What is Digg?Sponsored by Best Buy
My wife likes to take pictures of everything. Got any ideas? view!
bestbuy.com - With a Kodak(r) EasyShareTM 3X Zoom, she'll have impressive 10.2-megapixel performance, right at her fingertips
205 Comments
- BalancingAct, on 05/09/2009, -2/+126Indeed it is everywhere.
Little known fact: as the Fibonacci Series approaches infinity, the ratio between each digit in the series and the preceding one approaches the Golden Ratio. The Golden ratio was used in most classical art because it was thought that it represented the most attractive dimensions. For example, many of Leonard Di Vinci's works made use of the Golden Ratio where (say) numerator represented the width and the denominator represented the length, or vice versa.
The Golden Ratio was such that 1/A + 1 = A
(ie 1/1.618 + 1 = 1.618) - kayco, on 05/10/2009, -5/+107I just want to clarify this as a mathematician:
* Yes, Fibonacci sequence is found many places in nature, including in several flowers, pine cones, shells, etc. There are 'magical' qualities about that number.
* No, the Fibonacci number is NOT found in the human body as often as people think. The mathematical community is really stretching to relate the golden ratio to man. After several studies on the mater, it was found that claims that the golden ratio can be found in arm/hand length ratios are NOT accurate. Instead, we find a ratio more like 1.55; not 1.61803399 (phi, the golden ratio). Our arm lengths are within a small order of magnitude of the golden ratio, but unfortunately the golden ratio does not determine arm length ratios. - TexMexRex, on 05/10/2009, -1/+91What did sunflowers and all that look like before Fibonacci invented this?
- peterjmag, on 05/10/2009, -3/+91"Leonardo brought this number system to Europe and eventually we invented Sudoku with it."
It made me chuckle. - javiero, on 05/10/2009, -3/+70This is exactly the type of chat topics that have gotten me so many one night stands at clubs
- BalancingAct, on 05/10/2009, -0/+47"I wish my brain functioned that way."
It already does. It's just a confidence thing. Lots of people see a maths equation and instantly form a mental block, but when you get past that and look at it logically, it's very straightforward. Everything follows logical rules and there are no hidden subtleties. - i4mt3hwin, on 05/10/2009, -5/+46Fibonacci sequence as illustrated by tool.
http://www.youtube.com/watch?v=wS7CZIJVxFY
I know - it's been posted 10,000 times - but still badass. - barthrh, on 05/10/2009, -0/+37"His most notable contribution to your life is probably found on the top row of your keyboard."
Leonardo invented the F-keys? Now *that* is forward-thinking. - rjshatz, on 05/10/2009, -0/+37I love nature. It appeals to the intellectuals but it's also fun to look at.
- JshMRsn, on 05/10/2009, -1/+35FTA: "Efforts have been made to improve the illustration with special effects. "
- jman583, on 05/10/2009, -1/+35The Golden Ratio can also be calculated as:
(1 + the square root of 5)/2
MATH NERD, AWAY!!!! - crombat, on 05/10/2009, -3/+32Why is there a tank in the background of the spiral picture?
- Xwhy, on 05/10/2009, -0/+25Keep going. You'll get there. It converges on it, but you won't get there in 7 or 8 terms.
- MrInfallible, on 05/10/2009, -1/+22Whats your point? Does this somehow disprove evolution?
Your butt is not a very compelling argument. - MrInfallible, on 05/10/2009, -0/+20It appears in the facial features of good looking people, but there are few sequences in the human body that are similar to those found in flowers, pine cones, shells.
- QuackMasterDan, on 05/10/2009, -0/+20The golden ratio (or Phi), is an excellent ratio for packing together structures in nature. Lay on your back with your head looking up the trunk of a conifer, and you can see the larger branches are arranged in a fibonacci spiral, this is to maximize the amount of light collected by each branch and its leaves. The same is true for how many trees (like conifers) densely pack in their seeds into a cone, or how a pineapple arranges its spines.
Some say that the golden ratio is found in the human body, which is partially true. It is less an approximation of the human body, as it is an 'ideal' human body. Men and women with a ratio of 1.618 (total height) / 1 (waist to ground) are considered to have very attractive proportions. The same is true for measurements of the face, arms, and other body parts. There is also a golden rectangle, a rectangle whose longer sides are 1.618 the length of the shorter sides. In a comparison between rectangles (extremely long and skinny, near square, etc) the golden rectangle is more often chosen as the best looking rectangle. This feature is what compelled the ancient Greeks to construct the Parthenon with golden rectangles (the front) and golden triangles (the cap).
Fun stuff. - BingoPower, on 05/10/2009, -0/+18You did it all wrong.
Girl: Why are you staring at that blank piece of paper for so long?
