Math 0025 Geometry and Art course page, Fall 2025
Book: "Perspective and Projective Geometry" by Crannell, Frantz and Futamura
(Princeton University Press, 2019).
In stock at the University Bookstore, or order it at this link:
link to Princeton University Press website for the book (use code BLOOM50 at checkout) - wait, this code appears to be broken, use the Penn Bookstore for now!
Please buy the book, don't rent it. Some of the pages are meant to be
drawn on or written on.
Groups for time period starting
MON Nov 3
Some window taping photos
Left window
Right window
Left window ; tape only
Right window ; tape only
Homework problems from Chapter 1 are due Wednesday September 17 at the
beginning of class.
Homework problems from Chapter 2 are due Wednesday September 24 at the
beginning of class.
Homework problems from Chapter 3 are due Wednesday October 01 at the
beginning of class.
Homework problems from Chapter 4 are due Wednesday October 08 at the
beginning of class. DO NOT DO problem P4.2.3. Instead, do the problem
found at this link:
replacement problem
Homework problems from Chapter 5 are due Monday October 20 at the
beginning of class.
A few students may need to do a redo for half
credit on Problem 4.3 replacement; this will be due along with
the Chapter 5 homework.
An optical illusion created using perspective techniques:
Borromini's colonnade in the Palazzo Spada
click here for the Wikipedia entry
First installment of homework problems from Chapter 6 are due Wednesday
October 29 at the beginning of class:
Problems E6.1 - 6.3 and
P6.1 - 6.4.
Second installment of homework problems from Chapter 6 are due Wednesday
November 5 at the beginning of class:
Problems E6.4 - 6.6, A6.1
(photography) and the extra problem on trisection, posted at
this link
Selection of problems from Chapter 7 due Wednesday November 12 at
the beginning of class: Problems E7.1.1, E7.1.2 and A7.1.1.
For problem E7.1.2: Carefully complete the drawing along the lines
we designed in class. Write a precise account of the construction at
each step.
Please leave all construction lines visible, drawn lightly,
then darken the line segments forming the edges of the kite shadow
and shade in the kite.
Homework problems from Chapter 9 are due Monday November 24 at the
beginning of class. For E9.2 you may assume that the picture is in
one-point perspective; if you do, please indicate in your solution
where you use this assumption. Please also indicate in your solution
where you use the assumption that the tabletop is a square.
This selection of homework problems from Chapter 10 is now due Monday
December 8 at the beginning of class. For hints, see below.
    Problem E10.1 (inscribed square)
    Problem E10.2 (octahedron)
    Problem A10.1 but you only need to do 2 letters, not 4.
Click here for the hints on E10.1 and
E10.2. You will need to turn in a sketch and written description that
does the problem, or as much of it as you can, as you normally would.
That is, weave together sketching and justifying into a narrative answer,
rather than just listing answers to the hints.