(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that the unit sphere {(x, y, z) : x^2 + y^2 + z^2 = 1} in R^3 is arcwise connected.

2. Relevant equations

3. The attempt at a solution

find a continous map f(t ) such that f( 0) = a, f(1 ) = b. a, b, in R^3 and are on the unit sphere. then show for every t in [0,1] f(t ) is on the sphere. just having trouble finding the right f . Tried f = ta + (1-t)b but only noticed that it is a line segment , so it should be wrong..

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# Unit sphere arcwise connected?

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