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

>>9029273
What exactly is it about geometry that intimidates you?

>>9029273
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

>>9029279
nothing particularly, i'm just not very bright

>>9029280
>You didn't take geometry in school, though?
terrible memory, can't remember names of shapes very well, and had shit teachers, abusive family

>>9029289
Sounds simple enough

>>9029357
>>9029289
But impossible(well, very difficult)

>>9029289
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?

>>9029273
https://math.stackexchange.com/questions/34442/book-recommendation-on-plane-euclidean-geometry
elements as a textbook is shit, don't touch it

>>9029289
>construct square with same area as cirle
how?

>>9029538
it's a well known impossible construction for compass-straightedge

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>>9029534
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

>>9029273
play the compass and straightedge game at euclidea.xyz

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R=Length of one side of the square

>>9029931
I mean not R, the red line

up

>>9029534
Anon that >>9029289 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.

>>9029301
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.

>>9029273
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.

>>9029273
Give this game a go.
https://www.euclidea.xyz

I like the springer undergraduate book on geometry

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>>9029901
>appeal to intuition

Nice try brainlet.

>>9029931
[math]\sqrt{2} + \sqrt{3} \neq \pi[/math]

>>9029289
>same volume
Too easy

>>9029931
That's a pretty good approximation but it's off by .132051...%

>>9032456
I like euclidea but I want proof for everything to help me understand better while learning intuitively

>>9033599
the constructions are the proofs
or are you seriously an nth level turbobrainlet?

>>9033602
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.

>>9029289
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?

>>9033950
>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)

>>9033950
>squaring the cube
Do you mean doubling the cube?
https://en.wikipedia.org/wiki/Doubling_the_cube

>>9033988
Its ring theory homework.
>>9034280
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.

>>9035750
it's the same as squaring the circle
create a square with an area of x^3 for a general constructible x

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>>9029289
>with the same volume

>>9029362
no, its literally impossible with just a straightedge and compass (and taking the assumptions that euclid and classical geometers took)

>>9035755
I thought of that, but thats construable, and the question asks for a proof on impossibility.

>>9035824
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.

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>>9036174
Math has nothing to do with the universe.

>>9029301
lol

>>9029536
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 /sci/ list of books to understand modern geometry.