Me: I'm trying to see if the length to width is the golden ratio.
Girl: What's that?
Me: My ***** in you. - telomeres, on 05/10/2009, -1/+17With the Fibonacci Sequence we aren't just counting a number of things or dividing ***** up... it's a pattern that occurs nearly everywhere in its exact proportions. It's counter-intuitive to think that something unconscious like nature can reuse the same number or pattern in many of its designs. It brings up the question of why this exact number? What importance does it have? Everything in nature has a purpose or reason for existing, and this is one aspect that is simple but hard to explain.
- LiberalKid, on 05/10/2009, -1/+16This is because the closed form of the fibonacci sequence is
f(n) = 1/(sqrt(5) * ( (1+sqrt(5)/2)^(n+1) - ( (1-sqrt(5)/2)^(n+1)
This would be when f(0)=f(1)=1, not when f(0)=0 and f(1)=1, which would just be changing the exponent to n, as opposed to n+1.
Not that anyone cares, but a brief derivation.
f(n)=f(n-1)+f(n-2)
f(n)-f(n-1)+f(n-2)=0
Now we assume there exists a closed form such that a(n)=f(n), and a(n)=c^n
c^n+c(n-1)+c(n-2)=0
c^(n-2)*(c^2-c-1)=0
The solutions to c^2-c-1=0, are (1+sqrt(5))/2, (1-sqrt(5))/2. (yes the golden ratio)
With which we can say, due to it being a second order recurrence relation.
f(n)=A*((1+sqrt(5))/2)^n + B*((1-sqrt(5))/2)^n
Then it's just a matter of solving the equation
Math is fun! - grmclaren, on 05/10/2009, -0/+13Try Wikipedia
"The modern puzzle was invented by an American architect, Howard Garns, in 1979 and published by Dell Magazines under the name "Numbers in Place.""
Sudoku's creation has nothing to do with Japan except the ***** name. - Wingin, on 05/10/2009, -1/+14Loved that comment - and the choice of "special effects".
- greenroom628, on 05/10/2009, -4/+17its also in the tool song, "lateralus"
http://www.youtube.com/watch?v=wS7CZIJVxFY&fmt ... - Lane, on 05/10/2009, -0/+12In fact his butt is not compelling in many aspects well beyond argument.
- cambob76, on 05/10/2009, -0/+11News to me , thanks guys.
- bushnoh, on 05/10/2009, -1/+11Ha, Megan Fox, you look like a pine cone!
- telomeres, on 05/10/2009, -0/+9Also, keep in mind that not all spirals are perfect examples of phi or the fibonacci sequence. Humans like to look for order in chaos and it's always necessary to assess things with that in mind. The real core of why this is all interesting should be asking questions about why we notice this and does it help us explain other patterns. Nature acts without thought and always takes the best course. The value of phi may only be what we think we see in it, rather than if it 'governs' or explains a process.
- paidhima, on 05/10/2009, -0/+9There are four reasons the sequence holds such a 'mystical' fascination:
1. Simplicity: The sequence, as a mathematical function, is simplicity itself. You don't need an advanced degree in mathematics to understand and illustrate the sequence in its simplest form. The ease at which people can understand is certainly a draw for the average layman.
2. Observation: Going a bit deeper, the sequence and related concepts (particularly the golden ratio) are easily observed in nature. You don't need a microscope or rigorous scientific testing to uncover it. The fact that it's relatively uncomplicated makes it that much easier to recognize it.
3. Universality: The sequence and related concepts (particularly the golden ratio) describe phenomena across a wide swath of natural and man made constructs. While it is by no means the only universal constant in the world, its one that can easily be observed in such varied media.
4. Beauty: For many people math is an abstract, ugly thing - all symbols and numbers and angles. The expression of the concept in nature is beautiful to our human eyes. Something of beauty, orderly and predictable, holds particular interest to us.
The basis of mysticism is, in many ways, order from an unknown source. Simple, observable, universal and attractive patterns in nature have always held a fascination for people. The instinctual question when we see the expression of the sequence naturally occurring in such a wide variety of places is: "What does it mean?"
That right there is mysticism in a nutshell. - RubberTree, on 05/10/2009, -0/+9http://www.youtube.com/watch?v=X_tyRPerr6c#t=02m08 ...
Donald Duck FTW - merkler, on 05/10/2009, -0/+9Swing on the sunflower...
- Krillin, on 05/10/2009, -3/+12http://www.youtube.com/watch?v=wS7CZIJVxFY
- JoeHague, on 05/10/2009, -1/+9I've never understood the kind of mystical fascination with the Fibonacci Sequence. Maybe someone can explain to me why using mathematics to explain the natural word is so special. We use mathematics to describe anything and everything in the known universe and everything an anything in the unknown universe.
