Course Web Page

    Course: MATH 3110/5110

    Title: College Geometry

    Section: 100 (Class Numbers 5881/5906)

    Campus: Ohio University, Athens Campus

    Department: Mathematics

    Academic Year: 2018 - 2019

    Term: Spring Semester

    Instructor: Mark Barsamian

    Contact Information: My contact information is posted on my web page .

    Office Hours for 2018 - 2019 Spring Semester: 9am - 10am Mon - Fri in Morton 538

    Course Description: A rigorous course in axiomatic geometry. Birkoff's metric approach (in which the axioms incorporate the concept of real numbers) is used. Throughout the course, various models will be introduced to illustrate the axioms, definitions and theorems. These models include the familiar Cartesian Plane and Spherical Geometry models, but also less familiar models such as the Poincaré Upper Half Plane, the Taxicab Plane, and the Moulton Plane. Substantial introduction to the method of proof will be provided, including discussion of conditional statements and quantified conditional statements and their negations, and discussion of proof structure for direct proofs, proving the contrapositive, and proof by contradiction.

    Prerequisites: (MATH 3050 Discrete Math or CS 3000 Introduction to Discrete Structures) and (MATH 3200 Applied Linear Algebra or MATH 3210 Linear Algebra)

    Cross-Listing: Note that this is a cross-listed course: Undergraduate students register for MATH 3110; graduate students, for MATH 5110.

    Special Needs: If you have physical, psychiatric, or learning disabilities that require accommodations, please let me know as soon as possible so that your needs may be appropriately met.

    Class meetings: This class used to meet Mon, Wed, Fri 12:55pm - 1:50pm in Morton Hall Room 126

    Move to Online Instruction for Spring 2020

    Ohio University moved all of its 2019 � 2020 Spring Semester courses to an online format during Spring Break, in March 2020. This web page is undergoing redesign in order to better suit the needs of instructors running online courses.

    Helpful Cellphone App: Camscanner

    Camscanner is a useful app that uses a cellphone camera to take a picture of a document, and then crops and sharpens the image and turns it into a PDF file. This is very useful for students who need to submit homework electronically. It is helpful to the instructor, because when the instructor receives a PDF of the homework, it is easy to add comments. ( link to Camscanner web page )

    Final Exam Date: Friday, May 1, 2020, 3:10pm - 5:10pm in Morton 126

    Syllabus: For Section 100 (Class Numbers 5881 and 5906), taught by Mark Barsamian, this web page replaces the usual paper syllabus. If you need a paper syllabus (now or in the future), unhide the next four portions of hidden content (Textbook, Calendar, , Course Structure) and then print this web page.

    Textbook Information:

    Textbook Information for 2019 - 2020 Spring Semester MATH 3110/5110

    Title: Geometry: A Metric Approach With Models, 2 nd Edition

    Authors: Millman and Parker

    Publisher: Springer, 1991

    ISBN Numbers:

    • Softcover ISBN-13: 978-0-387-20139-9
    • Hardcover ISBN-13: 978-0-387-97412-5

    Link to Supplemental Reading on Logical Terminology, Notation, and Proof Structure: Logical Terminology

    Calendar:

    Calendar for 2019 - 2020 Spring Semester MATH 3110/5110 Section 100 (Class Numbers 5881/5906), taught by Mark Barsamian

    Week 1: Mon Jan 13 - Fri Jan 17

    • Day #1:
      • Topics: Preliminary Notions: Axiom Systems
      • Book Section: Chapter 1 Sections 1.1
    • Day #2:
      • Topics: Relations; Start discussing Logical Terminology & Notation
      • Reading:
        • Textbook Section1.2
        • Supplemental Reading on Logical Terminology, Notation, and Proof Structure: Logical Terminology
    • Day #3:
      • Topics: More disussion of Logical Terminology & Notation
      • Reading: Supplemental Reading on Logical Terminology, Notation, and Proof Structure: Logical Terminology

    Week 2: Mon Jan 20 - Fri Jan 24 (Monday is MLK Day Holiday)

    • Monday is Martin Luther King Day Holiday: No Class
    • Day #4:
    • Day #5:
      • Topics: Functions
      • Book Section: 1.3
      • Homework H01 Due
      • Quiz 1

    Week 3: Mon Jan 27 - Fri Jan 31

    • Day #6:
      • Topics: Properties of Functions
      • Book Section: 1.3
    • Day #7:
      • Topics: Properties of Functions; Definition and Models of Incidence Geometry
      • Book Section: 1.3, 2.1
    • Day #8:
      • Topics: Abstract Geometry, Incidence Geometry
      • Book Section: 2.1 Models of Incidence Geometry
      • Homework H02 Due ( Homework H02 Cover Sheet )
      • Quiz 2

    Week 4: Mon Feb 3 - Fri Feb 7

    • Day #9:
      • Topics: Parallel Lines, Distance Functions
      • Book Section:
        • 2.1 Models of Incidence Geometry
        • 2.2 Metric Geometry
    • Day #10:
      • Topics: Distance Functions, Coordinate Systems (Rulers), Metric Geometries
      • Book Section:
        • 2.2 Metric Geometry
        • 2.3 Special Coordinate Systems
    • Day #11:
      • Topics: Ruler Placement
      • Book Section: 2.3 Special Coordinate Systems
      • Homework H03 Due ( Homework H03 Cover Sheet )
      • Quiz 3

    Week 5: Mon Feb 10 - Fri Feb 14

    Week 6: Mon Feb 17 - Fri Feb 21

    • Day #15:
      • Topics: Betweenness, Line segments, Rays
      • Book Section:
        • 3.2 Betweenness
        • 3.3 Line Segments and Rays
    • Day #16:
      • Topics: Line segments, Rays
      • Book Section: 3.3 Line Segments and Rays
    • Day #17:

    Week 7: Mon Feb 24 - Fri Feb 28

    Week 8: Mon Mar 2 - Fri Mar 6

    • Day #21:
      • Topics: Interiors and the Crossbar Theorem
      • Book Section: 4.4 Interiors and the Crossbar Theorem
    • Day #22:
      • Topics: More Discussion of Interiors; Quadrilaterals
      • Book Section:
        • 4.4 Interiors and the Crossbar Theorem
        • 4.5 Convex Quadrilaterals
    • Day #23: Exam 2 Covering Chapters 3 and 4 (Problems from Sections 4.3, 4.4, 4.5 will just be making drawings as in the suggested exercises. No proofs from those three sections.)

    Week 9 & 10: Mon Mar 9 - Fri Mar 20 is Spring Break: No Class

    Week 11: Mon Mar 23 - Fri Mar 27

    • Day #24:
      • Topics: More Discussion of Interiors and Convex Quadrilaterals
      • Book Section:
        • 4.4 Interiors and the Crossbar Theorem
        • 4.5 Convex Quadrilaterals
      • Meeting Notes: Meeting Notes
    • Day #25:
      • Topics: Angle Measure
      • Book Section: 5.1 The Measure of an Angle
      • Meeting Notes: Meeting Notes
    • Day #26:

    Week 12: Mon Mar 30 - Fri Apr 3

    • Day #27:
      • Topics: Perpendicularity
      • Book Section: 5.3 Perpendicularity and Angle Congruence
      • Meeting Notes: Meeting Notes
    • Day #28:
      • Topics: Angle Bisectors
      • Book Section: 5.3 Perpendicularity and Angle Congruence
      • Meeting Video: Meeting Video
      • Meeting Notes: Meeting Notes
    • Day #29:

    Week 13: Mon Apr 6 - Fri Apr 10

    • Day #30:
      • Topics: Basic Triangle Congruence Theorems
      • Book Section: 6.2
      • Homework: Homework 7 due on Sunday, April 5 by 11:59pm ( Homework H07 Cover Sheet )
      • Quiz 7 during Teams Meeting Mon April 6
      • Meeting Notes: Meeting Notes
    • Day #31:
    • Day #32: Discuss Graded Homework H06 and Review for Exam X3

    Week 14: Mon Apr 13 - Fri Apr 17

    • Day #33: Exam 3
      • Will be four problems
        • One problem from 4.3, 4.4, 4.5 (Exam 2 included these sections but only making drawings to illustrate the statements. On Exam 3, you will be asked to do something more.)
        • One problem involving Euclidean & Hyperbolic angle measure (5.1 concepts)
        • One problem from 5.3
        • One problem from 6.1, 6.2
      • Will be four types of problems (not in same order as the list above)
        • A computation problem
        • A conceptual problem
        • A problem asking you to illustrate & justify the statements of part of a given proof from the reading
        • Prove a theorem or a claim
    • Day #34:
      • Topics: The Exterior Angle Theorem and some of its Consequences
      • Book Section: 6.3
      • Meeting Video: Meeting Video
      • Meeting Notes: Meeting Notes
    • Day #35:
      • Topics: The Exterior Angle Theorem and some of its Consequences
      • Book Section: 6.3
      • Meeting Video: Meeting Video
      • Meeting Notes: Meeting Notes

