Honors

There are 3 options for how to earn Honors credit in this class: (1) Standard Honors, (2) Reading the Shape of Space, or (3) reading Arithmetic.  These are explained in more detail below.

Standard Honors: This is basically what it sounds like - more challenging problems testing your understanding of Geometry to the limit, as well as a few additional Geometry topics directly related to the curriculum we don't have time to cover in class. If you're mostly looking for what we do in class, but a harder version, do this!

The Shape of Space: Is the universe infinite? If not, does that mean at some point you'd hit an "edge" of the universe, and if so, what's beyond that edge? This project invites you to take a tour of the geometry needed to understand the shape of the universe from a rational, scientific point of view. You'll learn about topology, how space itself might "curve", and how to classify the possible shapes of the universe. The project itself consists of learning and completing books reports (which involve significant mathematics) from the book "The Shape of Space" by Jeffrey Weeks. Prepare to come to office hours regularly if you choose this option, as much of the material is of very high level and chances are you'll have lots of questions and confusions. But the reward is worth it - you can impress your friends by REALLY understanding what modern science says about the universe as a whole!

Arithmetic: Arguably the most important single piece of mathematics invented in human history is decimal representation of numbers, and the associated methods for adding, multiplying, subtracting and dividing numbers written in decimal and fraction form. Although you've all "learned" this, you are probably not aware of the incredible, multi-cultural history behind its development, and you might wonder, are there other ways to do arithmetic? If you are interested in history or learning more deeply about a signifcant bit of mathematics we've all had drilled into us for many years, this book is for you! As with the Shape of Space, you will be completing regular book reports, this time from "Arithmetic" by Paul Lockhart. The book reports require significant mathematical work - they are not just summaries of what you've read!

How to do Honors: 

1.  Sign up for Honors. To do this, just send me an email with the subject heading "Geometry Honors", and in the body of the email write that you wish to pursue Honors, and tell me which option. For example, write "Hi Peter, this is Jimbo and I want to do the Shape of Space Honors for Geometry". That's it on my end.  Don't forget: You ALSO need to fill in Morgan's form that he sends out to all students, informing him that you have chosen to do Honors in Geometry.     

2. Complete the assignments listed below, for the option you have chosen. The due dates are spaced about 2-3 weeks apart, always on a Friday (even if you don't have my class that Friday). The due dates are the same for all Honors options.

Standard Honors

This Honors option goes into more depth on topics learned in class, and introduces a few mainstream Geometry concepts we didn't have time for in the curriculum. 

See below for the assignments:

Shape of Space Honors

This year-long Honors project invites you to read a book that teaches you about the basic geometry needed to understand the possible shapes of the universe. Even though the universe is incomprehensibly vast (perhaps infinite), mathematics and logic, as well as observational data, put significant restrictions on   You'll learn about some totally new parts of geometry that most high schoolers never learn: topology and the geometry of curved spaces!

You can order a copy of the book here.  Try to get the third edition; if you end up with the second edition, let me know as some of the problem numbers are different, and Ch. 5 is totally different.

See below for the assignments:

Arithmetic Honors

In this project you learn about the history of our system of arithmetic - in a way that hopefully makes sense how our system naturally evolved.  

You can order a copy of the book here.

See below for the assignments: