Math 410, Geometry and Arts, Fall 2016

Instructor: Vladimir Bolotnikov

Office: Jones 129, Tel:221-2009, Fax: 221-2988

E-mail: vladi@math.wm.edu, http://www/math.wm.edu/~vladi

Class meetings: TR, 11:00 am - 12:20 p.m. in Jones Hall 112

Ofice hours: TR 2:30 - 3:30 p.m. or by appointments

Course Description

Grading:  The mid-term exam (tentatively, on October 6) - 35%, 
the final (December 14, 2-5 pm, Jones Hall 112) - 40%, 
the in-class presentation 10%, 
homework assignments - 10%
participation 5%. 

 There will be NO CURVING.

Grade computation:  A >= 93 % > A- >= 90 % > B+ >= 87 % > B >= 82 % > B- >= 79 %     
                    > C+ >= 76 % > C >= 71 % > C- >= 68 % > D+ >= 65 % > D >= 60 % > F.


The topics to be covered:

I. GEOMETRY:

1.  Euclidean axioms.
2.  Triangles, quadrilaterals and other polygons.
3.  Circles, inscribed, cicumscribed, central and other angles.
4.  Transformations: symmetry, shift, homothety, rotation, inversion.
5.  Geometric constructions.
6.  Areas.
7.  Geometric inequalities.
8.  Extremal problems.
9.  Convexity.
10. Spherical geometry.
11. Hyperbolic geometry.

II. ARTS:

1.  Polygons in Cubist Art (P. Picasso, J. Gri, P. Klee).
2.  Polygons and tiling: Regular tilings, Archimedean (semiregular) tilings, Pentagonal tilings.
3.  Arbelos. Archemedian circle.
4.  Tondo -- circular composition in art.
5.  Golden ratio. Golden triangle and the logarithmic spiral.
6.  De Prospectiva Pingendi} (Piero della Francesca on solids and perspective).
7.  De divina proportione} (Luca Pacioli and Leonardo da Vinci on proportions and their applications to geometry and architecture).
8.  Albrecht D\"urer's work in geometry: "Four Books on Measurement", "Four Books on Human Proportion".
9.  Origami Geometry: doubling the cube, trisecting the angle.
10. M. Escher and Hyperbolic Geometry.
11. M. Escher and Spherical Geometry.