

funsway Inner circle old things in new ways  new things in old ways 9061 Posts 
In 7th grade I learned something considered 'magical' whenever I have shown it since. We constructed all of the basic plane geometric shapes by "advancing a point through a line" of some sort  physically demonstrating the mathematical equation. We folded wax paper with a line on it and a point. By folding the point over the line visible through the paper and creasing a new line, you form a vector that meets the formula definition. Make enough crease lines and you form the shape.
Folding a single point through a straight line forms a parabola. A point (inside) folded through a circle forms an ellipse, with the circle center being the other foci  and so on. The real 'magic' is that we were taught these things back then ...
"the more one pretends at magic, the more awe and wonder will be found in real life." Arnold Furst
eBooks at https://www.lybrary.com/kenmullerm579928.html questions at ken@eversway.com 
Doctor Whoston Regular user Leeds, England 149 Posts 
So how do you get a hyperbola?
DW 
funsway Inner circle old things in new ways  new things in old ways 9061 Posts 
A point outside the circle, I think, to draw one half  then the center of the cicle uses that as a line  not sure though
"the more one pretends at magic, the more awe and wonder will be found in real life." Arnold Furst
eBooks at https://www.lybrary.com/kenmullerm579928.html questions at ken@eversway.com 
Doctor Whoston Regular user Leeds, England 149 Posts 
Outside the circle seems reasonable. But I haven't been able to prove it works yet!
DW 
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