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Their approach to geometry could be quite different though. Eg. they could use non-Euclidean geometry by default, 2D only being a special/edge case, and Pi, whi
by V-2 10y ago
Their approach to geometry could be quite different though. Eg. they could use non-Euclidean geometry by default, 2D only being a special/edge case, and Pi, while encountered in calculations once in a while, wouldn't have a status of a well-known constant: which I understand would be the minimum to meet the requirement behind the question. If not, the question would be akin to whether they "know" 1, hard to say what it means
- Smaug123 10y agoPi shows up either in Einstein's field equations, or in Newton's gravitational equations. It's probably possible to formulate them both without reference to pi, but off the top of my head I don't see how. (As mathematicians go, I'm not at all applied, though.)
- petters 10y agoPi only shows up in the field equations multiplied with an arbitrary constant. Therefore they are trivial to formulate without.
- Smaug123 10y agoThe arbitrary constant is related to G, which is Newton's gravitational constant, and to the speed of light. If I've understood correctly, if you don't want pi to appear in the field equations, then it will appear in Newton's equations as part of G.
- Ensorceled 10y agoWell, G is an arbitrary constant but Pi is not. So while you can _formulate_ using a new arbitrary constant, it is HIGHLY improbable you reached tbe point of making that formulation without discovering Pi along the way.
- Ensorceled 10y agoIt's really hard to do engineering without Euclidean geometry.