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6 cm, 8 cm

Here we compare the two versions of the ellipse.
[The drawing shows the ellipse for AB = 6 cm, and the movie generates the ellipse for AB = 8 cm.]

Did you predict what happens to the height?
Did you predict what happens to the width?

It turns out that the width stays the same. We stumbled on this result while constructing the task and found it very surprising. It goes against the intuition that as A and B move further apart, more string is 'available' for the width of the ellipse. Perhaps this is based on the false notion that the width is achieved by pulling the string out in two directions simultaneously.

Can you explain why the width doesn't change? We consider some reasons on the next three pages.