Author | Trudeau, Richard J. author |
---|---|
Title | The Non-Euclidean Revolution [electronic resource] : With an Introduction by H.S.M Coxeter / by Richard J. Trudeau |
Imprint | Boston, MA : Birkhรคuser Boston, 2001 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-2102-9 |
Descript | XIV, 270 p. online resource |
1 First Things -- The Origin of Deductive Geometry -- ?aterial Axiomatic Systems -- Logic -- Proofs -- A Simple Example of a ?aterial Axiomatic System -- Exercises -- Notes -- 2 Euclidean Geometry -- ?ow ?ig Is a Point? -- Euclidโs Primitive Terms -- Euclidโs Defined Terms (Part 1) -- โSufficient for Each Day Is the Rigor Thereofโ -- Euclidโs Defined Terms (Part 2) -- Euclidโs Axiorns -- Theorems Proven Without Postulate 5 -- Theorems Proven With Postulate 5 -- Index to Euclidean Geometry -- Exercises -- Notes -- 3 Geometry and the Diamond Theory of Truth -- ?antโs Distinctions -- Synthetic A Priori Statements -- Geometry as Synthetic A Priori -- ?antโs Doctrine of Space -- The Diamond Theory of Truth -- Notes -- 4 The Problem With Postulate 5 -- Poseidonios -- Proof of Postulate 5, After Poseidonios -- Metageometry -- Evaluation of Poseidoniosโ Reorganization -- Overview of Later Attempts -- So Near -- An Experimental Test of Postulate 5 -- Exercises -- Notes -- 5 The Possibility of Non-Euclidean Geometry -- The Logical Possibility of Non-Euclidean Geometry -- The Founders of Non-Euclidean Geometry -- The Psychological Impossibility of Non-Euclidean Geometry -- Formal Axiomatic Systems -- A Simple Example of a Formal Axiomatic System -- How to Not Let the Pictures Bother You -- Exercise -- Notes -- 6 Hyperbolic Geometry -- Hyperbolic Geometry (Part 1) -- Reconciliation With Common Sense -- Hyperbolic Geometry (Part 2) -- Glimpses -- Exercises -- Notes -- 7 Consistency -- Models -- Poincarรฉโs Model -- Can We Be Sure Euclidean Geometry Is Consistent? -- Notes -- 8 Geometry and the Story Theory of Truth -- Kant Revisited -- The LuneburgโBlank Theory of Visual Space -- The Diamond Theory in Decline -- The Story Theory of Truth -- Notes