Cool Pictures VI: Viciously cool 3,14159

[Kyriakos]

Previous Threads​

Cool Pictures I: The Original Thousand(the original!)
Cool Pictures II: One Million Amazing Words
Cool Pictures III: Bringing Gladness to a Weary Heart
Cool Pictures IV: The Awesomeness is Volatile
Cool Pictures V: So Cool We Can Freeze Time Itself ​

And a new pic:

The above is part of Archimedes' conclusions on the relations in volume and area between a sphere and its circumscribed cylinder, both being 2:3

Even more elegant is his calculation of the relation between the area of a sphere, and the area of its largest circle:

 

[Takhisis]

 

[Borachio]

The above is part of Archimedes' conclusions on the relations in volume and area between a sphere and its circumscribed cylinder, both being 2:3

Even more elegant is his calculation of the relation between the area of a sphere, and the area of its largest circle:

How, without calculus, did he work these out?

 

[Kyriakos]

^Not sure about calculus in a future examination of this issue, but Archimedes was working in the era of notable focus among Greek mathematicians on circles and elliptic shapes, so (although i did not read his own proof) i suppose he only utilised geometry. I do plan to read the original work in the near future, currently i have been on an extensive break from math/geometry

Worth noting that Archimedes himself regarded his theorems on the sphere and circumscribed cylinder to have been his major accomplishement..

 

[Borachio]

Calculus would provide the only route I know how to prove this. It's quite straightforward to do. With calculus.

Without it, I don't see anyway at all. But that's probably only because I've been brought up to think in terms of calculus.

 

[Arakhor]

The ancient Greeks were pretty amazing people, all told.

 

[Takhisis]

They did have quite a complex numeral system of their own, so who know what was lost? They even had prototype steam engines.

Now, post pics! Or I'll start posting cats.

 

[Borachio]

 

[Monsterzuma]

 

[Cutlass]

Worth looking at

 

[Cutlass]

 

[hobbsyoyo]

Calculus would provide the only route I know how to prove this. It's quite straightforward to do. With calculus.

Without it, I don't see anyway at all. But that's probably only because I've been brought up to think in terms of calculus.

They used the 'method of exhaustion' wherein they essentially work a problem out for an insanely long amount of time (i.e. decimal places), picked a good point to call it quits and called it a 'proof'. The method wouldn't fly these days, but it was more or less effective for the purposes it was used for during the time it was used.

 

[Kyriakos]

Just fly above the trees

 

[eduhum]

Were I to put a place in that bridge, I'd say Norway… ? Source please

 

[Kyriakos]

 

[Borachio]

They used the 'method of exhaustion' wherein they essentially work a problem out for an insanely long amount of time (i.e. decimal places), picked a good point to call it quits and called it a 'proof'. The method wouldn't fly these days, but it was more or less effective for the purposes it was used for during the time it was used.

Oh right. That makes sense. Especially as more difficult integrals are calculated that way even today. (Sort of.)

 

[Kyriakos]

Borachio, don't listen to barbarians when you can listen to Greeks Just check the elegance of Eukleid's three line proof of there being an "infinite" amount of prime numbers

(the following is not a direct translation, and for starters Eukleid did not use the terms finite and infinite, but "more than any group which can be accounted for)

http://en.wikipedia.org/wiki/Euclid's_theorem

Produced in the same era, early Hellenistic.

 

[hobbsyoyo]

Oh right. That makes sense. Especially as more difficult integrals are calculated that way even today. (Sort of.)

They sure are!

 

[Cutlass]

 

[Monsterzuma]