If

is conservative, then there is a scalar function

such that

Setting the first components equal to one another, we can integrate both sides to find

Differentiating both sides with respect to

gives



so that

By the fundamental theorem of calculus, we have that
In Euclidian geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is greater than 180 degrees. As well as <span>In Euclidian geometry the sum of the interior angle measures of a triangle is 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees. Are the answers.</span>