Geometry in High School: Is it Worthwhile Studying?

[Bashyboy]

Hello,

I never took Geometry in high school, and I am currently in college studying both math and physics. Consequently, I decided to pick up a basic geometry textbook to try and learn it on my own; but I have found I have limited time due to my college studies. I am wondering, is it even worthwhile to try and do this--since I am limited on time--, and will I learn any of the geometry typically learned in high school during my time spent at college?

 

[micromass]

You have to realize that a lot of high school geometry will be essentially useless to you. For example, deriving things from their basic geometric axioms will be useless. And crap like two-column proofs is completely not what you need.

On the other hand, being familiar with vectors and equations of lines, etc. is very useful to you, but this is not always taught in high school geometry.

A good book is "Geometry" by Serge Lang. It deals with the kind of geometry you will have to deal with in university. I suggest you study from that book or a book like it.

 

[Bashyboy]

Sounds reasonable enough. I am studying Calculus I and Calculus Based Physics I, so should I just focus on those two things for now and read the geometry book you suggested at a later time? And if I should read a book like that when would you suggest would be an appropriate.

 

[micromass]

Only being familiar with the two things I mentioned will not be enough. I did not mean to say that this will be ALL you ever need. You will need to be familiar with quite a lot of things, certainly for physics.

I recommend you read a geometry book right now. It won't be very difficult for you.

 

[qspeechc]

Although you never took geometry, you probably did learn some geometry. For instance, you know Pythagoras's theorem, right?

The type of geometry you will need to know is co-ordinate geometry, i.e. using algebra to do geometry, e.g. the equations of a straight line, parabolas, hyperbola etc. and their properties; but it is very unlikely you did not cover this in school. But even this geometry needs some knowledge of Euclidean geometry.

But on a different note, if you plan on going into mathematics, it will be a little odd and sad if you don't know any Euclidean geometry. Eventually you'll learn higher and different forms of geometry, and it will be deeply interesting to compare them with Euclidean geometry. And Euclidean geometry is a tradition part of a mathematics education, which is why it will be a bit odd not knowing it, even if you never really use it. Also, I find Euclidean very interesting, but I doubt many people would agree with me.

I was in the same position as you. We did cover Euclidean geometry in school, but it was very little and very badly done. I left school disliking and not understanding geometry. I just finished studying Euclidean geometry on my own, and this is after I have my maths degree! It was well worth my time, I feel.

Try to spent an hour a day over the weekend on the geometry book you have, or whatever time you can spare. Otherwise leave it to your vacation and study the book then. It's just my opinion, but I think studying Euclidean geometry is worth while.

 

[Bashyboy]

Oh, I highly agree with you, qspeechc; I was reading Euclid's Element and I found them fascinating. I undoubtedly want to study, but I am rather short on time, and I was just wondering if I could hold of learning that sort of geometry until later.

 

[OldEngr63]

I would certainly not disparage two column proofs. They are really good foundations in logical thinking because they force you to justify every statement you make. Actually, you should be able to do this for every mathematical problem you work, justifying every mathematical operation you perform in order to reach a solution. If you cannot, there is reason to question the validity of your calculations.

 

[mathwonk]

On my page:

http://www.math.uga.edu/~roy/camp2011/10.pdf

You will find a complete set of notes from a 2 week course I taught, covering most of books I-IV of Euclid last summer, except for the constructions.

They are at #10, "Epsilon camp notes", and are free.

I suggest it to you as a possible quick trip through basic elements of Euclid.

I am one of those old fogies who thinks knowledge of Euclid is probably the best beginning math education you can have, followed by Euler's Elements of algebra.

Indeed most students who fail basic calculus do so because they lack fundamental knowledge of geometry and skill in algebra.

Actually, I recommend reading Euclid himself, with a good guide such as Hartshorne's Geometry: Euclid and beyond. Working your way through the first chapter of Hartshorne, combined with Euclid books I-IV should give you a very good start on the basics.