Friday, October 25, 2019

Solutions to Exercises of section 12.6 in A Survey of Geometry

In a blog entropy of 20 June 2019 we talked about cross ratios in the Gauss plane, the topic of section 12.6 of Howard Eves' A Survey of Geometry. One thing that distinguishes this text is the wonderful set of exercises the author includes. They give the reader the chance to deepen their understanding of the theory presented in the book while extending the results covered by the author. In many cases, readers don't have time to explore these carefully selected exercises in full.

Although the real fun and true value of exercises is in doing them oneself, not everyone has the time to do so. Since I enjoy working out such things and in this case did so, I am including this link to them  Solutions to Exercises of section 12.6 in A Survey of Geometry  in case someone might like to learn more about cross ratios. There a few results in this set which are pretty useful results in themselves. My favorites were the Constructions in 12.6-14 and the Theorems that follow from Schick's Theorem in 12.6-16.

I hope that there are no typos or other such nuisances and apologize in advance if there are. If there are questions or concerns about any solution, I would welcome comments in that regard.

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