ChrisK hits 2,500!

[D2o]

ChrisK:

2,500 posts already! This seems like it ought to be some sort of cause for celebration or something

I understand approximately 1.61803398874989484820 out of every 2.61803398874989484820 of your posts ( ... or at least I like to think I understand that much ... maybe I only understand approximately 1.61803398874989484820 / 2.61803398874989484820ths of each of your posts ... but that's splitting hairs, isn't it? ;D)

The remainder of your posts go completely over my head, but I willingly assume the quality of those highly technical posts to also be golden.

What would this place be without you and your endless assistance?

I think I speak on behalf of all of us - Thanks a million, Chris!

[D2o]

I tried to find some good fireworks to mark the occasion, but ... Anyway, if you squint your eyes in just the right way and use your imagination:



Woo-hoo!

... now come back and make your 2,500th! ...

[newey]

If one becomes a God at 500 posts, I guess we'll have to make ChrisK the head of the Pantheon.

Zeus. Or Jupiter, by Jove, if one is in the mood for Italian. ;D

[ChrisK]

if you squint your eyes in just the right way and use your imagination

If I squint my eyes in just the right way, I don't need to use my imagination.


Wow, thanks.

Really, I never pay attention.

Really.


I suspect that this level actually indicates a person of "truly absolutely no life". (My wife would concur, now just exactly where did I misplace her?)


Actually, I'm still waiting fer that there dang box of karmals that I thought that I'd get at 2,000.


Hmmm, there's gold in them there ratios.... (5ive's alive)

1/0.61803398874989484820458683436564 = 1.61803398874989484820458683436564

1.6180339887498948482045868343656^2 = 2.6180339887498948482045868343656

1.61803398874989484820458683436564 / 2.61803398874989484820458683436564 =
0.61803398874989484820458683436564

2.61803398874989484820458683436564 - 1.61803398874989484820458683436564 = 1

Which one didn't you get?

[ashcatlt]

Well, there's a +1 for ya. You deserve a few more.

I usually think I know what I'm talking about, almost always know what I think I'm talking about. I'm quite positive that you know what you're talking about, but I'm not always quite sure exactly what that is.

[D2o]

Hmmm, there's gold in them there ratios.... (5ive's alive)

Yep, it's actually pretty cool, in it's own golden way.



(the following is copied from this website: cuip.uchicago.edu/~dlnarain/golden/ )

This sequence of numbers was first discovered by a man named Leonardo Fibonacci, and hence is known as Fibonacci's sequence. The relationship of this sequence to the Golden Ratio lies not in the actual numbers of the sequence, but in the ratio of the consecutive numbers. Let's look at some of these ratios:

2/1 = 2.0

3/2 = 1.5

5/3 = 1.67

8/5 = 1.6

13/8 = 1.625

21/13 = 1.615

34/21 = 1.619

55/34 = 1.618

89/55 = 1.618

Aha! Notice that as we continue down the sequence, the ratios seem to be converging upon one number (from both sides of the number)! Notice that I have rounded my ratios to the third decimal place. If we examine 55/34 and 89/55 more closely, we will see that their decimal values are actually not the same. But what do you think will happen if we continue to look at the ratios as the numbers in the sequence get larger and larger? That's right: the ratio will eventually become the same number, and that number is the Golden Ratio!

... And as if that isn't exciting enough, here are those misplaced karmals.

[ChrisK]

I'm quite positive that you know what you're talking about, but I'm not always quite sure exactly what that is.

Me neither but no one ever questions it.

the ratio will eventually become the same number

Not unless eventually actually means infinity; it converges on it. It may appear to become the same due to the limitations of the resolution of the number system or machine used to calculate it, but it never does.

Proof:

Each new term is equal to the sum of the previous two.
[n1 + n2 = n3] a term
[n2 + n3 = n4] the next term

For them to "become the same";

[n1 + n2 = n3] = [n2 + n3 = n4]

or

n1 + n2 = n2 + n3

since

n1 + n2 = n3

the following would have to be true

n1 + n2 = n2 + [n1 + n2]

or

n2 = 2 * n2, which is not possible

Since the series cannot be seeded with two zeros (otherwise it isn’t), the ratio can never “become the same”. A real ratio of two integers is converging on an irrational number (a number that cannot be represented by a ratio of two integers).


en.wikipedia.org/wiki/Leonardo_Fibonacci


The characteristics of the Fibonacci number is one of my absolutely most favorite things to think upon. I have constructed number systems based on its extrapolated sequences that have disturbing characteristics.

en.wikipedia.org/wiki/Fibonacci_number


Interestingly, taking ANY two seed integers (one of which is not zero) and executing the series algorithm [n_-1 + n = n₊₁] results in a sequence that converges to the golden ratio.

You don't have to start with 0 and 1.