If you took Geometry in High School, you almost definitely learned it as a subject based on rules and axioms discovered by the ancient Greeks. The details of this subject, which I must admit was ...
MR. FRANKLAND (NATURE, September 7) has raised the old problem of Bertrand's proof of the parallel-axiom by a consideration of infinite areas. This is perhaps the most subtle and the most specious of ...
IN my “Theories of Parallelism” I expressed my sense of failure in controverting Bertrand's simple proof (by the consideration of infinite sectors and infinite strips) of Euclid's parallel axiom. This ...
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