I took a class on euclidean and non-euclidean geometry in year 11.
We read Poetry of the universe
It deals with exactly the kinds of things you mention. And it is wonderfully written.
Pick it up and I'm sure it will help.
I need to teach senior high school students (Year 11) in finding distances along circles of constant latitude or constant longitude on the surface of the Earth.
What would be an innovative and student-centred way of approaching this concept to students?
All I have thought of so far, is to bring a globe with me to the class to help students understand better.
Any popping ideas???
I took a course on non-Euclidean geometries my first year. The book I have is Poincare Half-Plane. It does require to be good in Calculus III. It is not the best written book but understandable. It takes about different models and approaches. I believe the Sphere is also studied (though we never did that part).
Note the book I mentioned is the complete book. Strange, is it not?