/seriously - JoeHague, on 05/10/2009, -2/+10@blackinthemidlle
Telomeres is incorrect. Nature does not "always take the best course". Evolution is the product of trial an error. For example if an animal mutates in a negative way- which happens quite a bit- it becomes statistically less likely to survive- which in turns makes it statistically less likely to procreate- animals that do not procreate cannot pass on their genetic mutations. - lhbaker, on 05/10/2009, -0/+8I'll bet math with Roman Numerals was a real bitch.
- JshMRsn, on 05/10/2009, -1/+9I think these numbers are interesting, but it's way to easy for people to get carried away with its importance. Thanks for clarifying!
- Malarie, on 05/10/2009, -0/+8you lost me at f(n)
- guinpen, on 05/10/2009, -1/+8pun intended?
- ajfunk, on 05/10/2009, -2/+9Black and
white are
all I see
in my infancy
red then yellow then came to be
reaching out to me
lets me see. - kayco, on 05/10/2009, -2/+8I heard the sequence 4,8,15,16,23,42 is found in nature, as well!
- anokun7, on 05/10/2009, -0/+6I think that would be wrong also - the 0-9 system (which we take so much for granted) was invented by Indian mathematics and is known as the Hindu-numeral system.
Source: http://en.wikipedia.org/wiki/Hindu-Arabic_numeral_ ... - inactive, on 05/10/2009, -0/+6I myself am of fan of Chairman Gdo of Thailand.
- Netrilix, on 05/10/2009, -0/+6Well, at least in that order. Many of us are great fans of dogs. We also like long walks on the beach.
- MtheoryX, on 05/10/2009, -0/+6I always figured Donatello would be the one to do it.
We all know Michelangelo was too busy eating pizza and playing video games. And Raphael was just pissed at the whole lot of 'em. - Kimberlyyan, on 05/10/2009, -0/+6I wish my brain functioned that way.
- lhbaker, on 05/10/2009, -0/+50 isn't arbitrary. It's zero.
- inactive, on 05/10/2009, -0/+5Fibonacci sequence is so badass!!!
- Sporky023, on 05/12/2009, -0/+5@DestroyFascism: I totally agree. Sometimes a good teacher versus a crappy one can be the difference between a lifetime of seeing something as natural and easy versus a lifetime of seeing it as impenetrable and confusing.
But of course, no one should rely on their teachers. All kids still in school out there: if your teacher sucks, don't let that paint your view of a topic. If you're having a hard time but you enjoy it when you DO get something, that means you've got a gem and it's just covered in mud (most likely from your teacher's fumbling attempts to explain it). Move away from that dude - he didn't invent whatever it is you're studying. Go over his head and straight to the source. Or find someone else who's really good at it, and offer to trade them: you'll teach them something you know that they may have had a hard time with, and they do the same for you.
final soundbite: your teachers aren't gods; they're human beings trying to keep their laundry clean and convey complex thins to thirty different minds at a time. Our education system is so F'd up we think education is all about following rules and working with a machine (funny, Pink Floyd's singing "hey, teachers, leave those kids alone" in the coffee shop I'm sitting in). Be inspired by the universe itself, not the government-appointed tutor/drill sergeant whose job it is to mass-produce knowledge.
Of course, if you do find a good teacher, someone whose mind clicks with yours and who you pick things up easily from, pour your energy into that relationship. Go out for a cup of coffee with them, pick their brains, whatever. Don't be their pet; the relationship is more equal than that. If you approach this person with a mindset of mutual respect, and be clear about the fact that you rationally admire their accomplishment while at the same time aren't going to blindly accept what they say (and maybe have to keep up appearances with your peers on the "teacher's pet" angle), that teacher will see you as a worthy recipient of their knowledge and you'll both have an excellent time and you'll both get smarter.
Have fun, work hard, and try your best to find your own things to study instead of just swallowing the crap on the public school menu. - MrSparkle666, on 05/10/2009, -0/+5I've been dying to try fractal broccoli for years.
- rhodydog, on 05/10/2009, -0/+5How is the golden ratio related to DNA? As a biochemist I am not entirely sure what you mean by "enzymatic chaining of our red blood cells"?
- itsripitsrip, on 05/10/2009, -2/+7i'm not the religious type, but sometimes i think that math may be a 'proof' of a god. or millions of years of evolution.
bleh. who knows. it's all fun to think about though =] - lhbaker, on 05/10/2009, -1/+6If by that you mean that we can see 'God' in a series of numbers, I'm with you. Just as the angry, voyeuristic sky God gives meaning to the world, math gives order to the universe. The main difference being that math doesn't make you feel guilty after masturbating.
-
Show 51 - 100 of 211 discussions
© Digg Inc. 2009
— Content created and posted by Digg users is