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esisk
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I apologize that I am posting this in this section, but...
I wish that people did not reply to a thread and then merely state what they_do not know_ about the subject and what their experinece has been in life regarding the subject matter...
Unfortunately,as a consequence, seeing that a question has "been replied to" many qualified people tend to not to look at the question thinking that the person got the help. I am sorry for over reacting... I am clearly asking the question because I do not understand the basics, not because I want to discuss the various subtle aspects.
You be the judge. Here is my question and here also is the "reply":
ME: Can somebody give me an example whereby I use the inversion with respect to a circle (unit circle or otherwise) and the problem becomes easier. I guess I am asking: how do I make use of this notion. Or a problem that involves inversion, period.
Thank you
Reply: The only time I have used inversion in a circle was in Poincare's disk model for hyperbolic geometry. There "congruence" is defined in terms of reflections in a "line", "lines" are the portions of circles orthogonal to the disk inside the disk, and "reflection" in such a line is inversion in the circle.
In this article, http://en.wikipedia.org/wiki/Inversive_geometry, Wikipedia refers to using inversion in a circle to construct a "Peaucellier linkage", apparently important in "converting between linear and circular motion". I have heard that one can use inversion in a circle to model Wankel Rotary Engine but have no certain information on that
I wish that people did not reply to a thread and then merely state what they_do not know_ about the subject and what their experinece has been in life regarding the subject matter...
Unfortunately,as a consequence, seeing that a question has "been replied to" many qualified people tend to not to look at the question thinking that the person got the help. I am sorry for over reacting... I am clearly asking the question because I do not understand the basics, not because I want to discuss the various subtle aspects.
You be the judge. Here is my question and here also is the "reply":
ME: Can somebody give me an example whereby I use the inversion with respect to a circle (unit circle or otherwise) and the problem becomes easier. I guess I am asking: how do I make use of this notion. Or a problem that involves inversion, period.
Thank you
Reply: The only time I have used inversion in a circle was in Poincare's disk model for hyperbolic geometry. There "congruence" is defined in terms of reflections in a "line", "lines" are the portions of circles orthogonal to the disk inside the disk, and "reflection" in such a line is inversion in the circle.
In this article, http://en.wikipedia.org/wiki/Inversive_geometry, Wikipedia refers to using inversion in a circle to construct a "Peaucellier linkage", apparently important in "converting between linear and circular motion". I have heard that one can use inversion in a circle to model Wankel Rotary Engine but have no certain information on that
