Syllabus

What Is It?

A prior incarnation of this site was called "Elementary Euclidean Geometry". That's a good name. (Sometimes I'm sorry I gave it  up.) Let me tell you what it means.

1. Yes, it is geometry. Our subject is shapes - lines, segments, angles, triangles, circles and all the rest.

2. But we approach that subject in a way that will likely come as a surprise. I won't simply tell you what's true. Instead we'll prove it all. This is what Euclid did. This is what we'll do.

3. What do I mean when I say "prove"? Well, that's a little complex. I'll propose a number of so-called "postulates". These serve as basic assumptions; we won't give proofs of them. I think you'll find them quite obviously true. Here's one: through a pair of given points one and only one line passes. Once the postulates are in place, we'll give our proofs; and in those proofs, we'll methodically derive the propositions we wish to prove from the postulates. (Actually, we often make use of other theorems in our proofs, but those other theorems can be traced back to the postulates.) 

4. A proposition, once proven, will be called a "theorem". So in this class, we're provers of theorems; that is, we derive theorems from postulates. Of course you'll want to know what I mean by "derive". Well, you'll have to wait on that. The best way to explain is with examples, and we won't be ready for examples until Chapter 3.

5. Once we're done with the class, we won't have a heap of unconnected facts (which regrettably is how mathematics is often taught). Instead we'll have a system. Each theorem can be traced back to prior theorems, which in turn can be traced back to prior theorems; and finally we bottom out in the postulates.

6. These derivations that we'll give are explanations. They explain why the theorems proven are true. Have you ever wondered why the angles of a triangle sum to 180° , or why in a right triangle the sum of the squares of the legs equals the square of the hypotenuse? Perhaps you haven't,  but you should have; and in this class, we'll give the reason why.

7. I make a most solemn promise to you: I'll never ask you to accept anything simply because I say it is so. Instead everything will be explained (everything anyway that needs an explanation).

How to Excel

No doubt you’ll want advice about how to excel in this class. Here it is.

1. Pay attention when I speak. Take notes. Students who do poorly do neither. Students who do well do both.

2. Do your work. All of it. On time.

3. Ask questions.

4. Keep all of your work. You’ll need it when the time comes to prepare for an exam.

 Know that I will treat you like the young adult you are, not the child that you were. If you slack off, I won’t appear at your desk and tell you to get to work. You already know that.

The Text

This is it.  Everything is here. Please take a few minutes to click around. You'll find every PowerPoint and every worksheet. You'll find solutions. You'll find  all the definitions, postulates, theorems and constructions for the year.  You'll find a number of selected proofs. Moreover, expect that I'll add a video for each section as the year progresses. I always meant to do that, but COVID finally forced my hand.

There is a physical text. We don't use it, but if you'd like a copy, just let me know. It's less bad that most other texts I know.

Your Grade

Here’s the break-down:

Quarter 1: 70% test, 30% homework

Quarters 2, 3 and 4: 70% test, 15% homework, 15% Myriad

Semester: 40% for each quarter, 20% for the final exam

On tests, you have precisely 50 minutes. I don’t give extra time (unless of course you have an IEP which requires that I do). My tests are designed to identify students who have mastered the material and can answer questions quickly.

My usual practice for homework is this: on days of my choice, I’ll have you copy out your work for problems that I will select on paper that I will give you. I call these "homework samples", or "samples" for short.  I won’t do this every day, but I will ask for problems from every assignment. 

I'll introduce The Myriad in Quarter 2.

Make-Up

If you miss, the responsibility is yours to get all make-up work done. The responsibility is yours to schedule a make-up quiz or test. You have a week to get it done. 

Conduct

It’s simple, really. Be kind. Unclear? Here are a few unkind behaviors:

1. Talk when someone else has the floor. If you have a point you wish to make, wait your turn.

2. Make a racket when people are at work.

3. Arrive late. I’ll be ready when the bell rings. You will be too.

4. Make a mess. I hate that. I will notice.

5. Keep cell phones tucked away unless you've asked permission to use them.

6. Use SmartPass when you need to leave. In most cases, you'll create the pass