Are there any alternative axioms for Euclidean geometry?

Question

I was recently listening to a lecture by Richard Feynman where he talks about how there are different formulations of theories in physics. The different formulations start from different axioms but they are all mathematically equivalent.

He talks about how these mathematically equivalent formulations are mentally far from equivalent. When we are thinking of extending a theory one set of axioms may be easier to think about than others.

So I was wondering if this is true for mathematical systems such as Euclidean geometry.

of course https://en.wikipedia.org/wiki/Non-Euclidean_geometry — user, Feb 08 '18 at 09:52
@gimusi I meant alternative in the sense of mathematically equivalent. Non-Euclidean geometry is not equivalent to Euclidean geometry. But I think it can be said to be an extension of Euclidean geometry. — Ibraheem Moosa, Feb 08 '18 at 09:57
You can find in the post: reference-request-for-set-theoretic-foundations-of-geometry for references. — Mauro ALLEGRANZA, Feb 08 '18 at 10:17

score 1 · Accepted Answer · answered Feb 08 '18 at 09:53

1

An example are Birkhoff's axioms. These are axioms for Euclidean geometry which are build upon the real numbers.

There are also Tarki's axioms. They don't cover the whole Euclidean geometry, but they do cover a substantial part of it.

answered Feb 08 '18 at 09:53

José Carlos Santos

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Are there any alternative axioms for Euclidean geometry?

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