 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ib/paper-4/11e/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

d s^{2} = \frac{4 ( d x ^{2} + d y ^{2} )}{( 1 - x ^{2} - y ^{2} ) ^{2}} .

Rotations about the origin are hyperbolic isometries, so a Euclidean circle centred there is a hyperbolic circle. Its radius is the radial length

R = \int_{0}^{r} \frac{2 , d t}{1 - t ^{2}} = lo g \frac{1 + r}{1 - r} = 2 artanh r .

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