A Prayer for Archimedes: ... he had begun to discover the principles of calculus.

ScienceNews ^ | january 24 2009 | Julie Rehmeyer

[Daffynition]

For seventy years, a prayer book moldered in the closet of a family in France, passed down from one generation to the next. Its mildewed parchment pages were stiff and contorted, tarnished by burn marks and waxy smudges. Behind the text of the prayers, faint Greek letters marched in lines up the page, with an occasional diagram disappearing into the spine.

The owners wondered if the strange book might have some value, so they took it to Christie's Auction House of London. And in 1998, Christie's auctioned it off—for two million dollars.

For this was not just a prayer book. The faint Greek inscriptions and accompanying diagrams were, in fact, the only surviving copies of several works by the great Greek mathematician Archimedes.

An intensive research effort over the last nine years has led to the decoding of much of the almost-obliterated Greek text. The results were more revolutionary than anyone had expected. The researchers have discovered that Archimedes was working out principles that, centuries later, would form the heart of calculus and that he had a more sophisticated understanding of the concept of infinity than anyone had realized. [snip]

[patton]

Contably compact Space

[patton]

Countable Chain Condition

[troglodyte]

I used that trick in a math exam, sophomore year. I could not get the proof, so I multiplied both side by zero and added the right answer. Got me an “A”. Was it cheating? Damned right it was!

[dr_lew]

$ cat birth.c
int bdays[12];

main(argc,argv)
int argc;
char **argv;
{
int i,j,N;
double drand48();

N = atoi(argv[1]);
srand48( getpid() );

for( i=0 ; i<N ; i++ ){
j = 12 * drand48();
++bdays[ j ];
}
for( i=0 ; i<12 ; i++ ) printf(”%3d “, bdays[i]);
printf(”\n”);

}
$ for i in 1 2 3 4 5 6 7 8 9 0
do
birth 20
done
0 2 0 3 1 1 4 3 4 1 1 0
1 1 1 3 2 1 0 3 3 2 2 1
0 4 2 2 1 3 3 1 2 0 2 0
1 3 3 1 5 2 1 1 0 1 1 1
0 3 3 4 1 3 1 2 0 1 0 2
3 3 0 4 0 0 2 0 4 1 1 2
1 1 2 2 0 1 2 2 2 0 2 5
0 4 3 2 1 0 1 3 2 4 0 0
1 3 1 1 0 2 3 1 3 0 3 2
1 1 3 3 1 1 0 1 2 3 1 3

[patton]

I use that trick to disqualify job candidates. If they don’t go “Hey, idiot, you can’t divide by zero!”, I have security put them off the property.

[patton]

Too stochastic, average them and give me the deterministic answer.

[17th Miss Regt]

can you tell me wether the countable chain condition implies that a space is compact?

If you wish, I can send you some links about chain conditions.

Saturday night at the math follies...

[patton]

Don’t drink and derive....

[patton]

But, MAN, I really would like an hour alone with that book.

Er....,that book and a really good scanner.

[17th Miss Regt]

I agree. This may be a very significant find for the history of mathematics. Maybe Archimedes would have chosen to use English letters instead of Greek letters in math proofs. Can you imagine if instead of epsilons and deltas, we had e’s and d’s arguments? Give me an e and I will find a d... Seems awful bland.

[Ernest_at_the_Beach]

The Alexander Horned Sphere did me in!

[17th Miss Regt]

Q: How do you know that the Mayflower was not closed and bounded without the passengers?

A: Because the passengers made the Mayflower Compact!

Limp, limp, limp,.....

[patton]

Maybe he used aremaic symbols. LOL.

[patton]

Awwww, that hurt.

[patton]

Horned sphere?

[dr_lew]

The deterministic answer to what ?

[Ernest_at_the_Beach]

See this:

Alexander’s Horned Sphere

[Daffynition]

Archimedes computed the area of the curved figure (left) by enclosing it in a bigger one with straight edges (right). He then examined random slices to compute the volume—using the concept of actual infinity.
Credit: The owner of the Archimedes Palimpsest.

[TexasTransplant]

bookmark

[chesley]

Not to be picky, but the Arabs neither invented nor discovered the ‘zero’. They borrowed it from India, as with most of the great Muslim acccomplishments.