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Gauss has proven in his famous Theorema Egregium, that it is possible, to calculate the gaussian curvature from measuring angles and distances on the surface, irrespective of how the surface is embedded into space.

Question:

 

is it also possible, to calculate the euclidean distance of two points on the surface, also from distance- and angle-measurements on the surface, alone?

Gauss has proven in his famous Theorema Egregium, that it is possible, to calculate the gaussian curvature from measuring angles and distances on the surface, irrespective of how the surface is embedded into space.

Question:

 

is it also possible, to calculate the euclidean distance of two points on the surface, also from distance- and angle-measurements on the surface, alone?

Gauss has proven in his famous Theorema Egregium, that it is possible, to calculate the gaussian curvature from measuring angles and distances on the surface, irrespective of how the surface is embedded into space.

Question:

is it also possible, to calculate the euclidean distance of two points on the surface, also from distance- and angle-measurements on the surface, alone?

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Manfred Weis
Manfred Weis
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Calculating Exterior Distance from Measurements of Inner Geometry

Gauss has proven in his famous Theorema Egregium, that it is possible, to calculate the gaussian curvature from measuring angles and distances on the surface, irrespective of how the surface is embedded into space.

Question:

is it also possible, to calculate the euclidean distance of two points on the surface, also from distance- and angle-measurements on the surface, alone?