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February 18th, 2013, 09:57 AM   #11
jks
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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:

with a a real number.

A couple of solutions for are (i,0) and (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.
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February 18th, 2013, 07:13 PM   #12
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Re: Negative Radius Circle

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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
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February 18th, 2013, 07:18 PM   #13
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Re: Negative Radius Circle

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:

with a a real number.

A couple of solutions for are (i,0) and (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
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February 19th, 2013, 06:07 PM   #14
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Re: Negative Radius Circle

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.....
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February 19th, 2013, 06:36 PM   #15
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Nobody grumbles about negative curvature...
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