Errata
The bound copy available for purchase essentially matches the current, freely available version of the text. What follows is a list of errata in the bound copy that have been corrected in the online version of the text. I am grateful to readers for pointing out errors.
- pp. 124-5, in the proof of Theorem 5.4.19 the passage describing the construction of the common perpendicular has been corrected to the following passage, with changes emphasized in blue:
Then construct the common perpendicular of \(C\) and the imaginary axis, call this perpendicular \(D\text{.}\) We construct this common perpendicular as follows. First find the two points \(p\) and \(q\) symmetric to both \(C\) and the imaginary axis (see Theorem 3.2.16). The points \(p\) and \(q\) will live on the circle at infinity. The common perpendicular of \(C\) and the imaginary axis will be the cline through \(p\) and \(q\) that is also a hyperbolic line (i.e., orthogonal to the circle at infinity).
If \(C\) and the imaginary axis intersect, no such perpendicular exists (think triangle angles), so drag \(v_2\) away from \(v_1\) until these lines do not intersect. Then construct \(D\) as in the preceeding paragraph. Let \(v_4\) and \(v_5\) be the points of intersection of \(D\) with \(C\) and the imaginary axis, respectively.
- p. 128, Exercise 5.4.11 should read \begin{equation*} \cosh(c) = \frac{(1+|p|^2)(1+|q|^2)-4\text{Re}(p\overline{q})}{(1-|p|^2)(1-|q|^2)} \end{equation*}
- p. 130, Exercise 5.4.14 a) should read
In particular, show that \(\cosh(d_H(0,p)) = \cosh^2(a)\text{.}\)
- p. 130, Exercise 5.4.14 d) should read
Show that \(\cosh(d_H(p,q)) = \cosh^4(a)[1-\sin(2\theta)]+\sin(2\theta)\text{.}\)
- p. 215, the last full sentence on the page should read (change is in blue):
It turns out that every surface can be viewed as a quotient space of the form \(M/G\), where \(M\) is either the Euclidean plane \(\mathbb{C}\), the hyperbolic plane \(\mathbb{D}\), or the sphere \(\mathbb{S}^2\), and \(G\) is a group of isometries in Euclidean geometry, hyperbolic geometry, or elliptic geometry, respectively.