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Geometry with hyperbolic functions

by Jhenrique
Tags: functions, geometry, hyperbolic
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Jhenrique
#1
May17-14, 04:30 PM
P: 686
Is known that in every rectangle triangle the following relationships are true:



But, how use geometrically the function sinh, cosh, and tanh?
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micromass
#2
May17-14, 04:48 PM
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Study hyperbolic geometry
SteamKing
#3
May17-14, 04:49 PM
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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)

Jhenrique
#4
May17-14, 04:55 PM
P: 686
Geometry with hyperbolic functions

Quote Quote by SteamKing View Post
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.
micromass
#5
May17-14, 04:58 PM
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Quote Quote by Jhenrique View Post
But I still don't understood how the hyperbolic functions help me to solve geometric problems.
Why do you expect that they do?
Jhenrique
#6
May17-14, 05:34 PM
P: 686
Quote Quote by micromass View Post
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.
micromass
#7
May17-14, 05:36 PM
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Quote Quote by Jhenrique View Post
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
#8
May17-14, 06:17 PM
P: 686
Look these formulas:




http://en.wikipedia.org/wiki/Ellipti...sic_definition

I don't understand because x and y are equals to these expressions.
symbolipoint
#9
May17-14, 07:19 PM
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Quote Quote by Jhenrique View Post
Hyperbolic functions appears in hyperbolic and elliptic coordinate system, but I don't understand the geometric deduction for these formulas.
Quote Quote by Jhenrique View Post
But I still don't understood how the hyperbolic functions help me to solve geometric problems.
Quote Quote by micromass View Post
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.
Jhenrique
#10
May18-14, 12:42 AM
P: 686
I already studied and I continue don't understand how use it


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