My Math Forum Negative Radius Circle

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 February 18th, 2013, 09:57 AM #11 Senior Member     Joined: Jul 2012 From: DFW Area Posts: 642 Thanks: 99 Math Focus: Electrical Engineering Applications Re: Negative Radius Circle Hi tfullerton, is your student familiar with complex numbers? Maybe he/she could consider circles with radii in terms of the imaginary unit: $(x-x_o)^2+(y-y_o)^2=-a^2=(a \cdot i)^2 \$ with a a real number. A couple of solutions for $\ a=1, \ x_o=y_o=0 \$ are (i,0) and $\left(\frac{1}{2}+i\frac{\sqrt{3}}{2}, \ -\frac{1}{2}+i\frac{\sqrt{3}}{2}\right) \$ (of course x and y could be exchanged). If the student is not familiar with complex numbers, this might be a way to introduce them because I think that it would result in the student learning the basic properties of complex numbers including powers and roots (squares and square roots at least). My apologies if this is not appropriate for his/her study.
February 18th, 2013, 07:13 PM   #12
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 Originally Posted by anasfeelgood Or maybe a circle with positif radius would be looking inside, and with negatif radius would be looking outside, so the area of a circle with R > 0 would be Pi*R², but if R < 0 it would be +infinity
Wonderful! Thank you so much, I'll be sharing this and puzzling it through with him
Tom

February 18th, 2013, 07:18 PM   #13
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Quote:
 Originally Posted by jks Hi tfullerton, is your student familiar with complex numbers? Maybe he/she could consider circles with radii in terms of the imaginary unit: $(x-x_o)^2+(y-y_o)^2=-a^2=(a \cdot i)^2 \$ with a a real number. A couple of solutions for $\ a=1, \ x_o=y_o=0 \$ are (i,0) and $\left(\frac{1}{2}+i\frac{\sqrt{3}}{2}, \ -\frac{1}{2}+i\frac{\sqrt{3}}{2}\right) \$ (of course x and y could be exchanged). If the student is not familiar with complex numbers, this might be a way to introduce them because I think that it would result in the student learning the basic properties of complex numbers including powers and roots (squares and square roots at least). My apologies if this is not appropriate for his/her study.
Thank you! I'm not sure if he has heard of complex numbers but I'm sure he'll want to explore.
I know this has me (re)thinking circles.
Much appreciated,
Tom

February 19th, 2013, 06:07 PM   #14
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Quote:
 Originally Posted by Denis ...if you kick the ball in your own net during a soccer game, did you score -1 goals ? :P
Yes,thats correct Denis.
Thats why maybe nobody calls you a hatricker when you score 3 own goals...You are a negative hatricker.....

 February 19th, 2013, 06:36 PM #15 Global Moderator   Joined: Dec 2006 Posts: 20,919 Thanks: 2201 Nobody grumbles about negative curvature...

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can circle have a negative radius.

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