1
$\begingroup$

A book I'm reading suggests checking if a metric describes a curved space by calculating

$$ R = \lim_{\small{radius} \to 0} \frac 6 {(\hbox{radius})^2} \bigg(1 - \frac {\hbox{circumference}} {2\pi \ \hbox{radius}} \bigg) $$

I don't understand why this is better than just calculating the circumference, and seeing if it is different to $ 2 \pi $ times the radius.

Does anyone know the benefit of the limit formula?

Improve this question
$\endgroup$

1 Answer 1

Reset to default
0
$\begingroup$

You are trying to evaluate the curvature at a point: knowing 'there is some curvature in this region' is not the same thing at all. A good example of why this matters is the surface of a cone in 2 dimensions.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.