Works of Riemann related to Astronomy that I can understand?

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Discussion Overview

The discussion revolves around the mathematical contributions of Bernhard Riemann and their relevance to astronomy, particularly in the context of 19th-century mathematics. Participants explore the applicability of Riemann's work, specifically avoiding complex concepts like tensors.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant notes that Riemannian geometry is integral to general relativity, which is necessary for understanding astronomical phenomena at large distances, contrasting it with Newtonian physics.
  • Another participant questions the relationship between Riemann geometry and special relativity, suggesting that concepts like Lorentz contraction may be relevant.
  • A link to an external resource on relativity and geometry is provided for further exploration.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the connections between Riemann's work and both general and special relativity, indicating that multiple views on the applicability of Riemann's mathematics to astronomy exist.

Contextual Notes

Some participants express limitations in their understanding of advanced concepts, specifically avoiding discussions that involve tensors, which may restrict the depth of the mathematical connections explored.

Who May Find This Useful

Individuals interested in the historical context of mathematics in relation to astronomy, particularly those seeking to understand the foundational mathematical concepts without delving into advanced topics like tensors.

benorin
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Looking for a connection to astronomy for a history of mathematics report on 19th century mathematicians. I don't do astronomy. Would like to know of any mathematical developments of Riemann that are used in astronomy that I can understand (which expressly excludes any thing with the word tensor in it.) Don't work to hard on it (I have google too,) just thought you guys would know.

TIA,

Benorin
 
Astronomy news on Phys.org
Bernhard Riemann developed Riemannian geometry. This is used through out general relativity. Newton’s laws didn't work at very large (astronomical distances), that is why we use GR. Einstein wouldn't of been able to develop his theories in Euclidean geometry.
 
Is there any connection between Riemann geometry and special relativity, that subject is within my mental grasp. Perhaps the Lorentz contraction?
 
http://www.superstringtheory.com/basics/basic2a.html, read the section on relativity and geometry.
 

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