837 reputation
522
bio website modbookish.lefora.com
location
age
visits member for 3 years, 10 months
seen Nov 6 '13 at 3:42

Feb
25
answered What are the postulates that can be used to derive geometry?
Feb
25
answered What are the postulates that can be used to derive geometry?
Feb
25
answered What are the postulates that can be used to derive geometry?
Feb
25
asked What are the postulates that can be used to derive geometry?
Feb
24
answered How to find the distance between a point and line joining two points on a sphere?
Feb
24
awarded  Nice Answer
Feb
23
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
Feb
23
answered Three non-coplanar lines in the 3D-space always have a fourth one that intersect them all?
Feb
23
awarded  Critic
Feb
22
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@Joseph: The definitions and development I know best is from an unpublished manuscript by John M. Lee titled "Axiomatic Geometry".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.
Feb
22
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.
Feb
22
revised Why is Euclidean geometry scale-invariant?
edited body
Feb
22
revised Why is Euclidean geometry scale-invariant?
added 152 characters in body
Feb
21
revised Why is Euclidean geometry scale-invariant?
added 1823 characters in body
Feb
21
revised Why is Euclidean geometry scale-invariant?
added 1368 characters in body
Feb
21
revised Why is Euclidean geometry scale-invariant?
added 86 characters in body
Feb
21
revised Why is Euclidean geometry scale-invariant?
added 249 characters in body; added 11 characters in body
Feb
21
answered Why is Euclidean geometry scale-invariant?
Feb
21
accepted Linear Algebra of Symmetric Sums
Feb
20
comment Linear Algebra of Symmetric Sums
I played around with induction and got stumped by the inductive step. With the insight provided by the answers below, I now see where the inductive step was headed.