Math 4060 -- Foundations of Geometry
MWF 9-9:50 in GAB 317.
|Office Location: ||General Academic Building
||Mondays & Wednesdays 10-Noon
All students should have successfully completed Math 3000
(Real Analysis I) before taking this course. The reason for
this is that this course is a proof intensive course and students
should already be familiar with basic proof writing techniques and
Prior or concurrent enrollment in either Math 3610
(Real Analysis II) or Math 3510 (abstract algebra)
is also strongly recommended. This is meant to ensure familiarity with proof
and proof technique. Nothing from real analysis or abstract
algbra will actually be needed.
Students who have not yet taken Math 3610
or Math 3510, but who are confident in their proof-writing ability,
are welcome in the course.
Early interest in geometry was almost certainly motivated by
a desire to improve building techniques and to be able to
create interesting shapes for temples, altars, toys, and machines.
Scholars in ancient Greece "abstracted" the study of shapes
into an idealized form. The most widely read textbook in history
is a geometry text by Euclid known as the Elements.
Thousands of years later, much of what
we learn in high school geometry is based on the ideas in Euclid's
text. Euclid's goal was to create a logical foundation for idealized
geometry. He wanted to provide proofs for geometric facts based on
as few axioms as possible. The course will begin with a careful study
of parts of Euclid and an exploration of what he was trying to do and
why. The course will then move on to the contributions of
19th and 20th century scholars who built on Euclid's work. The second half of
the course will look at alternative geometries where the so-called
parallel postulate need not hold.
The course will emphasize the role of proof in geometry, its historical
development, and the philosophical implications that proof had on
the development of scientific thought. Students will begin by reading
Euclid and continually develop their own proof writing skills and
Robin Hartshorne, Geometry: Euclid and Beyond,
Springer Verlag, 2000. ISBN 9780387986500
Euclid's Elements, The Thomas L. Heath translation edited
by Dana Densmore, Green Lion Press, 2002. ISBN 9781888009194.
Euclid is also available online at
Grading in the course will be based on weekly homework assignments,
in class midterm, and an in class final exam.
Class attendance will be strictly monitored.
|Gometry Art Project||10%|
||28% (14% each)|
|Midterms: ||Monday, Mar. 6 and Monday, Apr. 10|
|Geometry Art Project Due: ||Monday, May 1|
|Final Exam: ||Wednesday, May 10,
8:00 - 10:00 a.m.|
Article on Rusty Compass Constructions
in Islamic Art
Notes on Euclid III.35
Information about the First Midterm Exam
Geogebra illustration of the Euler Line
Pictures Illustrating the 9-Point Circle Proof
Geogebra illustration of the 9-Pont Circle
Geometry Art Project Assignment (due May 1)
If you missed class, ask for the solutions to some of the homework
from section 7 (not available on the web).
Information about the Second Exam
Geogebra file with a tool for drawing P-lines
Geogebra file illustrating P-diameters of P-circles
Geogebra file with tools to drop and erect perpendiculars in the Poincare plane
Handout on the proof of Theorem 34.5
Project website (tries to determine if the geometry of the
universe is Euclidean or non-Euclidean); see also NASA's Universe 101 site.
about how isometries of the Poincare plane can be used in viewing brain
Articles by Jeffrey Weeks and Neil Cornish on the Poincare Dodecahedral Space and the
shape of the univerise:
Information about the Final Exam
Select "Construction Protocol" from the "View" menu to see the steps
of your construction or to print the steps.
Geometer's Sketchpad is available in the Arts & Sciences
computer labs in GAB, Wooten, and Terrill.
Click here for how to print construction
steps from Sketchpad.
Homework #1 due beginning Jan 23 (the back page is not available on the web; see me if you missed class)
Homework #2 and #3 due Jan 27 and 30.
Homework #4 and #5 due Feb 1 and 3 (due dates postponed to Feb 3 for assignment #4
and Feb 6 for assignment #5).
Homework #6 and #7 due Feb 8 and 10
Homework #8 due by Mar. 3 (the back page is not available on the web; see me if you missed class)
Homework #9 and #10 due Feb 13 and 15
Homework #11 due Feb 17
Homework #12-14 due Feb 20, 22 and 24 (due date postponed to Feb 27 for assignment #14).
Homework #15 and #16 due Mar 1 and 3
Homework #17 and #18 due Mar 8 and 10
Homework #19-21 due Mar 20, 22, and 24
Homework #22-24 due April 3, 5, and 7
Homework #25 due April 12
Homework #26-27 due April 14 and 17 (Homework #27 postponed to Wednesday, April 19)
Optional Extra Credit Homework #28 due April 21.
Homework #29 due April 24.
Homework #30 due April 26.
Homework #31 due April 28.
Homework #32 due May 3.
Trouble reading or printing links on this page?
The homework assignments and supplemental materials above are
in Adobe PDF (or Acrobat)
format. If you are having trouble reading or printing these hand-outs,
to William Cherry's home page