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Topic: Most theorems in Euclidean geometry are IFF theorems.
Replies: 11   Last Post: Sep 13, 2013 1:32 PM

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Brian Q. Hutchings

Posts: 6,427
Registered: 12/6/04
Re: Most theorems in Euclidean geometry are IFF theorems.
Posted: Sep 5, 2013 12:10 PM
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theorems about skew tetragona are theorems
about tetrahedra; teh emphaisis is different;
I think it is book 7 that is most of the numbertheory
in Euclid; Langlands said that it was unfinished

thus quoth:
different is Euclidean Geometry from e.g. number theory?

the development of geometry it was known that parallelograms have a certain property but later it was discovered that, more generally, quadrilaterals have that property. The second of the two results would have been what made its way into Euclid's Elements (assuming that it was known by then) but the second result (with a weaker premise) would have greater likelihood of having a true converse.

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