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


Colorado State University Spring semester 2002
Dr. Holger Kley MWF  3:10--4:00 pm
Hours:  Tu 3:10-4:00, F 12:10--1:00 Eddy 107

Announcements
Homework
Handouts
Projects


Announcements:


Projects: 4/29, 5/1 and 5/3 we will meet in Weber 205 for project presentations. Please be prompt. Announced April 22
Extra office hour: Thursday, 4/25, at 10:30--11:30. Also, on Friday 4/26, office hours will be 12:30--2:00. Announced April 22
Extra office hour: Thursday, 2/28, at 10:30--11:30. Also, on Friday 3/1, office hours will be 12:30--1:30. Announced February 25
Solutions to homework will be posted on my office door no later than Friday of the week the problems were due. Announced January 23
Room change! The class now meets in Eddy 107 Announced January 16


Homework:

Unless otherwise indicated, all Readings and Problems are from the course text Euclidean and non-Euclidean Geometry by Ryan, available at the University Bookstore. (ISBN: 0-521-27635-7)
 

Week 1 Reading: Introduction, and pp. 8--14. Exercises: on p. 35, do 5,7, 9, 10 and optionally, do 1--4.
Week 2 Reading: pp. 15--17. Exercises: on pp. 35-36, 11, 12, 15.
Week 3 Exercises: on pp.36--37, do 17, 18, 22 and do Exercise 1 from the groups handout.
Week 4 Exercises: on pp. 37-38, 23, 26, 28, 32 and optionally, 33.
Week 5 Exercises: on p. 38, do 35. Also problem assigned in class on moving a particular triangle.
Week 6 Exercises: on p. 67, do 3, 4. Also problem assigned in class on reflective polygonal tilings.
Week 8 Exercises: on p. 121, do 6, 7, 10.
Week 9 Exercises: on p. 122, do 19, 20, 22.
Week 10 Exercises: on p. 138, do 2.
Week 11 Exercises 1, 2, 3 from the supplemental notes on hyperbolic geometry.
Week 12 Exercises 4 and 5 from the supplemental notes on hyperbolic geometry.


Handouts:

In order to view the handouts from this course, you will need to have the (free) Adobe Acrobat Reader software installed;  download it for Macintosh, Windows,or UNIX.
 

Class Policies January 14 Test 1
Syllabus January 14 Test 1 Solutions
Supplemental notes on groups February 4 Supplemental notes on hyperbolic Geometry
Study Questions February 26 Study Questions II April 22
Study Questions Solutions February 28 Study Questions Solutions 2 April 25


Projects:

 

Dave Conner and Eli Immasche

Applications of Hyperbolic Geometry

http://plus.maths.org/issue18/xfile/
http://cs.unm.edu/~joel/NonEuclid/
http://www.personal.psu.edu/users/t/x/txd147/portfolio/inxight.htm
http://www.csc.fi/math_topics/Movies/HG.html

 

Shawn Farnell and Donald Hall

Geometry in Computer Graphics

http://www.javaworld.com/javaworld/jw-06-1997/jw-06-howto.html
http://www.geocities.com/boscobrothers/ambient3di.html
http://robotics.stanford.edu/~birch/projective/
http://www.gg.caltech.edu/
http://www.flipcode.com/geometry/index.shtml
http://mvc.man.ac.uk/training/postgrad/comp_shape/xform_html/
http://www.ics.uci.edu/~eppstein/gina/graphics.html
http://www.scienceu.com/library/articles/isometries/
http://pages.infinit.net/jstlouis/3dbhole/
http://www.keypress.com/sketchpad/talks/comp_graphics/
http://www.cs.colostate.edu/~cs410/

Kit Colbenson, Jennifer Manchego and Anthony Pena

Geometry in Astrophysics

http://holly.colostate.edu/~devieth

 

Jeri Garrett, Stan Kennedy, Sid Kramer and Matt Whipple

Spherical Geometry and its Applications

http://www.sciencenews.org/sn_arc98/10_10_98/Bob1.htm
http://msri.org/publications/books/gt3m/
http://www.astro.columbia.edu/~archung/labs/fall2001/images/equat_coord.jpg
http://www.coyotegulch.com/astronomy/na0002/na0002.html
http://www.neubert.net/PLASpher.html
http://www.ballsemi.com/medical/MedPage.Html
http://www.gh.wits.ac.za/craig/diagrams/cub3d.gif
http://www.pmms.cam.ac.uk/~gjm11/cpacking/info.html http://www.pmms.cam.ac.uk/~gjm11/cpacking/info.html
http://www.stetson.edu/~efriedma/packing.html  
http://www.rit.edu/~repeee/emcr201/lab/gatearray/gatearray.htm

 

Pam Peters, Eliz Scott-Janda and Brian Woody

Dilations and Spirals

Dilation
Spiral "Symmetry"
Spiral Demonstration
Rosettes
Shells
Similar Triangles
http://www.rose-hulman.edu/~brought/Epubs/soccer/soccerpics.html
http://www.ics.uci.edu/~eppstein/junkyard/spiraltile/
http://www.uwgb.edu/dutchs/symmetry/log-spir.htm
http://www.members.tripod.com/vismath4/gal/index.html
http://www.moonstar.com/~nedmay/chromat/fibonaci.htm
http://www.math.colostate.edu/~woody/proj470.htm

 

Tim Ellis, Abby Hoganson, Ashley Johnson, Gene Moore and Carmen Small

Geometry in Image Processing and Visualization


Digital Image Warping preface
An Introduction to Projective Geometry (computer vision)
Object recognition
Image correction
Texturing
Affine Transformations
Geometric processing and visualization
Geometry, Geometric Reasoning, and Visualization
Geometric Transformations
http://www.dai.ed.ac.uk/HIPR2/affine.htm

 

Kelly Buchanan and Andrea Daniel

Distance, and in Particular distance in Hausdorff space

http://cgm.cs.mcgill.ca/~godfried/teaching/cg-projects/98/normand/main.html
http://www.cut-the-knot.org/do_you_know/Hausdorff.shtml
http://www.cut-the-knot.org/do_you_know/far_near.shtml
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