in relativity theory, in a certain "rapid space" the distance between two neighboring points is given by-(adsbygoogle = window.adsbygoogle || []).push({});

ds=[2/(1-r^2)]√ (dr^2+(rd∅)^2)

(considering a 2D space )

use the euler lagrange equation to show that the shortest distance from origin to any point is straight line.

attempt-

i don't know what's a rapid space, but i took the function in the euler lagrange equation as

f= [2/(1-r^2)]√ (+(r∅')^2) [∅'=d∅/dr]

then since ∂f/∂∅=0, so ∂f/∂∅'= const= r^2/ [(1-r^2)]√ (dr^2+(rd∅)^2)]

but how does the integration lead to a straight line ? could anybody do that for me ?

p.s: this isn't a homework !

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# Finding the function from ds=[2/(1-r^2)]√ (dr^2+(rd∅)^2)

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