Geometry with hyperbolic functions

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Discussion Overview

The discussion revolves around the geometric applications of hyperbolic functions such as sinh, cosh, and tanh, particularly in the context of hyperbolic geometry and coordinate systems. Participants express confusion regarding how these functions relate to solving geometric problems.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • Some participants inquire about the geometric interpretation of hyperbolic functions and how they can be applied to solve geometric problems.
  • Others reference articles that provide geometric interpretations of sinh and cosh but express a lack of understanding regarding their practical applications.
  • One participant questions the expectation that hyperbolic functions would aid in solving geometric problems, suggesting a need for clarification on the underlying geometric deductions.
  • Another participant mentions that hyperbolic functions appear in hyperbolic and elliptic coordinate systems but struggles to understand the deductions for the related formulas.
  • Participants share links to resources that discuss elliptic coordinates and express confusion about specific formulas related to these concepts.
  • There is a mention of the relationship between trigonometry and geometry based on the unit circle, contrasting it with hyperbolic functions based on the unit hyperbola.
  • One participant states that despite studying the topic, they still do not understand how to use hyperbolic functions in geometric contexts.

Areas of Agreement / Disagreement

Participants generally express confusion and uncertainty regarding the application of hyperbolic functions in geometry. There is no consensus on how these functions can be utilized effectively in solving geometric problems.

Contextual Notes

Limitations include unclear deductions for specific formulas related to hyperbolic and elliptic coordinates, as well as varying levels of understanding among participants regarding the geometric implications of hyperbolic functions.

Jhenrique
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Is known that in every rectangle triangle the following relationships are true:

imagem.png


But, how use geometrically the function sinh, cosh, and tanh?
 
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Study hyperbolic geometry
 
SteamKing said:
This article gives one geometric interpretation of sinh and cosh:

http://en.wikipedia.org/wiki/Hyperbolic_function

(check out the figure at the upper RHS of the article)

But I still don't understood how the hyperbolic functions help me to solve geometric problems.
 
Jhenrique said:
But I still don't understood how the hyperbolic functions help me to solve geometric problems.

Why do you expect that they do?
 
micromass said:
Why do you expect that they do?

Hyperbolic functions appears in hyperbolic and elliptic coordinate system, but I don't understand the geometric deduction for these formulas.
 
Jhenrique said:
Hyperbolic functions appears in hyperbolic and elliptic coordinate system, but I don't understand the geometric deduction for these formulas.

OK. Which formulas don't you understand the deduction of? What is the deduction and what don't you understand about them?
 
Jhenrique said:
Hyperbolic functions appears in hyperbolic and elliptic coordinate system, but I don't understand the geometric deduction for these formulas.

Jhenrique said:
But I still don't understood how the hyperbolic functions help me to solve geometric problems.

micromass said:
Study hyperbolic geometry


This last one was said best.


Trigonometry is Geometry based on a unit circle.
Hyperbolic sines and cosines are based on the unit hyperbola.
Study the hyperbola and the exponential and logarithmic functions based on the Euler number base.
 
  • #10
I already studied and I continue don't understand how use it
 

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