Talk to me about Euclidean Geometry

[elegantlion]

My son has set forth a challenge. Part of it involves learning some Geometry. Me, I like algebra, Geometry is not my strong point. Ds has jumped ahead and decided he'd like to learn geometry in his spare time. :001_huh: (is this my child?!) I'll be learning with him. We'd also like to throw in some Euclidean Geometry. However, I'm not sure how much is relevant and how it is different than modern geometry.

 

I did find an online source here. http://aleph0.clarku.edu/~djoyce/java/elements/toc.html and would like to buy a printed copy, but how many of the books do we need to focus on?

Edited September 29, 2011 by elegantlion

[regentrude]

The plane geometry that is taught in a modern geometry course is Euklidean geometry (spherical geometry is not). It will probably be easier to understand a modern geometry treatment of the same material than Euklid, because it is easier to explain concisely with equations things Euklid had to say out in words and sentences. He was a genius, but back then algebra had not been invented and he had to spell everything out.

In that light, I would see the classical Euklid text as an interesting book for math history, but would recommend a modern text if you are just interested in learning the content. A modern geometry approach covers definitions, proofs and classical constructions.

[David-L]

I’ll describe my current geometry project. I did take geometry in high school and did very well but I’m also old and forgot quite a bit of it.

 

I’m using two DVD courses:

 

1) Geometry Help: The Geometry Tutor -- 2 DVD Set -- 9 Hour Course

http://www.mathtutordvd.com/products/item16.cfm

 

This course is about concepts. *Very* basic but it got me warmed up.

 

2) High School Level—Geometry Taught By Professor James Noggle

 

http://www.thegreatcourses.com/tgc/courses/course_detail.aspx?cid=105

 

This should be bought when it’s on sale. The sales happen pretty often.

 

More challenging, this is a very good course in the sense that the postulates, theorems, properties, and definitions are consistent and well thought out. This course is all about proofs which are done with some welcome precision. The instructor uses a black board and flip charts but the content is what’s important.

 

I photocopied the postulates, theorems, etc from the book so they could be right next to me. Before each lecture I reviewed each postulate, property, and theorem up to the point I had thus far reached in the course.

 

After working through these courses reading Euclid would be easier. In high school I don’t think I could have handled Euclid has my first exposure to geometry.

 

Possibly using software like the “The Geometer’s Sketchpad†( http://www.keypress.com/x24070.xml ) would be useful but I’m more into the logic and proofs of the course.

[elegantlion]

The plane geometry that is taught in a modern geometry course is Euklidean geometry (spherical geometry is not). It will probably be easier to understand a modern geometry treatment of the same material than Euklid, because it is easier to explain concisely with equations things Euklid had to say out in words and sentences. He was a genius, but back then algebra had not been invented and he had to spell everything out.

In that light, I would see the classical Euklid text as an interesting book for math history, but would recommend a modern text if you are just interested in learning the content. A modern geometry approach covers definitions, proofs and classical constructions.

 

So we could approach Euclid as math history? I do have a regular geometry book to use first. Thank you, that is helpful.

[Beth in Central TX]

Here's what I have for our study of Euclidean Geometry: http://www.amazon.com/Euclidean-Geometry-Course-Mark-Solomonovich/dp/1440153485 My DH will teach this course, so I probably can't answer any specific questions about geometry, but I can help if you have questions about the book itself.

 

We will also study Euclid's Elements in Omnibus IV this year (which uses this book: http://www.veritaspress.com/prodinfo.asp?number=190178). I have the Omnibus IV book, but my DH plans on using Euclid's Elements from our Great Books of the Western World set.

 

HTH!

 

~Beth

[elegantlion]

Here's what I have for our study of Euclidean Geometry: http://www.amazon.com/Euclidean-Geometry-Course-Mark-Solomonovich/dp/1440153485 My DH will teach this course, so I probably can't answer any specific questions about geometry, but I can help if you have questions about the book itself.

 

We will also study Euclid's Elements in Omnibus IV this year (which uses this book: http://www.veritaspress.com/prodinfo.asp?number=190178). I have the Omnibus IV book, but my DH plans on using Euclid's Elements from our Great Books of the Western World set.

 

HTH!

 

~Beth

 

Thank you, Beth. I saw the Elements on Amazon this morning, I knew I'd seen them in someone's catalog.

 

The other book looks good. I'm off to read more about it and the author.

[Jane in NC]

My son did a proof and construction oriented geometry course using a 1970's text by Dressler. At the end of the year, we worked through some Euclid because I did want my classically oriented lad to see the difference in the nature of the proofs. Algebra was not invented when Euclid wrote the Elements. While I feel that reading Euclid has merit, a modern student needs to approach geometry using the tools of the day which include things like Cartesian coordinates. The logic of the proof remains. To me, that is what is important to develop in a geometry course.