    Week 15: Mon Apr 20 - Fri Apr 24

    • Day #36:
    • Day #37:
      • Topics: Perpendicular Bisectors
      • Book Section: 6.4
      • Quiz: Q08, will involve illustrating & justifying steps from one of these theorems:
        • Theorem 6.3.3 (Exterior Angle Theorem)
        • Theorem 6.3.8 (Triangle Inequality)
      • Meeting Video: Meeting Video
      • Meeting Notes: Meeting Notes
    • Day #38:

    Week 16 (Finals Week): Fri May 1 Final Exam 3:10pm - 5:10pm

    Grading:

    Grading for Section 100 (Classs Number 5881/5906), taught by Mark Barsamian

    During the semester, you will accumulate a Points Total of up to 1000 possible points .

    • Homework: 7 Assignments @ 10 points each = 70 points possible, rescaled to 100 points possible
    • Quizzes: Best 6 of 8 Quizzes @ 25 points each = 150 points possible, rescaled to 200 points possible
    • In-Class Exams: Best 2 of 3 exams @ 150 points each = 300 points possible, rescaled to 450 points possible
    • Final Exam: 250 points possible

    Original Grading Points:

    The Original Grading Points were as follows

    During the semester, you will accumulate a Points Total of up to 1000 possible points .

    • Homework: 10 Assignments @ 10 points each = 100 points possible
    • Quizzes: Best 8 of 10 Quizzes @ 25 points each = 200 points possible
    • In-Class Exams: Best 3 of 4 exams @ 150 points each = 450 points possible
    • Final Exam: 250 points possible

    End of Original Grading Points

    At the end of the semester, your Points Total will be converted into your Course Letter Grade .

    • 900 - 1000 points = 90% - 100% = A-, A = You mastered all concepts, with no significant gaps.
    • 800 - 899 points = 80% - 89.9% = B-, B, B+ = You mastered all essential concepts and many advanced concepts, but have some significant gaps.
    • 700 - 799 points = 70% - 79.9% = C-, C, C+ = You mastered most essential concepts and some advanced concepts, but have many significant gaps.
    • 600 - 699 points = 60% - 69.9% = D-, D, D+ = You mastered some essential concepts.
    • 0 - 599 points = 0% - 59.9% = F = You did not master essential concepts..

    There is no curve.

    Throughout the semester, your current scores and current course grade will be available in an online gradebook on the Blackboard system.

    Course Structure:

    Course Structure for Section 100 (Class Numbers 5881/5906), taught by Mark Barsamian

    One learns math primarily by trying to solve problems. This course is designed to provide structure for you as you learn to solve problems, and to test how well you have learned to solve them. This structure is provided in the following ways.

    • Reading: To succeed in the course, you will need to read the textbook, study the examples in it. Many of the examples are similar to exercises on your exercise list.
    • Lectures: In lecture, I will sometimes highlight textbook material that is particularly important, sometimes present material in a manner different from the presentation in the book, and sometimes solve sample problems. We have 37 lectures, totaling 2035 minutes. It is not possible to cover the entire content of the course in 2035 minutes, and the lectures are not meant to do that. Lectures are meant to be a supplement to your reading the textbook and solving problems.
    • Office Hours: Come to my office hours for help on your Exercises
    • Tutoring: Free tutoring is available in the Morton Math Tutoring Lab, in the Math Library, Morton 415a. Make use of it!
    • Exercises: One learns math primarily by trying to solve problems. For that reason, the centerpiece of this course is the list of Exercises , found farther down this web page. The goal of the course is for you to be able to solve the exercises in this list. Some of the exercises are Assigned , to be turned in as Homework , and will be graded. Some of the exercises are Suggested , meaning that they are not to be turned in and won't be graded. But you should do as many of them as possible and keep your solutions in a notebook for study.
    • Quizzes and Exams: The quizzes and exams will be made up of problems similar to the exercises (both kinds, Homework and Suggested ).

