X Line in a 3D GraphDate: 03/10/2001 at 16:22:38 From: jane pfaender Subject: x, y, z coordinates Is the x line on a graph, as drawn on a page, vertical or horizontal? Thank you. Date: 03/10/2001 at 18:09:03 From: Doctor Achilles Subject: Re: x, y, z coordinates Hi Jane, Thanks for writing to Dr. Math. There are two conventional ways to draw a 3D graph on paper. Your first choice is this: +y | | | | | | (-x)---------------|----------------+x | | | | | | -y Where +y is the positive direction and -y is the negative direction for y. In this graph, z would be positive coming out of the page at you and negative going into the page. This is often drawn like this: +y -z | / | / | / | / | / |/ (-x)---------------|----------------+x /| / | / | / | / | / | +z -y Here the +z is understood to be coming out of the page and the -z is understood to be going in. Your second choice is this: +z +y | / | / | / | / | / |/ (-x)---------------|----------------+x /| / | / | / | / | / | -y -z In this case, +x is to the right and +z is up. -y is coming out of the page at you and +y is going into the page. These are actually equivalent representations. To see that they are, try doing this: hold up your right hand with your palm flat, your fingers extended, and your thumb pointing to the side. Point your thumb in the +x direction while pointing your fingers in the +y direction. Your palm will automatically be facing the +z direction in both systems. (Try it out for both systems.) Notice that in both of these conventional representations, x is horizontal. But there are other equivalent representations that don't have x pointing horizontally. For example: +x -z | / | / | / | / | / |/ +y---------------|----------------(-y) /| / | / | / | / | / | +z -x This is just another perspective on the same representation as the two conventional representations I showed you above. However, in the two conventional representations that I'm familiar with, x is always horizontal. Hope this helps. If you have any other questions about this or any other math topics, please write back. - Doctor Achilles, The Math Forum http://mathforum.org/dr.math/ |
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