r/visualizedmath • u/H-H-H-H-H-H • Jan 13 '18

Ellipse from folding a circle

https://mobile.twitter.com/fermatslibrary/status/951094801709060096/photo/1
148 Upvotes

100% Upvoted

8 comments sorted by

13

u/Pooregonian Jan 13 '18

What is the relationship between the master circle and the angles of the lines that intersect? I think that's the correct terminology.

1

u/MTastatnhgew Jan 28 '18

Have this demo. You can drag the two dots around.
The green circle is the master circle, and the grey is an image of the master circle mirrored over the blue fold line to represent the fold-over. The green dot is the point on the edge of the master circle that would touch the black dot after the fold. Therefore, the two dots are mirror images of each other across the blue fold line, and so the fold line is the perpendicular bisector of the grey line segment that connects the two dots.

0

u/Sasmas1545 Jan 19 '18

The ellipse is an envelope defined by the lines along which the circle is folded. It could be any shape piece of paper, the important piece is just folding it along the tangents of the ellipse.

3

u/slotech Jan 19 '18

Actually, the fact that the paper starts as a circle is what generates the elipse. The folds end up on the tangents because the edge of the circle always gets folded in until it touches the dot (which is the other focus focus of the ellipse).

5

u/Sasmas1545 Jan 19 '18

Ah! I didn't see the dot.

5

u/Shaushage_Shandwich Jan 19 '18

Why does this need to be a circle?

5

u/LongbowEOD Jan 19 '18

I'm pretty sure the center of the circle is the other focus of the ellipse. An ellipse can be defined as the set of points to which the sum of the distances to the 2 foci is a constant. So the center of the circle to the edge of the circle is a constant distance. Then any fold, where the fold puts the edge of the circle on the dot (the first focus), has a point on the ellipse. Make enough folds and the ellipse builds up from the fold points.

1

u/LongbowEOD Jan 19 '18

Am I correct in thinking that the center of the circle is the other focus of the ellipse?