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Euclid's Elements at High School Level?

by Geremia
Tags: elements, euclid, geometry, mathematics
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Geremia
#1
Apr3-09, 08:59 AM
P: 146
Has anyone taught geometry at the high school level using Euclid's Elements (e.g., Heath's translation) as a textbook? Einstein considered the Elements a "holy little geometry book."
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qntty
#2
Apr3-09, 04:04 PM
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I tried reading heath's translatino when I was studying geometry and didn't like it. I thought that the archaic terminology got in the way of the math. The content of the book was nice so if you can find a modern translation (heath's was done in the early 1900's) then it might be nice as long as the students have a good teacher that would explain the basics of geometry and proof-writing.
Geremia
#3
Apr4-09, 01:11 AM
P: 146
Quote Quote by qntty View Post
The content of the book was nice so if you can find a modern translation (heath's was done in the early 1900's) then it might be nice as long as the students have a good teacher that would explain the basics of geometry and proof-writing.
Which translation is better than Heath's, then? Fitzpatrick's translation is too literal.

Howers
#4
Apr10-09, 08:55 PM
P: 444
Euclid's Elements at High School Level?

Screw Euclid. Get a modern interpretation like Jacobs "Elementary Geometry".

Euclid is great for historical reasons, but modern methods are far more efficient. Not the mention you get practice problems with books. Einstein didnt use Euclid; he too used a modern interpretation by some German author.

If you insist on Euclid,make it this one: http://www.amazon.com/Euclids-Elemen.../dp/1888009195
whybother
#5
Apr10-09, 09:22 PM
P: 166
I read Elements in high school and got an incredible amount out of it. I think it would be a great tool for any mathematically motivated student. One of my math teachers in my junior year of high school gave us optional reading of it for extra credit and it was probably that initial push into geometry that lead me into pure mathematics. It can definitely be used at the high school level.
mathwonk
#6
Oct31-11, 12:35 PM
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I also recommend the Green Lion edition of Euclid linked by Howers. In my opinion Euclid is the absolute best geometry text for all ages including high school, by a huge margin. A very useful supplement and companion is Hartshorne's Geometry: Euclid and beyond. I even taught from Euclid this summer quite successfully to brilliant 8-10 year olds.

Harold Jacobs' is one of my favorite books as well, but it assumes a student knows about real numbers first, which of course none of them do.
Geremia
#7
Nov1-11, 12:14 AM
P: 146
Quote Quote by mathwonk View Post
I also recommend the Green Lion edition of Euclid linked by Howers. In my opinion Euclid is the absolute best geometry text for all ages including high school, by a huge margin. A very useful supplement and companion is Hartshorne's Geometry: Euclid and beyond. I even taught from Euclid this summer quite successfully to brilliant 8-10 year olds.
Yes, Green Lion Press is very good. I have their edition of Euclid's Elements, and it is very nice.
mathwonk
#8
Nov1-11, 10:28 PM
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here is my review of euclid from amazon:
This work of Euclid, made highly accessible in this edition is indeed incredible. How many people know that Euclid had a thorough grasp of the concept of a tangent line to a circle comparable to that of Newton? Certainly not me. I am currently teaching from this book and reading it in detail, to my great pleasure. In Proposition III.16, Euclid essentially shows the following 4 properties are equivalent for a line L meeting a circle C at a point P:
1) L meets C nowhere else, 2) L does not "cut" C, i.e. L contains no points interior to the circle, 3) L is perpendicular to the radius of C through P, 4) L makes angle zero with the circle C at P, i.e. the greatest lower bound of the angles between L and all secants of C through P is zero,

and his proof also shows: 5) the line L is the limit of secants of C through P as the second point of intersection approaches P, i.e. for every angle containing L as a side, there is a neighborhood of P such that all secants of C through P make with L a smaller angle than the given one.

The first property, that a tangent line should meet a circle only once, is the one I was taught in high school, and it is inadequate for discussing tangents to curves more complicated than globally convex ones. The property of not cutting the curve, or of not crossing it, is adequate for describing tangents to all locally convex curves, and the property of making an angle of zero, or of being a limit of secants is of course Newton's most sophisticated definition suited for describing tangents to all curves. I am now not surprised to learn that Newton read Euclid before producing his own work. I had no idea this was in Euclid, and I have had the same eye opening experience in several other places as I read this amazing book.

Thanks to Green Lion for this lovely edition, and to Robin Hartshorne for writing his book in such a way as to force me to read Euclid.

While teaching the first 4 books of this work this summer to brilliant 8-10 year olds I noticed that proposition 35 or 36 in book III already contains the fundamental theorem of similarity, and one can finesse the beautiful but complicated presentation in book 5 i believe. Moreover using the prop in book 3 gives similarity for non archimedean geometries as well, unlike the version in the later book. the point is that the theories of area and similarity are equivalent and the fundamental result for all of them is pythagoras' theorem.
AlephZero
#9
Nov2-11, 08:15 AM
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There is an online version, with interactlve "figures", at
http://aleph0.clarku.edu/~djoyce/jav.../elements.html
Woopydalan
#10
Mar10-12, 07:53 PM
P: 746
I found this book at the used bookstore for $1, I had to pick it up..I haven't looked at it though :P


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