B Geometric and arithmetic means and contraction factor

[south]

TL;DR

Geometric and arithmetic means and contraction factor

Is it correct to state that the relativistic contraction factor is the ratio of the geometric mean to the arithmetic mean of the terms $C+v$ and $C-v$?

 

[Ibix]

Why do you think so?

 

[south]

Why do you think so?

I think the following:
Although mathematically it coincides, interpreting the contraction factor as the quotient of two means may not fit the physical nature of the phenomenon.

 

[Ibix]

I think the following:
Although mathematically it coincides, interpreting the contraction factor as the quotient of two means may not fit the physical nature of the phenomenon.

There's nothing wrong with stating it. If you end up doing algebra in SR knowing identities for $\gamma$ is often helpful. I don't see that it adds any physical insight though. More useful to know that $\gamma =\cosh\psi$, where $\psi$ is the rapidity.

 

[south]

There's nothing wrong with stating it. If you end up doing algebra in SR knowing identities for $\gamma$ is often helpful. I don't see that it adds any physical insight though. More useful to know that $\gamma =\cosh\psi$, where $\psi$ is the rapidity.

I don't find any correlation with the physical situation in that statement about the means. It seems like an empty mathematical game to me.

 

[Ibix]

Yes. It might be a useful algebraic identity in some situation, but that's all.

 

[south]

Ok, agree. Thank you very much.