# AC and Euclidean Geometry [closed]

It there any relation between the axiom of choice and Euclidean Geometry ??

I mean what are the known statements, theorems or results in euclidean geometry that are dependent on AC ?? (this question has been asked by someone else as a comment to my last question. See HERE)

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Both things are called "axioms"... –  Asaf Karagila Jan 15 '13 at 19:21
@Asaf: As a set theorist you mean no relation exists. No statement or theorem or result in euclidean geometry is dependent on AC ? Is it provable ?? –  user30669 Jan 15 '13 at 19:27
I never said anything about that. It also depends on what you define as Euclidean geometry. One could argue that the Banach-Tarski theorem applies to Euclidean geometry; while another could argue that the classical Euclidean geometry is effectively a constructive theory and there is no appeal to infinitary arguments which would require the axiom of choice. I only said that both the axioms of Euclidean geometry and the axiom of choice are named "axioms". –  Asaf Karagila Jan 15 '13 at 19:35
@Asaf: I see :) –  user30669 Jan 15 '13 at 19:46
What do you mean by a relation? As it stands, this is not a real question. –  Emil Jeřábek Jan 15 '13 at 20:01