Home page for Math 470:  Euclidean and non-Euclidean Geometry



Colorado State University Spring semester 2003
Dr. Holger Kley MWF  3:10--4:00 pm
Hours:  M 10:00--11:00, Th 11:00--12:00, and by appointment. Engineering E 203


Announcements
Homework
Handouts
Projects


Announcements:



There will be no class on Friday, March 7th. But please read the Project Guidelines handout. Announced 3/5.
Please note that the first test has been moved to Wednesday, March 5th. Announced 2/19.
Please note that Thursday office hours have changed time: they are now from 11--12. Announced 1/24.


Homework:

Unless otherwise indicated, all Readings and Problems are from the course text Euclidean and non-Euclidean Geometries by Helena Noronha, available at the University Bookstore. (ISBN: 0-13-033717-X)
 


Week 1 Read Section 1.2; do problems 1, 2. Solutions
Week 2 Section 1.2: do problems 5, 7. Read section 1.4, do problem 1. Start reading section 1.5 Solutions
Week 3 Section 1.5: read problem 1, do problems 2, 4, 7; read section 1.6 and do problems 3, 4. Solutions
Week 4 Read section 2.1; do problems 1, 5, 7; read Sections 2.2, 2.3; do problems 4, 8, 9. Note that the statement of problem 8 (and hence 9) is incorrect; extra credit for finding the correct statement and proving it (and for stating and proving the converse.) Solutions
Week 5 Read section 2.4; do problems 1, 2, 3. Read Sections 2.5. Solutions
Week 6 Read section 3.1; do problems 3, 5, 6. Solutions
Week 7 Take the test! Read the Project Guidelines handout. Solutions to Test 1.
Week 8 Wednesday snow day! Finish reading 3.1; and do problems 8,9, and 12. Read 3.4. Solutions
Week 9 Read 7.1, 7.2, 7.3, 7.4; In 7.3, do problems 1, 3, 4. In 7.4, do problem 7.4 In addition, come up with a Gauss-Bonnet formula for spherical quadrilaterals and pentagons. Also, decide which of the axioms of neutral geometry do not hold in spherical geometry.
Week 10

Week 11 Read 8.2, 8.3, 8.4; In 7.4, do problems 2, 3, 7, 10. Solutions
Week 12 Read sections 3.3 and 9.2; in 3.3, do problems 2 and 4; in 9.2, do problems 1, 6, 14, 15. Solutions
Week 13 No new homework assigned!
Week 14 Take the test! Solutions to Test 2.
Week 15 Projects!


Handouts:

All handouts are in portable document format (pdf). If you have trouble viewing them, make sure you have the latest version of the (free) Adobe Acrobat Reader software installed;  download it for Macintosh, Windows,or UNIX.
 


Class Policies January 23 Project Guidelines March 5
Syllabus January 23 Test 2 May 2
Test 1 March 5

Facts for Test 2 April 30


Projects:

 
Fractals:  
Lashi Dodge and Natalie Young
  • Fractal Geometry
  • Cool 3d fractal
  • What is a fractal?
  • Mathart
  • Tilings:  
    Steve Benoit, Lara Kendrick, Angela Knopf
    and Janet Oien
  • Ozbird.net
  • Higher genus "soccer balls"
  • Tilings and tesselations
  • Totally tesselated
  • MCE
  • Intriguing tessellations
  • Black Holes:
    Mike Griesel, Sabrina Hahn, Dan Hejde
    and Megan Williams  
  • Geometry around black holes
  • Falling in to the singularity of the black hole
  • Movie index
  • Approaching the black hole
  • Schwarzschild geometry
  • The black earth
  • Something cool
  • Orbits in strongly curves spacetime
  • Relativistic disk images
  • Black holes
  • The future of the universe
  • Non-isometric transformations:
    Matt b Cornick and Felipe Ramirez 
  • Map projections
  • Affine transformations of a quadrilateral
  • Anamorphic art
  • Reflections
  • What is anamorphic art?
  • Hyperbolic Geometry:
    Charlie Cherrington, Cathy Cullinane, Eric Eiseman,
    MJ Jones and Jennifer Quinn 
  • The upper half-plane model
  • Circle inversion
  • Non-Euclid
  • Non-Euclidean geometry
  • Upper half-plane applet
  • Hyperbolic Geometry:  
    Billy Bromley, Jeff Gallegos and Lindsey Gardner
  • Hyperbolic Geometry using Cabri
  • Movie gallery
  • The world of hyperbolic geometry
  • Non-Euclidean geometry
  • Non-Euclid


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