Math 128, Modern Geometry
D. Joyce, Clark University 24 Oct 2005
Due Today. From Chapter 8: 1, 2, 8. Last time. We nished our study of the hyperbolic plane. We looked at area. We saw that the area of a triangle was equal to the angle defect of the triangl
Math 128, Modern Geometry
D. Joyce, Clark University 16 Sep 2005
Third, the composition T U of two Mbius o Due Today. Exercises from chapter 4: exercises transformations is another one. (See the text for 1, 2, 5. details.) Today. Begin Mbius geometry. o G
Math 128, Modern Geometry
D. Joyce, Clark University 5 Oct 2005
Due Friday. From Chapter 6: 3abc, 6, 7ab, 10. Read Chapter 7. Well start it today and nish it next time. Poincars model for hyperbolic geometry. e Rather than build hyperbolic plane geometry
Math 128, Modern Geometry
D. Joyce, Clark University 17 Oct 2005
Due Wednesday. From Chapter 7: 1, 6, 9, 10. Read for next time. Chapter 9 on hyperbolic length. We wont cover chapters 9 and 10 in detail since our course does not have calculus as a prerequ
Math 128, Modern Geometry
D. Joyce, Clark University 12 Sep 2005
Due Friday. Exercises from chapter 4: exercises First, the identity transformation I is included 1, 2, 5. in G. Thats the function I dened by I(x) = x for all x S. Read for Wednesday. Contin
Math 128, Modern Geometry
D. Joyce, Clark University 26 Sep 2005
At our last meeting we looked at a signicant gap to the right angles in the congruent trianges. But in our proof. It occurred after the construction that what we need to know is that the gur
Math 128, Modern Geometry
D. Joyce, Clark University 28 Oct 2005
Last time. Finished our discussion of elliptic geometry. Began a discussion of absolute geometry, also called neutral geometry, the properties of geometry that are common to hyperbolic, Eucl
Math 128, Modern Geometry
D. Joyce, Clark University 14 Oct 2005
Due Wednesday. From Chapter 7: 1, 6, 9, 10. For next time. Begin reading chapter 8. Last time. Examined the beginning of Book I of Euclids Elements. Before that, discussed Poincars model for
Math 128, Modern Geometry
D. Joyce, Clark University 26 Sep 2005
First test. This Friday, to cover through chapter ter, take a family of Steiner circles of the rst kind, apply the transformation mentioned above so that 5. Review on Wednesday. its transfor
Math 128, Modern Geometry
D. Joyce, Clark University 14 Sep 2005
Last week we looked at the assumptions of the proof the the Pythagorean theorem in more detail. Heres a modied proof with some of those details included. Given information. Let ABC be a righ
Math 128, Modern Geometry
D. Joyce, Clark University 7 Oct 2005
Weve analyzed a nice proof of the Pythagorean theorem and found that it depends on a number of assumptions. Some of these assumptions are merely denitions, and some we found we could prove ba
Math 128, Modern Geometry
D. Joyce, Clark University 19 Sep 2005
You may nd the denition of cross ratio easier to Due Friday. Exercises from chapter 5: 1, 2, 3a, 4, remember if you write it in the form z0 z 2 z1 z 2 6 (rst two), 8a. (z0 , z1 , z2 , z3 ) =
Math 128, Modern Geometry
D. Joyce, Clark University 4 Nov 2005
Due Monday. From chapter 13, exercises 1, 2, 6, dene cross products is to use the standard unit 11. vectors i = (1, 0, 0), j = (0, 1, 0), and k = (0, 0, 1). Then we can write Last time. Conti