# Mathematics 335 :  GeometrySpring 2023Introduction

Professor:        Jeff Johannes                                    Section 1    MWF    10:30-11:20a    Fraser 116
Office:            South 326A
Telephone:      245-5403
Office Hours:    Monday 5-6p Fraser 116, Tuesday 8-9p South 336, Wednesday 2-3p Fraser 104, Thursday 4-5p Fraser 116, Friday 12-1p Fraser 116, and by appointment or visit.
Web-page:        http://www.geneseo.edu/~johannes

### Textbook

Experiencing Geometry:  Euclidean and Non-Euclidean with History (Third Edition), David W. Henderson and Daina Taimina or
Experiencing Geometry:  Euclidean and Non-Euclidean with History (Fourth Edition), David W. Henderson and Daina Taimina

### Purposes

To develop a deep and personal understanding of Euclidean, spherical and hyperbolic geometries and how they relate to measuring the universe in which we live.

### Overview

This course will take a more philosophical perspective on geometry rather than a computational or result-based perspective.  In this class we will use several different methods to analyse geometries.  We will rarely have traditional lectures.  More frequently will be times for individual work, group work, and class discussion.  Primarily you will be writing personal discussions of homework problems.

I have intentionally chosen Henderson's book as an exploratory and philosophical text.  After our class introductions, please take time to carefully read the chapters in the book.  Notice use of the words “time" and “carefully"ť.  Read the sections slowly.  Read actively, that is while writing and with models at hand.  If you do not understand some statement reread it, think of some potential meanings and see if they are consistent, and if all else fails, ask me.  If you do not believe a statement, check it with your own examples.  Finally, if you understand and believe the statements, consider how you would convince someone else that they are true, in other words, how would you prove them?

### Learning Outcomes

Math 335 - Upon successful completion of Math 335 - Foundations of Geometry, a student will be able to:
• Compare and contrast the geometries of the Euclidean and hyperbolic planes,
• Analyze axioms for the Euclidean and hyperbolic planes and their consequences,
• Use transformational and axiomatic techniques to prove theorems,
• Analyze the different consequences and meanings of parallelism on the Euclidean and hyperbolic planes,
• Demonstrate knowledge of the historical development of Euclidean and non-Euclidean geometries,
• Use dynamical geometry software for constructions and testing conjectures, and
• Use concrete models to demonstrate geometric concepts.

Your grade in this course will be based upon your performance on homework, a project, and a final experience.  The weight assigned to each is designated below:
Homework Problems  3/5
Project                         1/5
Final Experience         1/5

### Homework Problems

Throughout the course you will write up discussions of “Problems" from Henderson's book.  Before these papers are handed in, I strongly suggest somehow submitting drafts to me for comments (most easily to submit them early via Canvas).  These drafts are not required, but will strengthen your understanding and your final products.  Drafts can either be submitted in paper or via email.  Either way I will return them with comments and suggestions.  The end goal of writing each problem will be presenting your complete understanding of the question in a well-written discussion.  These discussions will be graded on a ten point decile scale based on completeness, accuracy and writing.
These problems will be evaluated similarly to evaluating papers in an English class.
0    missing or plagiarised
3     question copied, nothing written
6    something written that appears that it was only written to take up space
7     substantially incomplete.  Something written, but does not really answer the main questions.  Major errors.  Very poor writing
8     mostly complete.  maybe a few minor errors
9     complete, no errors, some personal insight, well-written
10    wonderful (includes concise, and to the the point directly)

### Participation Modifier

For each homework problem there will be a discussion in class introducing it.  If you are present in class and actively and thoughtfully participating in the discussion on that topic, then you will earn an additional .5 for the associated homework problem.  If you would like to prepare for the topic, I suggest reading at least the table of contents for the question.  Beyond that, try not reading too much in advance so as to not spoil the fun.  Look here for an approximate unreliable daily schedule, but more importantly, pay attention in class to our progress.  Two "extra" day modifiers may be earned by visiting my office during the month of January.

### Solutions and Plagiarism

There are plenty of places that one can find all kinds of solutions to problems in this class.  Reading them and not referencing them in your work is plagiarism, and will be reported as an academic integrity violation.  Reading them and referencing them is not quite plagiarism, but does undermine the intent of the problems.  Therefore, if you reference solutions you will receive 0 points, but you will *not* be reported for an academic integrity.  Simply - please do not read any solutions for problems in this class.

### Projects

Each student is responsible for completing a project as part of a pair.  A project will consist of reading one of chapters 11, 14-22 from Henderson's book.  The materials for the projects must be chosen by February 23.  Each project will include a write-up of all the problems in the chosen part.  Finally, each of the projects will be presented in the last two weeks of class.

### Final Experience

The final experience will include extensive writing and focused on summarizing the experience of different aspects of the course.   This product will be due at the time of the scheduled final exam, May 15, 9-11a, when we will also meet to discuss the topic and the course as a whole.

### Geogebra

We may occasionally using Geogebra as a method of gaining intuition for geometry.  Details for working with this software will be described in class.

### Feedback

Occasionally you will be given anonymous feedback forms.  Please use them to share any thoughts or concerns for how the course is running.  Remember, the sooner you tell me your concerns, the more I can do about them.  I have also created a web-site which accepts anonymous comments.  If we have not yet discussed this in class, please encourage me to create a class code.  This site may also be accessed via our course page on a link entitled anonymous feedback.  Of course, you are always welcome to approach me outside of class to discuss these issues as well.

### Accommodations

SUNY Geneseo is dedicated to providing an equitable and inclusive educational experience for all students. The Office of Accessibility will coordinate accommodations, auxiliary aids, and/or services designed to ensure full participation and equal access to all academic programs, activities, and services at SUNY Geneseo. Students with letters of accommodation should submit a letter and discuss needs at the beginning of the semester. Please contact the Office of Accessibility Services for questions related to access and accommodations.  Erwin Hall 22 (585) 245-5112 access@geneseo.edu www.geneseo.edu/accessibility-office.

### Religious Holidays

It is my policy to give students who miss class because of observance of religious holidays the opportunity to make up missed work.  You are responsible for notifying me no later than February 7 of plans to observe the holiday.

### Military Obligations

Federal and New York State law requires institutions of higher education to provide an excused leave of absence from classes without penalty to students enrolled in the National Guard or armed forces reserves who are called to active duty. If you are called to active military duty and need to miss classes, please let me know and consult as soon as possible with the Dean of Students.

### Schedule

subject to change.  For more similarly unstable daily details, see here.

January 27 - February 15         Discuss Chapters 1-5 of Henderson
February 6                               As a homework exercise, show a model of a hyperbolic plane
February 17 - March 20            Discuss Chapters 6, 7, 9 of Henderson
February 20                             Drafts of Chapters 1-5 will not be accepted after
February 23                             Projects must be chosen by this date.
February 27                             Final write up of Chapters 1-5 “Problems" due
March 22 - April 7                    Discuss Chapters 8, 10 of Henderson
March 24                                 Drafts of Chapters 6, 7, 9 will not be accepted after
March 31                                 Final write up of Chapters 6, 7, 9 “Problems" due
April 10  - May 3?                   Discuss Chapters 12, 13 of Henderson, and Constructions
April 10                                     Drafts of Chapters 8, 10 will not be accepted after
April 17                                  Final write up of Chapters 8, 10 “Problems" due
April 29                                   Drafts of Chapters 12, 13 will not be accepted after
May 5  - May 15                    Project presentations
May 8                                   Written projects due.  Final write up of Chapters 12, 13 "Problems" due
Monday May 15, 9-11a       Final experience - leftover presentations.