General relativity does. Non-Euclidean geometry does not. I’m pretty certain you can approximate it well enough with Euclidean geometry. Gravitational time dilation is just a function of hight.
No, that is not the case. The spacetime geometry near the Earth is non-Euclidean, and using a Euclidean approximation does not produce the required accuracy.
Finally, that was just an example. If someone is interested in pure mathematics, and there’s an application for it, it’s just a coincidence. I’ve heard some mathematicians actually go as far as disliking it when people find applications for there work.
You are conflating “value” with “applications.” Different people see value in different things for different reasons.
Studying the territory improves the map.
No, that is not the case. The spacetime geometry near the Earth is non-Euclidean, and using a Euclidean approximation does not produce the required accuracy.
You are conflating “value” with “applications.” Different people see value in different things for different reasons.