All Questions
3
questions
3
votes
3
answers
250
views
Why can we prove facts about Euclidean geometry using coordinate method?
It's easy to show that coordinate geometry based on real number axioms satisfies the Euclidean postulates.
But how do we go the other way around?
Say we prove an arbitrary* statement about Euclidean ...
- 1,488
1
vote
0
answers
279
views
Are there an axioms for cartesian space?
Do we have any axioms that allow us represent Cartesian coordinates on a graph in euclidean space or is it purely intuitive? It's easy to intuitively justify where $(0,1)$ and $(1,1)$ would lie in ...
- 1,093
7
votes
0
answers
701
views
Geometric basis for the real numbers
I am aware of the standard method of summoning the real numbers into existence -- by considering limits of convergent sequences of quotients.
But I never actually think of real numbers in this way. I ...
- 2,146