    Exercises (Suggested Exercises and Homework Assignments)

    Exercises for Section 100 (Class Number 5881/5906), taught by Mark Barsamian

    One learns math primarily by trying to solve problems. For that reason, the centerpiece of this course is the list of Exercises below. The goal of the course is for you to be able to solve the exercises in this list. Some of the exercises are Assigned , to be turned in as Homework , and will be graded. Some of the exercises are Suggested , meaning that they are not to be turned in and won't be graded. But you should do as many of them as possible and keep your solutions in a notebook for study. (The quizzes and exams will be made up of problems similar to the exercises (both kinds, Homework and Suggested )

    Exercises for 2019 - 2020 Spring Semester MATH 3110/5110

    • Suggested:
      • 1.2 # 2, 3, 6, 8, 9, 13, 14, 15, 19
      • 1.3 # 1, 2, 3, 4, 5, 6, 9, 8, 10, 11, 12, 13
      • 2.1 # 1, 3, 5, 6, 8, 10, 11, 12, 13, 16, 18, 19, 24
      • 2.2 # 4, 5, 6, 7, 9, 10, 11, 18, 19, 20
      • 2.3 # 1, 2, 3, 4, 5, 6
      • 3.1 # 5, 7
      • 3.2 # 3, 10
      • 3.3 # 2, 3, 4, 9, 10
      • 3.4 # 1, 2, 3, 4
      • 4.1 # 1, 4, 5, 11, 13
      • 4.2 # 1, 2, 4
      • 4.3 # 1, 3, 7
      • 4.3
        • Make drawings to illustrate the statements to be proven in these exercises (but don't do the proofs):
          • 4.3 # 1 make drawings to illustrate the statement presented in the exercise
          • 4.3 # 3 make drawings to illustrate the statement of Theorem 4.4.8
        • Do the proofs indicated in these exercises:
          • 4.3 # 2 Prove the statement presented in the exercise
          • 4.3 # 7 Prove or disprove the statement presented in the exercise
      • 4.4
        • Make drawings to illustrate the statements to be proven in these exercises (but don't do the proof):
          • 4.4 # 8 make drawings to illustrate the statement presented in the exercise
          • 4.4 # 9 make drawings to illustrate the statement of Theorem 4.4.8
          • 4.4 # 10 make drawings to illustrate the statement of Theorem 4.4.9
          • 4.4 # 11 make drawings to illustrate the statement presented in the exercise
          • 4.4 # 12 make drawings to illustrate the statement presented in the exercise
        • Do the proofs indicated in these exercises:
          • 4.4 # 2 Prove Theorem 4.4.2
          • 4.4 # 4 Prove Theorem 4.4.6
          • 4.4 # 5 Prove the statement presented in the exercise
          • 4.4 # 10 Prove Theorem 4.4.10
      • 4.5
        • Make drawings:
          • 4.5 # 4 make drawings as specified
          • 4.5 # 11 make drawings to illustrate the statement presented in the exercise (but don't do the proof)
          • 4.5 # 12 make drawings to illustrate the statement of Theorem 4.4.8 (but don't do the proof)
        • Do the proofs indicated in these exercises:
          • 4.5 # 3 Prove Theorem 4.5.3
          • 4.5 # 5 Prove the statement presented in the exercise
          • 4.5 # 7 Prove the statement presented in the exercise
      • 5.1 # 1, 2, 3, 7
      • 5.3 # 6, 7, 8, 9, 11, 15, 19
      • 6.1
        • #5,8,9 (As always, when writing a proof, make a drawing that illustrates the statement of the claim and then also make a drawing for each step of the proof.)
        • #12 Give an example in the Taxicab Plane of an isosceles triangle whose base angles are not congruent. (Such an example demonstrates that the Taxicab Plane does not satisfy \(SAS\), and so is not a neutral geometry .)
      • 6.2 #5, 7, 8 (As always, when writing a proof, make a drawing that illustrates the statement of the claim and then also make a drawing for each step of the proof.)
      • 6.3
        • Do Exercises #3, 4, 5, 10
        • Illustrate & Justify the steps in the book's proofs of these two theorems:
          • Theorem 6.3.3 (Exterior Angle Theorem)
          • Theorem 6.3.8 (Triangle Inequality)
      • 6.4 #2, 3, 4, 5, 6, 7, 8, 10, 13 (As always, when writing a proof, make a drawing that illustrates the statement of the claim and then also make a drawing for each step of the proof.)
    • Assigned Homework
      • H01: 1.2 # 1, 6, 8, 13, 15 due Fri Jan 24 at the start of class
      • H02: due Fri Jan 31 at the start of class ( Homework H02 Cover Sheet )
      • H03: due Fri Feb 7 at the start of class ( Homework H03 Cover Sheet )
      • H04: due Fri Feb 21 at the start of class ( Homework H04 Cover Sheet )
      • H05: due Fri Feb 28 at the start of class ( Homework H05 Cover Sheet )
      • H06: due Fri Mar 20 at the start of class ( Homework H06 Cover Sheet )

      • H07: due Sun Apr 5 at the end of the day

        These three problems are your Homework Assignment H07 to be turned in.

