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/sci/ - Science & Math

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6548216 No.6548216[DELETED]  [Reply] [Original]

I basically know nothing about geometry.
Is euclid a good place to start?

>> No.6548219

>>6548216
As a general rule, starting by going back to ancient Greek texts is probably a bad idea.

Euclid was wrong about a bunch of stuff, and wasn't exactly writing to be easily understood as an introductory text by a layman 2000 years in the future.

>> No.6548230

>>6548219
>Euclid was wrong about a bunch of stuff

Such as?

>wasn't exactly writing to be easily understood as an introductory text by a layman 2000 years in the future.

But it is an introductory text. There is no prior knowledge needed whatsoever. And it's not like there's a cultural gap - lines and circles are the same now as they were then.

However, I agree it might not be the best place to start. I guess it depends on what you are looking for. Euclid will teach you very basic geometry with a very solid foundation - it is a series of proofs that build one off the other. So for example you start by proving that it is possible for an equilateral triangle to exist, and by proof 50 you have the Pythagorean Theorem.

If that sounds appealing, go for it. If you want to learn geometry for practical purposes, however, you should probably just get a modern textbook.

>> No.6548234

>>6548219
It still served as the introductory textbook to geometry for two thousand years. It's a pretty damn good one.

>> No.6548249
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6548249

>>6548234
It fails to keep up with the new discoveries in the field of introductory Mathematics.

>> No.6548260

>- lines and circles are the same now as they were then.

So true.

Try Robin Hartshorne's Geometry: Euclid and Beyond.

>> No.6548263
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6548263

What kind of geometry are we talking about.

Pic related or something a bit more advanced?

>> No.6548281

>>6548263
Just simple euclidean geometry like in the picture.

>> No.6548288
File: 64 KB, 818x1058, 1375057962674.gif [View same] [iqdb] [saucenao] [google]
6548288

>>6548281
ok here's another one

>> No.6548321

>>6548249
Lol. Americans.

>> No.6548361
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6548361

>>6548321

yup

>> No.6548391

What's a good book on introductory geometry?

>> No.6548409

>>6548361
>getting blown the fuck out by Europe

>> No.6548692
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6548692

>>6548216
>>6548230
the cultural difference actually does have an effect on the readability of the text, his syntax and language is something to get used to.
pic related, its like reading shakespeare

>> No.6548736

>>6548216
>Is Euclid a good place to start?

Yes

>> No.6548862

>>6548409
>comparing an entire continent to one country in an effort to confirm your bias
Hahahaha, this is honestly pretty pathetic.

>> No.6549140
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6549140

>>6548692

>mfw I have that translation

Good shit anon.

>> No.6550441

http://www.themathpage.com/aBookI/plane-geometry.htm
If unfamiliar with how proofs and logic work in maths, worth reading the introduction and the first few propositions. Helps you understand more what maths is about if you're used to just doing calculations. Take it further if you please.

>> No.6551728

>>6548692
To this day, I sware to myself, I will not read Elements until I understand what Euclid meant when he said stuff like "A point is that which has no part" (surely this requires a definition of "part"?). The same follows for the other definitions.

>> No.6551761

>>6548230
>Such as?
http://en.wikipedia.org/wiki/Pasch%27s_axiom

>> No.6551773

>>6551728
You should just avoid Euclid altogether. Those are the parts that aren't taken seriously anymore in modern treatments to synthetic geometry (they're the undefined terms of the axiomatic system, they have no inherent meaning).

>> No.6551793

>>6548249
Common Core probably uses Transformation Geometry as the approach to Euclidean Geometry.

http://en.wikipedia.org/wiki/Transformation_geometry

It is actually better than Euclid in many ways. Here are five axioms that define Euclidean PLANE (2D) Geometry.
1) You have a metric space M (then lines and points are defined as sets).
2) There are three non-collinear points (ensures 2D).
3) Every line in the metric space has an isomorphism to the real number line (lets you construct the Cartesian plane and create isomorphisms from your metric space to the cartesian plane and back).
4) Given a line L and a point P there exists one line parallel to L that crosses through P.
5) Given a line L and a point P incident with L, there exists one line perpendicular to L at P.

This is a lot more powerful than Euclid's axioms because you can do linear algebra on it and you've got a metric space. As an example, Pasch's axiom is provable as a theorem in this system instead of actually having to give it as an axiom (or leave it unprovable). Also, being able to define isomorphisms lets you do group theory on the space and turns a lot of otherwise tedious geometry proofs into easy one-liners. On the downside it's so powerful that it's pretty much completely unrelated to other axiomatic approaches to geometry (like beginning with incidence geometry).