Eric Nitardy
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 Feb25 revised What are the postulates that can be used to derive geometry? added 4 characters in body; edited title Feb25 comment Why is Euclidean geometry scale-invariant? @Joseph: Put up an answer to What are the postulates that can be use to derive geometry? question with a list of jack Lee's postulates. Feb25 answered What are the postulates that can be used to derive geometry? Feb25 answered What are the postulates that can be used to derive geometry? Feb25 answered What are the postulates that can be used to derive geometry? Feb25 asked What are the postulates that can be used to derive geometry? Feb24 answered How to find the distance between a point and line joining two points on a sphere? Feb24 awarded Nice Answer Feb23 revised Three non-coplanar lines in the 3D-space always have a fourth one that intersect them all? added 49 characters in body; added 6 characters in body Feb23 answered Three non-coplanar lines in the 3D-space always have a fourth one that intersect them all? Feb23 awarded Critic Feb22 comment Why is Euclidean geometry scale-invariant? @Joseph: The definitions and development I know best is from an unpublished manuscript by John M. Lee titled "Axiomatic Geometry". It is based in part on Birkhoff and in part on the School Mathematic Study Group postulates. For the past few weeks, I've been reading "Euclidean and Non-Euclidean Geometries" by Marvin J. Greenberg. I prefer John Lee's approach so far. I'll put Millman and Parker on my reading list. Feb22 comment Why is Euclidean geometry scale-invariant? @Joseph: The definition that I've used is: Two triangles △ABC and △DEF are similar under a correspondence A↔D, B↔E, and C↔F iff $\angle A \cong \angle D$,$\quad \angle B \cong \angle E$, $\: \angle C \cong \angle F$ and there is a positive number r such that $$r=\frac{AB}{DE}=\frac{BC}{EF}=\frac{CA}{FD}.$$ Using the reals with geometry for distance, angle measure and proportion, following G. D. Birkhoff, seems more natural than Hilbert's numberless approach. I suspect if the foundations of the reals was in better shape when he did his geometry work, Hilbert might have taken the same approach. Feb22 revised Why is Euclidean geometry scale-invariant? edited body Feb22 revised Why is Euclidean geometry scale-invariant? added 152 characters in body Feb21 revised Why is Euclidean geometry scale-invariant? added 1823 characters in body Feb21 revised Why is Euclidean geometry scale-invariant? added 1368 characters in body Feb21 revised Why is Euclidean geometry scale-invariant? added 86 characters in body Feb21 revised Why is Euclidean geometry scale-invariant? added 249 characters in body; added 11 characters in body Feb21 answered Why is Euclidean geometry scale-invariant?