He solved a problem posed by Beltrami of representing one surface on a second surface in such a way that geodesic lines in the first correspond to geodesic lines in the second.
A formula for the line integral of the geodesic curvature along a closed curve is known as the Gauss Bonnet theorem.
A geodesic sun-tracking model was developed to determine sun position in the sky.
We take as given that the desired curve C is the unique Euclidean circle that is orthogonal to every geodesic through A.
By 1738 the geodesic measurements carried out to measure the length of a meridian degree had produced very strong evidence for the flattening at the poles.
He introduced the geodesic curvature although he did not use the term which was due to Bonnet who discovered it independently in 1848.
When this happens, the necessary conditions for the existence and uniqueness of these geodesics are violated.
His work in studying the trajectories of point masses on a surface led to certain non-linear differential equations whose solution also gave properties of geodesics .
So many blobs are simply the result of stacked geodesics , like Grimshaw's Eden project, a series of bubble-forms that remind me of what geologists call globular clusters.
Klingenberg worked during his years at Bonn on closed geodesics .