Survey posted 2005-05-09 15:20 by Jon.

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Survey idea by me.

Well, I'll be the first to ask: Jon, What is a golden ratio?

I think I'll be the second.

I'll be the 1`st to answer:

== GOLDEN RATIO ==
(1+sqrt(5))/2, approximately 1.61803, which happens to be the ratio of a diagonal of a pentagon to its side. This constant shows up in many metrical properties of the dodecahedron and icosahedron just as the square root of 2 shows up in the metrical properties of the cube. A golden rectangle has sides in this ratio. A golden rhombus has diagonals in this ratio.

It also occurs as the ratio of the numbers of the Fibonacci sequence, as they grow larger (i.e. fith and sixth terms won't be very close to the ratio, but the terms 1,000,000 and 1,000,001 will be very close)

Also notably, a rectangle with the golden ratio between its sides can be devided into a square and another rectangle with the golden ratio between its sides. If you were to draw a rectangle, it would probably be very close to this, as the golden ratio is very pleasing to the eyes.

I didn't know that about the Fibonacci sequence. I do know, however, that one of those smart Greeks came up with it.

it was a guy called Fibonacci. That is why it is called Fibonacci's sequence.

Fibonacci is Italian.

Actually, his name wasn't Fibonacci, he just used that as a pen name. His real name was Leonardo of Pisa. He lived from 1175-1250 AD. Please don't ask why I know this...

And about the Greeks...the Parthenon has it's walls built (well, two of them) with the golden rectangle as their shape...the two other walls have some other significant ratio...

Perhaps I didn't make myself clear.

I did not know that the Fibonacci sequence had the property that:

Successive terms of the sequence fib(n)/fib(n+1) approach phi (the symbol for the Golden Ratio) as a limit.

I did know, however, that one of the smart ancient Greeks discovered/invented the Golden Ratio.

the greeks used it in their statues to make them look good

Yes, that also was another significance...there are things such as the ratio of your leg to your arm or something weird like that that have the golden ratio...there's like 6 of them just in the human body alone...apparently, it makes the body look more "pleasing to the eye."

there's also more about it in the Da Vinci Code. It's used in many pagan beliefs/nature worship, but it's associated with the devil in christian beliefs because of its association to the pentagon (see above reason), which is deemed to be evil for some reason.

This ratio is also known by the constant Phi (the capitalized Greek character that looks like a trident), and is the ratio of the lengths of two colinear consecutive widths of a perfect spiral. It shows up a lot in nature, and can be used to mathematically define beauty. For example, a human face is "beautiful" when the ratios of distances between various facial organs approaches Phi.

Except that it is lowercase (at least, most places I have seen it), which looks like a circle with a vertical line through it. Or, perhaps, the capital is the golden ratio & the lowercase is supposed to be its reciprocal (if people used it correctly).

It should be pointed out here that the reciprocal of the golden ratio is the same as the golden ration minus one.

phi = 1/Phi = Phi-1

That's very useful to know in everyday life.

Not only is the reciprocal of phi phi-1, but phi squared is equal to phi plus 1!
phi = 1/phi + 1 = phi^2 - 1

Gadzooks, you're right!

I don't think you really meant to write that "phi=phi-1", because if so, then 0=1 ! yay!

but he didn't, he said phi=Phi-1.

I have no idea what any of this means, I just thought I'd point that out

And therefore:

phi = phi - 1
phi-phi = 1
0 = 1

:p

phi does equal 1/Phi.. Phi is the number [with a captital "P"].. phi on the other hand is a lowercase version of Phi serving as a symbol of 1/Phi.. so he was correct:

phi [with a lowercase letter] = 1/Phi [with an uppercase letter]= Phi-1

in the da vinci code there is a whole section that talks about phi. if you want to know some cool things about it i would suggest reading the book, plus i thought it was really good all around anyway. in a star if you divide a line where it crosses with one of the 2 others and compair the longer end to the shorter you should get phi, if you drew the star right.

That's a really good book.

But...Jesus cannot have a child. Here is why. He is the 41st generation from Abraham (counting Abraham) on Joseph's side (which is therefore irrelevant because Joseph was not his biological father), so his child would be number 42, & since that number is so important, it would make his child more important, which is impossible. QED :)

hey you're right! did you also know that the answer to "what do you get when you multiply six by nine" is also 42? and that it took a computer a coupla million years to calculate the ultimate question, and it is 42, except they forgot the question.

Just for the record: that's only correct for a five pointed star.

yeah whatever you know what i ment

It doesnt look like a trident [a trident being a pitchfork shape right?.. if not, disregard this comment..]
Phi [capital] looks like a circle with a vertical secant through its center.. Unicode U+03A6 in Times New Roman font on WinXP in the Character map.. the small letter phi looks like well.. like a lollipop haha.. its a circle with a vertical line from the highest intersection with the circle extending through the bottom of the circle.. Unicode U+03C6 in the same area....

Heh, that's right. The "trident" is the letter psi. I've been playing with 3D rotations, which uses theta, phi, and psi, so I know what they look like.

00ps, my bad. I must make sure to study the Greek alphabet harder!

Actually, both Phi and phi look like a circle with a line through it (though Phi sometimes has serifs). Psi and psi are the tridents / "devil's forks".

I thought it was 5:2... :-[

It's a very useful ratio used to create many items, like the greek pantheon

Phi is also used in the placement of The Great Pyramids of Giza in respect to Atlantian North and the Spinx its center is a huge tomb
"Blueprint to Atlantis" great book

Parthenon...the Panthenon was a totally different building, and I don't think it was even greek...

The pantheon was what the gods of Mount Olympus were called as a group

And the Panthenon was a building with a big hole in the top of a dome called an "oculus" (sp?) that is Greek or Latin or something for "eye"...it was sort of like a window on the roof, only it didn't have glass...

you're talking about the parthenon

Of course it's Greek you *%^$#@!

anyone know any peanut websites? tell me because my friend is allergic and i have to play a prank by giving him a pizza filled with peanut butter. it's for my science project and i need to see him choke and die. Thank you!

^^link^^

pantheon is greek, parthenon is roman

Way off topic:

Besides Gemini, Wolfenstein, and Doom 83, is there any more ASM 3d shooters? Sorry, I cant find any in the search engine.. it searches for keyword matching and not categories, so I thought, why not ask the people that play em [or make em really..]

These games are awesome, but only a few exist for the 83(+)!