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## 'Golden Eggs' printed from http://nrich.maths.org/

1) An ellipse with semi axes $a$ and $b$ fits between two circles
of radii $a$ and $b$ (where $b> a$) as shown in the diagram. If
the area of the ellipse is equal to the area of the annulus what is
the ratio $b:a$?

(2) Find the value of $R$ if this sequence of 'nested square roots'
continues indefinitely: $$R=\sqrt{1 + \sqrt{1 + \sqrt {1 + \sqrt {1
+ ...}}}}.$$