MTG 3212 – 8789
Spring 2016
______________________________________________________
Time: MWF period 5
Place: Little 125
Phone: 352-294-2339
Office: 438 Little Hall
Email: avince@ufl.edu
Textbook: Foundations of Geometry by G. A. Venema
Office Hours: Monday, Wednesday, Friday period 6
(or by appointment)
Links
Homework
An extra square in the lower triangle?
Page 45 #3,7,8 Page 51 #1 (due Wed 20 Jan)
Page 77 #1,2,4 Page 81 #8,9
How did I trick you in the proof that a right angle is congruent to an obtuse angle. (due Wed 27 Jan)
Page 109 #2,3 Prove that the diagonals of a rhombus are perpendicular. (due Mon 1 Feb)
Sketchpad problem on perpendicular bisectors, angle bisectors, medians, and altitudes of a triangle.
Sketchpad related to “proof” that an obtuse angle equals a right angle. (due Fri 5 Feb)
Page 200 #6 Page 212 #6,7
Sketchpad drawings of circumscribed circle and inscribed circle .
Relationship between angle and arc measure (two problems assigned in class). (due Wed 17 Feb)
Page 179 #9
Construction problems assigned in class (due Wed 24 Feb)
Page 252 #11,14 Page 259 #1,4
What transformation is the composition of two reflections in parallel mirrors?
H1, H2 = half turns, T = translation. What is the composition: H1 H2 ? H1 T ? T H1 ? (the last two are harder) (due Fri 11 March)
Prove: There can be at most one common point on three cirlces with non-collinear centers. (due Mon 14 March)
Two circles problem from class.
H R is a reflection when where R is a reflection and H is a half turn with center on the axis of R.
List the symmetries of a square.
List the symmetries of the letter patterns given in class (due Fri, March 25)
Prove that the inverse of a similitude with ratio r is a similitude with ratio 1/r.
What is the image of the square under the affine transformation given in class? (due Mon March 28)
Describe in words what the two linear transformations given in class do.Three problems on the coordinate geometry of the real projective plane.
Sketchpad exercise on Desargue’s theorem. (due Wed 6 April)
Two problems on symmetries of the cube.
Two proofs from class concerning a circle.
Sketchpad: given two distinct points in the Poincare disk, construct a hyperbolic line joining them.
(due Wed 13 April)
Topics
- Euclidean plain geometry
- The structure and history of Euclid’s Elements
- Models
- Axioms for plane geometry
- Neutral geometry
- Euclidean geometry vs Non-Euclidean geometry
- Theorems of Euclidean geometry
- triangles, polygons
- congruence, similarity
- area
- circles
- constructions
- 3-dimensional geometry
- Polyhedra
- Transformations
- Affine and Projective Geometry
Messages
Exam 1 – Feb 8
Exam 2 – March 16
Exam 3 – April 18
Free tutoring at the Teaching Center, SW Broward Hall. Check www.teachingcenter.ufl.edu for the time schedule.
Students with disabilities requesting accommodations should first register with the Disability Resource Center (352-392-8565, www.dso.ufl.edu/drc/) by providing appropriate documentation. Once registered, students will receive an accommodation letter which must be presented to the instructor when requesting accommodation. Students with disabilities should follow this procedure as early as possible in the semester.
The course will be conducted in accordance with the University honor code, academic honesty policy, and policy regarding the use of copyrighted material. Requirements for class attendance and make-up exams, assignments, and other work in this course are consistent with university policies that can be found at: https://catalog.ufl.edu/ugrad/current/regulations/info/attendance.aspx.
Information on current UF grading policies for assigning grade points may be found at: https://catalog.ufl.edu/ugrad/current/regulations/info/grades.aspx.
Students are expected to provide feedback on the quality of instruction in this course by completing online evaluations at https://evaluations.ufl.edu. Evaluations are typically open during the last two or three weeks of the semester, but students will be given specific times when they are open. Summary results of these assessments are available to students at https://evaluations.ufl.edu/results/.
Grades
three exams 30%
homework 10%