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Introduction
to the x,y-Plane Sections: Introduction to the plane, Plotting points, The four quadrants Way back when, math was divided into geometry and algebra, and these were two totally separate subjects. You pretty much didn't do equations in geometry, and you pretty much didn't do pictures in algebra. Then, around 1637, a French guy named René Descartes (pronounced "ray-NAY day-CART") came up with a way to put these two subjects together. To explain Descartes' method, first think about using a street map. If you're trying to find a street that you've never been on before, you look for the street name in the index of the street map. Suppose the index says that the street is located at D12. This means that you go across the top of the map and find "D", and then go down the side and find "12". You trace down and across to find the box labelled as "D12", and then you look inside the box for the street you need. Somebody figured out this way to give you directions on the map, by telling you "how far over" and "how far down" you need to look. Descartes did something similar. Copyright © Elizabeth Stapel 2006-2008 All Rights Reserved You learned about the basic (counting) number line back in elementary school:
Later on, you were introduced to zero and negatives, which completed the number line:
Descartes' breakthrough was in taking a second number line, standing it up on its end, and crossing the first number line at zero:
The number lines, when drawn like this, are called "axes" (pronounced "ACK-seez"). The horizontal number line is called the "x-axis" ("eks-ACK-siss"); the vertical one is the y-axis. By the way, the arrows at the ends of the axes indicate the direction in which the numbers are getting larger. Therefore, only the axes should have arrows, and the arrows should be on one end only. Yes, many textbooks are wrong. So are many teachers. Don't point this out to them; for some reason, they're extremely touchy on this subject. The whole flat expanse, top to bottom, side to side, is called the "plane". When you put the axes in the plane like this, it is called the "Cartesian" ("carr-TEE-zhun") plane. The name "Cartesian" is derived from the name "Descartes", after its creator, Rene Descartes. Please don't ask me to explain that derivation; I think it's Latin, and I can barely handle English. Top | 1 | 2 | 3 | Return to Index Next >>
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Copyright © 2006-2008 Elizabeth Stapel | About | Terms of Use |
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