André Nicolas on stack-exchange:
"Hilbert shows that any plane that satisfies his quite geometric axioms must be
isomorphic to the coordinate plane over a complete ordered field.
And it is a standard result that up to isomorphism there is only one complete ordered field, namely ℝ." Wikipedia: "The set ℝ^2 of the ordered pairs of real numbers (the real coordinate plane),
equipped with the dot product,
is often called the Euclidean plane, since every Euclidean plane is isomorphic to it."
Instructor:
Dr. Stefan Forcey
Office: CAS 275
Office Phone: 330 972 6779
Email is sforcey@uakron.edu
(...this is the best way to get a hold of
me)
Office hours:
MTuW 3:45 - 4:45 and lots more by appointment!
If you can't make my office hours, let me know and we can try to
set up
a time to meet. Here is my schedule
for the semester.
Textbook: Geometry: The Line and the Circle by Maureen T. Carroll and Elyn Rykken, AMS/MAA Textbooks (ISBN: 978-1-4704-4843-1)
Nice additional reading
Test 3: Comprehensive Final Exam. Wednesday, December 11th from 2:30-4:30 pm in CAS 231
Here is the final
Review and
Review answers
Top menu.
Homework
Homework problems will be posted here. Homework will be assigned but usually NOT graded; but take-home quizzes will be given.
Homework 1 Not to be turned in. Take home quiz 1 due Sep 9 (new date).
Given the universe U = {3,5,7,8,12,53} and the sets A = {3,7,12,53} and B= {5,7,8}. Find all the transitive reflexive relations
on the set A-B. Find all the equivalence relations on B-A.
Homework 2: Not to be turned in. Take home quiz 2 due Sep 11.
Build an equilateral triangle, bisect an angle, copy an angle, bisect a line, build a circle, create a regular pentagon.
(In class, and search on mathopenref.com for video steps)
Homework 3: Take home quiz due Sept. 18.
Construct a perpendicular line to a given line through a point not on the line.
Construct a perpendicular line to a given line through a point on the line.
How to construct a regular pentagon. Are there more than 31 constructible odd-sided regular polygons?
For sequences: the Online Encylcopedia of Integer Sequences
Here is the open question of counting numbers of posets.
Here is the open question of counting numbers of polyhedra.