Hello all. I'm a math major attending a "math in history, art and philosophy" class as an elective. For that class, we have to give a presentation on a topic of our choice. As many of the people in the room aren't math majors or had much exposure to the subject, I was thinking about giving a presentation on proofs. Perhaps why they are so important, maybe give an example of an example which appears true but isn't (Gauss's overestimation conjecture or something). But I would like to finish off the presentation with a relatively non-trivial but elementary proof. I really can't think of anything, any suggestions would be nice.
Fishing for a presentation idea
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Deleted member 4993
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But I think "Euclid's proof of the infinitude of primes" is most elegant and understandable proof among all those......
If you are looking for a subject which covers mathematical history, art and (a little bit) philosophy then have a look here:
http://en.wikipedia.org/wiki/Catenary
For additional information see Hairer / Wanner, Analysis by Its History, Springer, New York, 1997, page 136 ff
(probably there exists a newer edition)
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Deleted member 4993
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One good book to read would be: "One, Two, Three .....Infinity" by George Gammow.
Hey, thanks a lot for all of the feedback. This presentation is nothing huge, I simply plan to maybe state a little bit of history of mathematical thought, and then talk about proof and its development a bit. Perhaps I will show the development from the "Behold!" proof of the Pythagorean theorem to a simple congruence proof.
I agree that the proof of the infinitude of primes is gorgeous, and for some reason I didn't think of that. Perhaps I will wrap up with that. Thanks a lot, I wasn't expecting all of this input.
I agree that the proof of the infinitude of primes is gorgeous, and for some reason I didn't think of that. Perhaps I will wrap up with that. Thanks a lot, I wasn't expecting all of this input.
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Deleted member 4993
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Euclid alone has looked on Beauty bare
by Edna St. Vincent Millay
Euclid alone has looked on Beauty bare.
Let all who prate of Beauty hold their peace,
And lay them prone upon the earth and cease
To ponder on themselves, the while they stare
At nothing, intricately drawn nowhere
In shapes of shifting lineage; let geese
Gabble and hiss, but heroes seek release
From dusty bondage into luminous air.
O blinding hour, O holy, terrible day,
When first the shaft into his vision shone
Of light anatomized! Euclid alone
Has looked on Beauty bare. Fortunate they
Who, though once only and then but far away,
Have heard her massive sandal set on stone.
by Edna St. Vincent Millay
Euclid alone has looked on Beauty bare.
Let all who prate of Beauty hold their peace,
And lay them prone upon the earth and cease
To ponder on themselves, the while they stare
At nothing, intricately drawn nowhere
In shapes of shifting lineage; let geese
Gabble and hiss, but heroes seek release
From dusty bondage into luminous air.
O blinding hour, O holy, terrible day,
When first the shaft into his vision shone
Of light anatomized! Euclid alone
Has looked on Beauty bare. Fortunate they
Who, though once only and then but far away,
Have heard her massive sandal set on stone.
D
Deleted member 4993
Guest
I have to admit - I did not catch your lapse in memory. I just faintly remembered this poem from my early days of struggle with geometry. Recovered and shared it with the help of Wiki... (what a wonderful thing)