What's the best way for a brainlet to get into geometry...

What's the best way for a brainlet to get into geometry? I was thinking about reading euclid's elements but I'm not sure if I'm intelligent enough to grasp the content and if it's still up to date or not.

Other urls found in this thread:

math.stackexchange.com/questions/34442/book-recommendation-on-plane-euclidean-geometry
euclidea.xyz
en.wikipedia.org/wiki/Doubling_the_cube
twitter.com/NSFWRedditVideo

What exactly is it about geometry that intimidates you?

literally any geometry textbook?

They're all pretty much just updated and modernized euclid's elements. You didn't take geometry in school, though?

Start off with a simple excercise, like drawing a circle and trying to construct a square with the same volume using only a straight edge and compass

nothing particularly, i'm just not very bright

>You didn't take geometry in school, though?
terrible memory, can't remember names of shapes very well, and had shit teachers, abusive family

Sounds simple enough

But impossible(well, very difficult)

OP here
draw cirle with compass
draw line that passes through midpoint of cirle
draw another line that's perpendicular to the first line and passes through the midpoint of circle
now all I have to do is connect the points where the lines intersect with the circle
did I do good?

math.stackexchange.com/questions/34442/book-recommendation-on-plane-euclidean-geometry
elements as a textbook is shit, don't touch it

>construct square with same area as cirle
how?

it's a well known impossible construction for compass-straightedge

All you've done is inscribe a square inside of a circle. The square would have a smaller volume than the circle. I could prove it but... come on, just look at it.

khan academy

play the compass and straightedge game at euclidea.xyz

R=Length of one side of the square

I mean not R, the red line

up

user that is trying to trick you (it's an impossible problem).

I wouldn't recommend elements just because it's pretty old and takes some work to parse through.

You should start here then. Look at the classes of shapes and see how they're categorized (i.e. by side length, by regularity, etc.). Try to understand what gives each shape it's character.

Then from there look up ways to compute the area of each shape, with emphasis on understanding the proofs. This will serve as a good foundation since it exercises spatial iq.

From there you should be ready to start with a standard middle/high school level geometry book.

Euclid's elements in more than geometry, it contains early number theory. It's not a good book for getting into geometry. I don't imagine you want to read about outdated versions of axioms, and other theory.

Give this game a go.
euclidea.xyz

I like the springer undergraduate book on geometry

>appeal to intuition

Nice try brainlet.

[math]\sqrt{2} + \sqrt{3} \neq \pi[/math]

>same volume
Too easy

That's a pretty good approximation but it's off by .132051...%

I like euclidea but I want proof for everything to help me understand better while learning intuitively

the constructions are the proofs
or are you seriously an nth level turbobrainlet?

Nah, he's right, I only posted Euclidea because it's a good game to practice and demonstrate what you already know, or sometimes accidentally find new things that work that you can try to figure out why it works. However, it's definitely no teaching tool, and definitely doesn't have proofs. The proofs are on the player to know or figure out, then apply to each puzzle.

well, sincethat post. im asking here (im asking everywhere)

What the hell is 'squaring the cube'? 'squaring the circle' is that that post asks, but how do you prove its impossible to 'square he cube' what does it even mean?

>squaring the cube
What was the context? That isn't really a common math phrase like "squaring the circle" which is the name of a specific impossible math problem. The only way "squaring the cube" makes sense to me is if you take it literally and take a number to the power of 3 (cubing it) and then to the power of 2 (squaring it)

>squaring the cube
Do you mean doubling the cube?
en.wikipedia.org/wiki/Doubling_the_cube

Its ring theory homework.
no, one question was 'Prove doubling the cube is impossible', which I did then the second question is 'Prove squaring the cube is impossible'. thats verbatim from the questions.

it's the same as squaring the circle
create a square with an area of x^3 for a general constructible x

>with the same volume

no, its literally impossible with just a straightedge and compass (and taking the assumptions that euclid and classical geometers took)

I thought of that, but thats construable, and the question asks for a proof on impossibility.

You can iterate on it and get closer to the correct length with every iteration, if you continue for a long time you will eventually hit the Planck length and your done.

>Hurr euclidean geometry isnt limited by the plank length
Euclidean geometry is math, which is made in this universe, and since everything in the universe is limited by the plank length, so to is math and thus euclidean geometry.

Math has nothing to do with the universe.

lol

Although this is true, Abe Lincoln did indeed read Euclid's Elements I thru V, and even quoted propositions in some of his speeches. After congress sessions he would spend hours reading Euclid because he was ashamed of his lack of education, and thought every 'learned man should know the Elements". There's countless streets in the US named after Euclid as well he was so popular back then as an ancient meme.

OP should go on libgen.io and get the book "Elements of Mathematics:
From Euclid to Gödel" by John Stillwell. It's an excellent survey book of elementary math that will help provide insight into what he wants to know. Then he can proceed with Veeky Forums list of books to understand modern geometry.