09.08 - Hand out (and discuss) revised time-sheets. Did you...

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Unformatted text preview: Hand out (and discuss) revised time-sheets. Did you all get the email I sent out yesterday? Get contact info for new students. Reminder: You will derive the maximum benefit from (and enjoyment of) class discussions if you have done the reading ahead of time. Class meetings are where we explore and firm up our grasp of the concepts, NOT the place where we encounter them for the first time. If you havent done the reading, its still better to come to class than not to, and you should still try to participate, but you wont get as much out of the class as you will if youve at least skimmed the section. Section 10.1 challenge problem: What single equation corresponds to the circle of radius 1 in the x , y plane, centered at (0,0,0)? ..?.. One solution (found by Eli Natti) is x 2 + y 2 = sqrt( z ) sqrt( z ) + 1. Lets find another solution (this one not using the square root function). That is: What single polynomial equation has as its solution set {( x , y , z ): z = 0 and x 2 + y 2 = 1)? ..?.. Hint: What single equation has as its solution set {(1,2,3)}? ..?.. We saw that the equation ( x 1) 2 +( y 2) 2 +( z 3) 2 = 0 has only the point (1,2,3) as a solution. Can someone remind us why? ..?.. Because a sum of squares can only equal zero if all of the quantities being squared equal zero. So let me ask the challenge problem again, in a slightly different way: What single polynomial equation has as its solution set {( x , y , z ): z = 0 and x 2 + y 2 1 = 0)?...
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09.08 - Hand out (and discuss) revised time-sheets. Did you...

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