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stewie wrote:

Barbo wrote:

Josef K wrote:Surely it must have volume? There is solid matter in the structure, if you lowered it into water there would be displacement therefore indicating volume. No?

That picture is just a visual representation of a mathematical construct. When the pattern is extended to infinitesimally small volumes, the resulting total volume converges to zero and the resulting surface area approaches infinity. At least, that is my understanding of it.

Jon

Sounds similar in principle to Zeno's Achilles paradox, but with distance traveled replaced by total volume.

It is in so much as both are at root about the concept of a limit. Zeno was unable to deal with the idea of an infinite number of non zero terms summing to a finite number. To be fair it took a couple thousand more years for this concept to be formalized.

cjh wrote:

Hosoi wrote:primes

Another subtle but engaging theorem concerning primes is Bertrand's postulate, simply stated: for n > 1, there is always a prime number between n and 2n. Why should that be?

This was proved most elegantly by amphetamine poppin' badass Paul Erdős whose extraordinary life is worth a moment of your time.

You're right. Thanks for that.

I always thought Buffon's Needle was pretty wild.

I like how 1/7 is:
.14
+
.0028
+
.000056
+
.00000112
+
.0000000224
+
.000000000448
and so on...

For those who don't see the pattern, each number in the series is the previous number doubled and divided by 100.

Okay, here's a proof for how .999 repeating can be considered equal to 1.
(I'm only in Math111 at the moment, so you college guys might consider this elementary)


If x = .999;

10x = 9.999
minus
x = .999
equals
9x = 9

9x = 9 simplified is x = 1

So, x = both .999 and 1, or stated another way, .999 and 1 are equal.

Brinkman wrote:Okay, here's a proof for how .999 repeating can be considered equal to 1.
(I'm only in Math111 at the moment, so you college guys might consider this elementary)

There are seven pages on this topic here.


Jon

Barbo wrote:

Brinkman wrote:Okay, here's a proof for how .999 repeating can be considered equal to 1.
(I'm only in Math111 at the moment, so you college guys might consider this elementary)

There are seven pages on this topic here.


Jon

Good grief.
My apologies gentlemen.

There's some math in this, but mostly it's just really, really trippy, man:

http://graphics.csie.ncku.edu.tw/SAI/

Dan

The only even prime number is 2. The rest are all odd. As such, the difference between subsequent prime numbers (after you've passed the 2 to 3 pair) is always an even number, and there always an odd number of non-prime numbers that occur between subsequent primes.