Note: This was Friday's (05/27/11) lesson
Today we went over some simple parametrizations, and how to prove a given vector parametrization is a specific shape. We then went over the idea of finding the surface area of a surface. This would simply be the small area in the parallelogram between the Rx and Ry components. The cross product of these components can also give us the normal vector, which would make it much easier to find the tangent plane to a surface. We ended on the note that the Area of a Parametric surface is:
Surface Area= SSsds = SS_D ||Ru x Rv|| dA
Where s is the traverse of the surfaces and ds is the addition of the little pieces of the surface
Today we went over some simple parametrizations, and how to prove a given vector parametrization is a specific shape. We then went over the idea of finding the surface area of a surface. This would simply be the small area in the parallelogram between the Rx and Ry components. The cross product of these components can also give us the normal vector, which would make it much easier to find the tangent plane to a surface. We ended on the note that the Area of a Parametric surface is:
Surface Area= SSsds = SS_D ||Ru x Rv|| dA
Where s is the traverse of the surfaces and ds is the addition of the little pieces of the surface
I read on a site that scientists use something called "parametric surface modeling" to create brain images to help them study the functions of the brain. Though accurate and efficient imaging of something as complex as the brain is challenging, at least parametric surfacing is taking science to another level. Perhaps in the future, scientists can use it to pinpoint the exact location/origin of certain brain problems.
ReplyDeleteThe homework for the weekend is to do pg 1109 #17-20, 25, 30, 38, 40, 54, and 57, along with bringing a short, detailed plan on your proposed video. This must include a title, brief overview (ex. what is the video going to be about?), staging (ex. what will you be recording?- writing on board? folding a pyramid? two people talking?), the location of where your video will take place, and the participants. All of this is due tuesday!
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