| MAT 515: |
Course description: This is a course covering the basics of planar Euclidean geometry, intended for future and practicing teachers. It is to help you understand the subject and issues in the subject well enough that you can teach the course.
Textbook: Kiselev's Geometry (Book I, Planimetry) Sumizdat, El Cerrito, Calif., 2006.
Other possibly useful resources:
While it is not necessary or required, I think gaining some experience with actual precise geometric constructions is very useful. Most of the time I will do only sketchy pictures on the lectures, and sketchy pictures are fine on the exams as well - as long as they clearly reflect the main ideas and you write down the precise construction by words and appropriate notation.
However, I suggest to try out geometric constructions by pencils, rulers, compass, and sometimes protractors, on paper sheets, to really see how things work in practice.
Both physical constructions by pencil, ruler, compass, and software geometry have certain advantages and disadvantages. On paper, it is easier to see what happened, how the picture was created, and it helps to build confidence and understanding of the main concepts, but if you want to change something, you have to make a new picture. Using a software, it is very easy to change the picture by changing the position of the input parameters (and in general, a software is a great tool to trace a position of points with certain properties), but sometimes the pictures are overcomplicated: the entire circle or entire infinite line is present, not just their relevant arcs or segments, and making a picture more clear requires extra effort.
I strongly suggest to play a bit with pencils, rulers, compasses as well as software tools to experience geometry and see the nice and less nice sides of both methods.
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