Translation, Reflection, Rotation
Date: 05/16/2001 at 10:14:02 From: MIKE Subject: Geometry What is the difference between slide, flip, and turn? I find it really hard. What are shapes - can you send me a list?
Date: 05/16/2001 at 13:01:44 From: Doctor Peterson Subject: Re: Geometry Hi, Mike. Slide, flip, and turn are meant to be kid-friendly replacements for the technical terms translation, reflection, and rotation. You're supposed to be able to picture them more easily using the simpler words. So let's relate their math meaning to their everyday use. If I SLIDE into home plate, I am basically moving sideways without turning. Here I'll slide a square from one side of the page to the other: +-----+ +-----+ | | | | | | | | +-----+ +-----+ This only changes the shape's position, not its orientation (the direction it faces). Maybe there's a gyroscope inside the shape! If I TURN around, I pivot so that I face a different direction. Here I'll turn, or rotate, a square by about 45 degrees: + +---------+ / \ | | / \ | | + + | | \ / | | \ / +---------+ + A rotation doesn't change the shape, but it will change the position of parts of it, and the direction it faces. It's best to picture rotation as rotation in place, that is, imagine my first square as a piece of paper, put a pin through the middle, and rotate it round the pin, so the center of my second picture is actually in the same place as the center of the first. If I FLIP a pancake, I'm turning it over. The same sort of thing happens if I look at myself in a mirror; the left and right sides switch places. Here I'll flip a right triangle over: + : + |\ : /| | \ : / | | \ : / | +---+ : +---+ Notice that I can't make this same change by sliding or turning; if the triangle were a separate piece of paper, I would have had to turn it over. If I had to keep the same side on top, I would have to replace it with a new copy made backward; or I could just put a mirror along the dotted line and only see the reflection of the original triangle in the new position. You can also imagine turning (flipping) a page in a book; the dotted line is then the middle of the book. If you need more help, you might want to send in a problem involving these motions, and tell me where you have trouble with it. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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