Is It Really Possible to Draw a Graph?Date: 02/01/2007 at 22:23:24 From: Zak Subject: What is the best way to draw a graph While doing pre-calculus, a common thing for our teacher to ask of us was to "draw a graph". For example, she might ask us to draw f(x)=x. (Continue reading, it gets more interesting!) To start off, by definition this graph is a "collection of points," and points have no dimension (depth/length/height). By drawing the graph with a pencil, you are giving the graph a "3D" framework, because the "thinness" (I can't think of a better word) would be infinitely small, too small to see. The dimensions of a graph are too small to draw, and therefore only a "representative graph" can be drawn. My teacher looked at me strangely. I was wondering if you could help answer this question. Date: 02/02/2007 at 08:36:30 From: Doctor Peterson Subject: Re: What is the best way to draw a graph Hi, Zak. You're right: When we draw a graph, we aren't really drawing that set of points; we are making a representative picture of the graph. In the same way, if I asked you to draw your house, what you put on paper would not be the house itself, just a picture of the house, showing approximately what the house looks like. That doesn't mean that you can't draw your house! You just have to know what we mean when we say that. In geometry, when we draw a circle or line, it is never a real circle or line, because those have no thickness, are not made of atoms, and (in the case of the line) extend forever. Our paper is not really a plane. All these things are just representations or models of abstract concepts in our minds: ideal lines, ideal circles, ideal graphs. Sometimes we confuse the real with the ideal, and imagine that what we are drawing is the actual circle or graph; it's important to call attention to the difference, as you are doing. Bottom line: You CAN draw a graph--but it's only a picture, not the real thing. Does that clarify things? - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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