        • Write your solutions on your own paper.
        • Assemble your solutions in order.
        • Use the CamScanner App to take pictures of your solutions and save them as a single PDF file.
        • Submit the PDF file in the Blackboard Assignment area.
        • The assignment is due at the end of the day on Sunday, April 5, 2020.

        [1] In our Teams meeting for Day #27 (Mon Mar 30), we discussed Theorem 5.3.2 The Linear Pair Theorem :

        If \( \angle ABC \) and \( \angle CBD \) form a linear pair , then they are supplementary

        We discussed the structure of the book�s proof.

        • We discussed the structure of the book�s proof:
          • Proof Part 1: Prove that \( \alpha + \beta < 180 \) cannot happen.
          • Proof Part 2: Prove that \( \alpha + \beta > 180 \) cannot happen.
          • Therefore \( \alpha + \beta = 180 \)
        • And I presented a more fully-explained version of the book�s proof of Part 1.
          • I broke the sentences up into single statements. (The book sometimes combined more than one statement into a single sentence.
          • I illustrated each statement
          • I justified each statement
        Your assignment is to present a more fully-explained version of the book�s proof of Part 2, as I did for Part 1.

        [2] (Book�s exercise [5.3#6]) Prove Theorem 5.3.9 The Vertical Angle Theorem (Bowtie Angle Theorem) :

        In a protractor geometry, if \( \angle ABC \) and \( \angle A'B'C' \) form a vertical pair (Bowtie Angles) , then \( \angle ABC \simeq \angle A'B'C' \).

        General note about writing proofs in Geometry:

        • Make a drawing that illustrates the statement of the claim.
        • Also make a drawing for each step of the proof.

        [3] (Book�s exercise [5.3#9]) Show that for \( \Delta ABC \) as given in Example 5.1.3, $$(AC)^2 \neq (AB)^2+(BC)^2$$ This example illustrates that the Pythagorean Theorem need not be true in a protractor geometry.

    Attendance Policy:

    Attendance Policy for Section 100 (Class Numbers 5881/5906), taught by Mark Barsamian

    Attendance is required for all lectures and exams, and will be recorded using sign-in sheets and traditional roll call.

    Missing Class: If you miss a class for any reason, it is your responsibility to copy someone's notes. I won't use office hours to teach topics discussed in class to students who were absent.

    Missing a Quiz or Exam Because of Illness: If you are too sick to take a quiz or exam, then you must

    1. send me an e-mail before the quiz/exam, telling me that you are going to miss it because of illness, then
    2. then go to the Hudson Student Health Center.
    3. Later, you will need to bring me documentation from Hudson showing that you were treated there.
    Without those three things, you will not be given a make-up.

    Missing Quizzes or Exams Because of University Activity: If you have a University Activity that conflicts with one of our quizzes or exams, you must contact me before the quiz or exam to discuss arrangements for a make-up. I will need to see documentation of your activity. If you miss a quiz or an exam because of a University Activity without notifying me in advance, you will not be given a make-up.

    Missing Quizzes or Exams Because of Personal Travel Plans: Many of our quizzes and in-class exams are on Fridays or Mondays. Students sometimes ask me if they can make take a quiz or exam early or late because they have plans to miss a Friday or Monday class in order to lengthen a weekend or a holiday. The answer is always, No you may not take the quiz or exam early or late. You will just have to change your travel plans or forfeit that quiz or exam.

    Policy on Cheating:

    Policy on Cheating for Section 100 (Class Numbers 5881/5906), taught by Mark Barsamian

    If cheat on a quiz or exam, you will receive a zero on that quiz or exam and I will submit a report to the Office of Community Standards and Student Responsibility (OCSSR).

    If you cheat on another quiz or exam, you will receive a grade of F in the course and I will again submit a report to the OCSSR.

    Calculators and Free Online Math Resources:

    Calculators and Math Websites

    Calculators:

    Calculators may or may not be allowed on particular quizzes or exams, depending on the topic. I will clearly announce the policy for each quiz and exam in advance of the date for that quiz or exam.

    Websites with Useful Math Resources:

    In lectures, I often use a computer for graphing and calculating. The computer tools that I use are free online resources that are easily accessible at the following link.

    Link to Free Online Math Resources

    I use the same online resources in my office, instead of a calculator. You are encouraged to use these same free resources at home, instead of a calculator.

    Link

    page maintained by Mark Barsamian , last updated April 24, 2020

    View Site in Mobile | Classic
    Share by: