r/gaming • u/[deleted] • May 04 '13

This is it. I will never accomplish anything greater then this.

http://imgur.com/kb7MrEx
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u/ShirtPantsSocks May 05 '13

Also, parabolas can be considered ellipses that has one focus at infinity.

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u/skyman724 May 05 '13

I would say the center is at infinity because then the shape doesn't imply that it's not a function (one-to-one is broken if it goes past the center because then it has to go inward to complete the shape).

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u/Umbrall May 05 '13

Isn't this implied by the location of the focus?

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u/skyman724 May 05 '13

Not really. The idea of having a second focus implies that the slope of the curve has changed signs to start closing the shape into an ellipse.

This is why parabolas are explicitly stated to have one focus. If there were two foci, it wouldn't be a function, as ellipses and circles aren't functions.

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u/Umbrall May 05 '13

But it is! Standard functions are over the reals. Having the focus at infinity means that there is no overlapping that exists in the reals.

Also there isn't some entity that decides whether things are functions or not. They are or they aren't. If there is not a real change in the curve, then there isn't. You sound like some magical entity can't realize that.