Van Schooten's ellipse problem

jojoba26 shared this question 11 years ago
Answered

Van Schooten's ellipse problem

Line a,b intersect at point O,

Moving ΔABC vertex A,B along to Line a,b

then the locus of the third vertex is an ellispe.

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I draw the graph with geogebra as in the attached file,

Something happened , the ellipse is not complete......

How to draw the complete ellipse?

Any comment will be appreciated !

schooten

https://ggbm.at/540145

Comments (7)

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Hi,

Your construction is based on the intersection point at B. When you pull A too far there is no more intersection point. You need to draw both sides of the ellipse at once by reflecting your construction across line a.


The Van Schooten ellipse that I know is from a linkage mechanism that transforms circular motion into elliptical motion. In this case A is pulled around a circle. See here:


http://homepage.mac.com/dsc...


Your construction uses linear motion. Pulling A too far corresponds to solving a quadratic to get a square root function and then entering a negative value in the square root.

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Hi jojoba26


I think you want this:


https://ggbm.at/540147

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Hi, waldo and piman

thanks for your reply

I draw the graph again, and this is what I want.

You may read Van Schooten ellipse problem in the book

Heinrich Doerrie: 100 Great Problems of Elementary Mathematics, p.214.

(GOOGLE van schooten 100 math will fing the online edition)


vanschooten

https://ggbm.at/540149

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Hi

when I followed the Piman ellipes with animation ,I could not get the locus[D,C]

any advice

?

https://ggbm.at/540155

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I saw this excellent gif on tumblr of Van Schooten's Ellipse.

http://mathhombre.tumblr.com/post/65887395750/mirandamolina-elipse-de-van-schooten

http://31.media.tumblr.com/6052a5d697e2ca2cf0020c92cd27fb1a/tumblr_merqwsQRTV1rsz0ajo1_500.gif


In making it I found four relevant intersection points:

http://i1218.photobucket.com/albums/dd420/mathhombre/VanSchootenEllipses-double_zps051612c3.png


I couldn't figure out how to make it one consistent linkage. So I cheated and added a slider and then switched among them.

VanSchootenEllipses2-2_zps5e54c769


Any ideas on how to make it a single linkage? Then it would have a nice locus. Material attached.

https://ggbm.at/564159

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The mobile version does the flipped thing with the intersection points. http://www.geogebratube.org...

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Any ideas on how to make it a single linkage?


Yes :)


http://tube.geogebra.org/st...


Another reference:

http://web.mat.bham.ac.uk/C...

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