How can a highschool student study the nonuclidean geometry himself ?

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Discussion Overview

The discussion centers on how a high school student can study non-Euclidean geometry in relation to understanding Einstein's theory of relativity. Participants explore resources and foundational knowledge necessary for grasping these concepts, particularly in the context of general and special relativity.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant expresses difficulty with a mathematics-heavy resource on non-Euclidean geometry and seeks alternatives suitable for a high school level.
  • Another participant suggests that studying non-Euclidean geometry may not be the best approach for understanding general relativity, emphasizing the importance of Riemannian geometry, which involves calculus.
  • A participant inquires about the distinction between special and general relativity, noting that special relativity is more accessible mathematically compared to general relativity, which requires advanced math.
  • One participant indicates a desire to understand general relativity but feels unprepared and seeks guidance on where to start.
  • A later reply recommends "The Geometry of Minkowski Spacetime" as a suitable resource for understanding the mathematics of special relativity.

Areas of Agreement / Disagreement

Participants express differing views on the appropriateness of studying non-Euclidean geometry as a pathway to understanding relativity, with some advocating for a focus on Riemannian geometry and others emphasizing the need for foundational knowledge in calculus. The discussion remains unresolved regarding the best starting point for a high school student.

Contextual Notes

There is an acknowledgment of the varying levels of mathematical understanding among participants, which may affect their ability to engage with the recommended resources. The discussion does not resolve the specific prerequisites needed for studying general relativity.

ahoura
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Hello,

I'm really interested in understanding Einstein's theory of relativity but I'm still a newbie, so I need to study the nonuclidean geometry, I tried to read "Euclidean and Non Euclidean Geometries" by Greenberg but since it was for the pure mathematics students and it was full of the logical theorems and definitions i was forced to give up.

is there any good resource for a high school student to understand a little of "the nonuclidean geometry" needed for relativity ?

Thanks
 
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I'm not sure that I would recommend studying non-Euclildean geometry in general as a road to general relativity. Einstein uses, specifically, "Riemannian geometry" which, while it certainly is a non-Euclidean geometry, makes heavy use of calculus, which is not true of non-Euclidean geometry in general.
 
HallsofIvy said:
I'm not sure that I would recommend studying non-Euclildean geometry in general as a road to general relativity. Einstein uses, specifically, "Riemannian geometry" which, while it certainly is a non-Euclidean geometry, makes heavy use of calculus, which is not true of non-Euclidean geometry in general.

I have to start from a point but i don't know from where i should start, would you give me some advices about this ?
 
Do you want to learn special relativity or general relativity? Special relativity should be no problem and doesn't require any advanced math for the most part. On the other hand, general relativity requires a lot of advanced math if you want to calculate anything.
 
maze said:
Do you want to learn special relativity or general relativity? Special relativity should be no problem and doesn't require any advanced math for the most part. On the other hand, general relativity requires a lot of advanced math if you want to calculate anything.

general relativity, I only want to get a glimpse into how this world works, but i don't know how i can find the right way, I already read a lot about special relativity and as u said I had no problem with it but special relativity doesn't satisfy me and can't answer my questions

actually I'm seeking for a start point to understand how the world works
 
Hello ahoura.

I have so far found that the first few chapters of The Geometry of Minkowski Spacetime - an Introduction to the Mathematics of the Special Theory of Relativity by Gregory L. Naber very good for my level of understanding.

Matheinste.
 

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