 

Following our dabbles into Euclid, I assigned the book Experiments in Topology by Stephen Barr. This is not a mathematical study of Topology (too much hand waving for the serious) but it does introduce some new ideas to students. In topology, shape is less important than certain qualitative aspects. The classic example is that to a topologist there is no difference between a mug and a doughnut--both have one hole. (Demo here.) Coming on the heels of geometry, I found that topology brought some annoyingly mind blowing ideas to my son.

 

By the way, the Barr book is available from Dover at a reasonable cost.

[elegantlion]

Thanks, Jane. I have a Jurgensen text with TE and a 60s Dolciani Geometry (not TE or solutions manual), those will be our main texts. I'll add the topology book to our wish list, that looks like the kind of study he'd enjoy.

 

I am fascinated by the interests ds develops as he matures. His favorite word is why? Right now I'm not sure if that incessant questioning will lead him toward science, philosophy, math, or a combination of all. He is becoming a fascinating individual and I'm just pleased to be a part of the journey. I thank you all who are helping along the way.

[Corraleno]

Paula, here are some fun supplements for geometry:

 

Bradford Hansen-Smith's incredible paperfolding website. You can buy his books from RedHenToys.com (I think it's linked on his website)

 

Zome Geometry

 

TTC The Shape of Nature

 

TTC Mathematics from the Visual World

 

Geometer's Sketchpad software — on sale through HSBC for $15, expires tomorrow (9/30)

 

We also have the hardback of this edition of Euclid's Elements, which is a beautiful book, but it will be a couple of years before DS gets to it.

 

Jackie

[elegantlion]

I’ll describe my current geometry project. I did take geometry in high school and did very well but I’m also old and forgot quite a bit of it.

 

I’m using two DVD courses:

 

1) Geometry Help: The Geometry Tutor -- 2 DVD Set -- 9 Hour Course

http://www.mathtutordvd.com/products/item16.cfm

 

This course is about concepts. *Very* basic but it got me warmed up.

 

2) High School Level—Geometry Taught By Professor James Noggle

 

http://www.thegreatcourses.com/tgc/courses/course_detail.aspx?cid=105

 

This should be bought when it’s on sale. The sales happen pretty often.

 

More challenging, this is a very good course in the sense that the postulates, theorems, properties, and definitions are consistent and well thought out. This course is all about proofs which are done with some welcome precision. The instructor uses a black board and flip charts but the content is what’s important.

 

I photocopied the postulates, theorems, etc from the book so they could be right next to me. Before each lecture I reviewed each postulate, property, and theorem up to the point I had thus far reached in the course.

 

After working through these courses reading Euclid would be easier. In high school I don’t think I could have handled Euclid has my first exposure to geometry.

 

Possibly using software like the “The Geometer’s Sketchpad†( http://www.keypress.com/x24070.xml ) would be useful but I’m more into the logic and proofs of the course.

 

Thanks, David, I missed your post yesterday. I'll look into these as soon as the coffee kicks in. :D

 

Paula, here are some fun supplements for geometry:

 

Bradford Hansen-Smith's incredible paperfolding website. You can buy his books from RedHenToys.com (I think it's linked on his website)

 

Zome Geometry

 

TTC The Shape of Nature

 

TTC Mathematics from the Visual World

 

Geometer's Sketchpad software — on sale through HSBC for $15, expires tomorrow (9/30)

 

We also have the hardback of this edition of Euclid's Elements, which is a beautiful book, but it will be a couple of years before DS gets to it.

 

Jackie

 

Hey, Jackie, good to see you. Thank you. I put the Euclid's Elements, the pretty one, in my cart yesterday. I'm thinking about getting that for ds for Christmas.

 

I started geometry yesterday while ds was studying for an algebra test. I thought my brain was going to explode. Between answering questions for ds and trying to wrap my brain around all of it, we spent two hours on math. :001_huh: It might be easier if I have ds teach me while he learns, I think he'll get geometry very easily. :tongue_smilie:

[Tullia]

It's a nice bridge between modern texts and EE. He includes an interesting discussion of the fifth postulate and refers to EE throughout the book. We used Solomonovich mostly for reference and supplementary work. My son enjoyed the construction problems in Chapter 5, and section 5.3 on developing strategies for construction was especially helpful. (BTW, I think the history of work on the fifth postulate is found in that section.) I have a supplementary book called Problems and Questions, and am not sure if it's the same thing as the Instructor's Manual that's described on Amazon. The apt quotations from Winnie the Poo add to the fun.

[elegantlion]

It's a nice bridge between modern texts and EE. He includes an interesting discussion of the fifth postulate and refers to EE throughout the book. We used Solomonovich mostly for reference and supplementary work. My son enjoyed the construction problems in Chapter 5, and section 5.3 on developing strategies for construction was especially helpful. (BTW, I think the history of work on the fifth postulate is found in that section.) I have a supplementary book called Problems and Questions, and am not sure if it's the same thing as the Instructor's Manual that's described on Amazon. The apt quotations from Winnie the Poo add to the fun.

 

Thank you. I'm adding that to my list.