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The Magic Cafe Forum Index » » Magical equations » » Advancing a Point (0 Likes) Printer Friendly Version

funsway
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Inner circle
old things in new ways - new things in old ways
9061 Posts

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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/ken-muller-m-579928.html questions at ken@eversway.com
Doctor Whoston
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Leeds, England
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So how do you get a hyperbola?
DW
funsway
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Inner circle
old things in new ways - new things in old ways
9061 Posts

Profile of funsway
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/ken-muller-m-579928.html questions at ken@eversway.com
Doctor Whoston
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Leeds, England
149 Posts

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Outside the circle seems reasonable. But I haven't been able to prove it works yet!
DW
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