First Year Seminar: for instructors of Mathematics of Art 
 The Summer assignment
 The
Syllabus
 A list of supplies to buy
 The weekly schedule
 The list of onepage papers
2. Some
things that might be helpful to instructors of math and art
Projective Geometry applied to Perspective art: A proofsbased course 
1. Window
Taping: the After Math 
• basic understanding of parallel lines and
planes; • images of lines in a picture plane; • plan views; • definition of vanishing point; • importance of the notion of “parallel” in determining the existence and location of the vanishing point. 
2. Drawing
ART 
• problem solving • artistic application of the rules “Lines parallel to the picture plane have parallel images; lines not parallel to the picture plane but parallel to one another converge to the same vanishing point”. 
3. Image
of a line 
Students explore possible definitions of
projection of points and lines onto a plane. Topics: • visualizing projections of points and lines in R2 and R3; •considering “special cases” of projection; •understanding the difference between artistic applications and mathematical definitions. 
4. Geogebra
lines and points 
• introduction to GeoGebra • review definition of vanishing points • motivate notion of “points at infinity” 
5. Extended
Real Space 
• The axioms of the extended plane and extended
real space; • logical consequences of those axioms; • proving statements by using axioms and definitions; • visualizing points and lines at infinity. 
6. Meshes
and Mesh Maps 
Students explore the basic structure of a mesh
and a formal definition of projection onto a plane. As an
application, they draw and devise solutions to geometric
division problems. The notion of a mesh is not a standard one in projective geometry. A mesh is useful, however, in artistic applications such describing a 3d object like a house: for this object, we want to draw some lines (such as the top edge of the roof) but not others (we don’t draw the line that connects the front top of the roof to the back lower left corner of the house). Similarly, for this object we care about some points of intersection (the four corners of the floor) but not others (the front left edge of the roof does not intersect the back right edge of the roof in a point in R3, even though their images intersect in Figure 2). 
7. Geometric
Division 
Fence division problems and their relation to
the crossratio 
7. Geometric
Division (follow up) 
A powerpoint developed for our minicourse
participants to expand on the worksheet above 
8. Squares in
2point perspective 
Students discover the viewing circle; they
locate the viewing target and viewing distance for a
square in twopoint perspectives. From there, they learn
to draw a box and then a cube in 2point perspective. We foreshadow the need for harmonic sets of points. 
9. Desargues
Discovery and Streetlight page 
• How to draw shadows; • defining perspective from a point and perspective from a line; • exploring Desargues’s Theorem. 
9. Desargues Proof 
In which we prove the theorem. (Uses a
"modified Mooremethod" approach). 
10. Colineations 
An intro to colineations, in particular
perspective colineations in the plane 
10. Harmonic
Homologies 
We show that period2 homologies (like
reflections) relate to the above worksheet on squares in
2point perspective. 
10. Elations 
We practice constructing elations; these are
like the fencepostrepeating problems above 
11. Invariants:
Casey Angles 

11. Invariants:
Circular products 

11: Invariants:
Cross ratio 

11: Invariants:
Cross ratio and the vanishing point 
