Geometry

Important links

  • Gradescope (Instructions available in the FAQ below.)
  • Office hours meetings can be scheduled here.
  • Not sure yet, but more to come.

Weekly Plan

This week we are going to try to continue with our collaborative learning model. To facilitate this we'll be doing several things:

  1. I'll have versions of the worksheets up in Gradescope for you to collaborate on answering in small groups.
  2. We'll be meeting at the usual time via Zoom. I'll divide you up into smaller workgroups, and you can collaborate on your answers over Zoom and by adding your group members to your copy of the worksheet in Gradescope. I'll be moving back and forth through the groups to answer questions. We'll take the last ten minutes of class to review your solutions and make sure we've got stuff worked out well.
  3. Recordings of the sessions will be made available to class members who are in distant time zones (we're going to have at least one). I'll be sending the links to the whole class every day.

Please make sure you have reviewed the COVID FAQ below. I'm updating it daily.

  • 4/20: We start § 11.1.
  • 4/22: Presentations of projects, plus either finish § 11.1 or start § 11.2
  • 4/24: § 11.2-§ 11.3
    • Reflection essays: I'm expecting 1-2 pages talking about your experience with your project. What did you learn from it? What worked well? What didn’t work well? Time permitting, what would you do differently? What advice would you give to someone taking this class in the future about this assignment?
  • 4/27: § 11.3 and Review.
  • 4/30: Final exam will become available at 10:15 AM. The exam will be comprehensive in nature, with an emphasis on material since the last midterm. It will be available for you to complete by 5 PM on Friday 5/1. The exam was written so that you should be able to complete it in two hours (not counting photographs and uploads), and I am giving you six hour window to complete and submit it. Ground rules are the same as for the second midterm exam:
    • This exam is open note and open book, by which I mean:
      • You may use any notes you have in your possession while sitting for the exam.
      • You may refer to our textbooks Perspective and Projective Geometry and Geometry in a Nutshell.
    • Other things you should know:
      • You are allowed to use GeoGebra, Geometer's Sketchpad, something to scan or take pictures of your written work.
      • You are welcome to use standard drawing tools (pen, pencil, ruler, markers, pair of compasses).
    • You will be asked to affirm that you will adhere to the following rules while taking this exam:
      • You will not look things up on the internet while working the exam.
      • You will not discuss the contents of the exam with anyone besides the instructor.
      • The work you present will be your own.

Announcements

  • When taking a photograph of your work, you can eliminate bad shadows and things by hanging it on a refrigerator or door.
  • You can significantly decrease upload times in Gradescope by using a scanning app instead of just directly uploading a photo (the file sizes tend to be much smaller).
  • If you are using your phone for web conferencing, you can make a stand out of cardboard or Lego so you can operate it hands-free.
  • I'm moving the second exam to April 3... this will give us a chance to adjust to the new reality before trying to do anything as complicated as take an exam.
  • I've added two problems from Monson to assignment 11.
  • The current summary sheet is available. It's Stefano's turn to update it. You can download the current version (a good study guide probably) here.
  • If you ran into trouble on the billiards problem on the homework, I suggest taking a second look at example Problem 1.3.1 and the following discussion.
  • Your appearance grade now includes how you are using punctuation and line breaks.
  • You need to remember to turn off your axes and grid when exporting GeoGebra files for use in LaTeX, and make sure your labels are large enough to read.
  • I frequently make use of standard proofreading marks when grading.
  • Homework Formatting: By this point you should be preparing your written homework using the template I provided, and you should make sure that your proofs are formatted at least doublespaced. If you are having problems with LaTeX, come see me! I've uploaded a slightly revised template that should make a lot of this easier, you'll just need to use my \bproof and \eproof commands to begin and end your solutions. Examples are included in the revised template. I've also decided to include a slightly fancier way of including a GeoGebra file so that it flows better on the page. If you want to submit homework that you have prepared not using LaTeX, make sure your homework is being prepared to the standard provided by the template (i.e., typed neatly, solutions double spaced, full problem statements included).
  • If I receive your homework before I start grading it, you can get full credit. If you don't turn in a proof assignment in time for the first round, but do turn it in by the revisions due date, I will still accept it. You should DEFINITELY not make a habit of this, since you are likely to get MORE points after you incorporate my feedback from round one.
  • Art assignments should be done on plain white letter paper unless otherwise instructed.
  • Including GeoGebra files can sometimes cause errors with compilation. If you run into trouble, send me your LaTeX file and your questions, and I'll try to help you figure out what the fix is. For example, one I was working on recently was throwing up errors because the picture was too big. I fixed this by modifying the size of the x= and y= specifications at the beginning of the \begin{tikzpicture} line, as well as modifying the line width commands to make things look nice.
  • If you want to make a calligraphic letter (e.g., for a pencil of lines), type $\mathcal L$. To get the dot used for the intersection of two things, use $\cdot$.
  • Office Hours: Monday, Wednesday and Thursday, 1-3 PM in Chapman 306 D.
  • I want to make sure we are getting the most we can out of the homework, and I want to make sure I'm not killing you with work. For the first few weeks of the semester I want you to keep track of when and how long you spend on each exercise and you are expected to include this information with your homework submissions (both proofs and art).

COVID Response

This is a FAQ providing detailed information about how we are going to proceed this semester.

  • How are you?
    • Fine, thank you for asking! However, since I traveled over break, I'm forbidden from coming on campus to work for two weeks. This means, like many of you, I have a slower than usual internet connection to work with for at least the next couple of weeks. How are you?
  • What are we going to do about class meetings?
    • For the first week we may be restricted to audio only connections if my network can't handle things.
    • I may end up posting some videos and things to supplement class meetings. If so, I'll be emailing links to the class.
  • What are we doing about homework?
    • I'm setting up a Gradescope portal for the course. I'll post more information about how to make use of that here. You will also receive invites soon to access it.
  • What are we doing about tests?
    • Similar to what we are doing for homework, but those assignments will be time limited in two ways: a shorter time period (e.g., a day) during which they are available to be accessed, and once your start a test, you will have a limited time period to complete it (e.g., 90 minutes).
  • Office hours?
    • These will be by appointment (through Google Calendar), and will be conducted using Zoom or Join.me.
  • Project due dates?
    • I'm thinking about this. Answers soon.
  • Can I use LaTeX to type math into a short answer solution in Gradescope?
    • YES! But you need to surround the math with double dollar signs, e.g., $$\angle\theta$$ will give you ∠θ.
  • Here are some instructions on how to submit an assignment in Gradescope.
  • Other questions?
    • Shoot me an email, and I'll answer them here.

Resources

  • The course syllabus.
  • The textbook.
  • Barry Monson's Geometry in a Nutshell.
  • LaTeX template. This is a zip file containing the template, as well as a sample TikZ graphic and a copy of the compiled PDF.
  • GeoGebra and, optionally, Geometer's Sketchpad.
  • Viewpoints: Mathematical Perspective and Fractal Geometry in Art by M. Frantz and A. Crannell.
  • Geometry by Brannan, Esplen and Gray, 2nd edition.
  • Projective Geometry by H. S. M. Coxeter.

Homework

There are three kinds of problems that can show up on the homework. Exercises (marked with an E enclosed by a circle in the text), Art Assignments (marked with an A enclosed by a triangle), and Proof/Counterexample problems (marked with a P enclosed by a square). I use circles, triangles, and squares when listing homework problems of the corresponding types below.

Homework