Can anyone define the fourth dimension geometrically?

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shawnr
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I know about the tessaract and I'd like to understand more about it from a Euclidean perspective so I may translate it algebraically.
 
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shawnr said:
I'd like to understand more about it from a Euclidean perspective

I'm not sure what you mean by this. A manifold with a Euclidean metric works the same regardless of the number of dimensions, so if you understand how 2- and 3-dimensional Euclidean spaces work, you understand how 4-dimensional Euclidean spaces work. What else do you need to know?
 
shawnr said:
My goal is to find ways to start linking the dimensions for a few book hypotheses I have written.
Per the rules of this forum (https://www.physicsforums.com/threads/physics-forums-global-guidelines.414380/ ):
Non-mainstream theories:
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Well I just want some help and answers, but since you brought it up.

"Generally, in the forums we do not allow the following"
Generally meaning it is due to the tone of the message and not the letter.
My questions don't have to relate to my book at all. I am asking about 4-dimensional space on a three dimensional graph. In much the same way that you put a straight line (1 dimensional) on any chart. I'm asking about an already established idea. You can forget the book, I was just asking questions.

Back to the post: Can someone answer my last threads question or expound on manifolds for me please.
 
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shawnr said:
I don't know what a Manifold is, I'll look it up.

Ok, good.

shawnr said:
Perhaps you can help my other thread question.

If you don't understand what a manifold is, then you need to learn that on your own first. Trying to answer your questions at this point would amount to giving you a course in geometry and topology, and that's beyond the scope of PF.
 
shawnr said:
Generally meaning it is due to the tone of the message and not the letter.

No; "generally" meaning it's a rule unless a particular exception is made, and any exceptions to the rule are at the discretion of the moderators.

shawnr said:
I am asking about 4-dimensional space on a three dimensional graph. In much the same way that you put a straight line (1 dimensional) on any chart.

These are not the same thing at all. A 1-dimensional straight line has fewer dimensions than a chart (at least as long as the chart has 2 or more dimensions). A 4-dimensional space has more dimensions than a 3-dimensional graph.

shawnr said:
Can someone answer my last threads question or expound on manifolds for me please.

As I said in my previous post, you need to learn the basics for yourself first. That includes manifolds, per my previous post; it also includes coordinate charts and projections (since in order to represent a space of n dimensions on a graph of fewer than n dimensions, you need to do some kind of projection). The questions you are asking are too general at this point to be answered within the scope of PF. Thread closed.
 
shawnr said:
Well I just want some help and answers, but since you brought it up.
No, actually, you brought it up when you said this (which I quoted):
My goal is to find ways to start linking the dimensions for a few book hypotheses I have written.
You're a new member here, so might not be aware of our rules, especially those on personal theories and the like.