Dear Dr. Math, My group of grade 4 regular ed. students are wondering if curved lines can be parallel lines. For instance, if we drew two s's so they were parallel. Also, is a cylinder a circular prism? Another question: Do polygons have to have straight lines? Let's say you have a squarish figure with a "bite" taken out of it that is a half circle. (Wish I could draw it for you). Is that called a polygon? It is a closed figure. Are circles like bull's eyes parallel? Thank you for your help. These questions have caused lots of discussion around dinner tables of the teachers and educational assistants. Becky Eggers, Chapter 1 Edison Elementary School Kennewick, WA 99337
Date: 26 Apr 1995 00:09:52 -0400 From: Dr. Ken Subject: Re: Geometry Question Hello there! "My group of grade 4 regular ed. students are wondering if curved lines can be paralled lines. For instance, if we drew two s's so they were parallel." Well, the term "parallel" really only applies to actual lines. What it means is that the two lines don't intersect anywhere (there are other definitions of the term like the two lines are the same distance apart everywhere, but the most commonly accepted definition is that they don't intersect anywhere). So I suppose that you could try to generalize the concept of "parallel" to arbitrary curves, but it probably wouldn't be such a useful tool, and it's probably better to talk about curves that "don't intersect" or that are "the same distance apart everywhere." "Also, is a cylinder a circular prism?" Well, technically speaking, no. An ice-cream cone is a circular prism. A prism is what you get when you take a closed figure in a plane and you connect all its points to a point that's not in the plane. So perhaps you could say that a cylinder is a circular prism, but the point that the circle's points are connected to is infinitely far away. That's what's known as a degenerate case of a circular prism. "Do polygons have to have straight lines? Let's say you have a squarish figure with a "bite" taken out of it that is a half circle. (Wish I could draw it for you) is that called a polygon. It is a closed figure." Well, this kind of depends on who you talk to and what context you're in. In some subjects it's convenient to think about polygons with curved edges. In other subjects (like Euclidean geometry) it's really not convenient to think about polygons with curved edges. For instance, if you allow that kind of thing, a triangle no longer has to contain 180 degrees; it could contain more or less. In general, you only talk about polygons being made up of "lines," which in Euclidean geometry means "straight lines." "Are circles like bull's eyes parallel?" The term for circles that share the same center is "concentric." "Thank you for your help. These questions have caused lots of discussion around dinner tables of the teachers and educational assistants." Sure, we're glad to help! -Ken "Dr." Math
Date: Wed, 26 Apr 1995 14:20:46 +0000 From: Dr. Math Subject: Re: Geometry Question Hello there! I'm afraid I said something stupid to you in my last response. I confused the terms "prism" and "pyramid." All that stuff I said before is about pyramids, and wherever you see the word prism in my message, replace it with pyramid. I also found out that the word "cone" is usually used to refer to pyramids when the base isn't a polygon with straight sides. The term "prism" is defined as "a polyhedron with two congruent and parallel faces that are joined by a set of parallelograms." So strictly speaking, a cylinder isn't quite a circular prism, but if you take the limiting case of a regular polygon where the number of sides is going to infinity, you'll end up with a circle. If you use that circle to generate a prism, you'll end up with a cylinder. So in a sense, a cylinder is the a limiting case of a prism (called a degenerate case of a prism). Hope this clears up any confusion! -Ken "Dr." Math
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