Thank you for that. Didn't understand a bit of the math, but the concept is praiseworthy and a cause for worship on this otherwise groggy Monday morning.
One of our graduating seniors at Trinitas Christian School wrote her senior thesis on the Fibonacci Sequence, which helps explain the Golden Ratio. Dan, I can post a link to a video that talks about the math in a bit simpler terms if you like. Or folks are free to Google their little hearts out.al sends
Sure, Al, go for it.
Here it is...By the way, the Music that is playing in the background has the Golden Ratio, Fibonacci Sequence as it's core.al sends
Thanks for that. My oldest son is so intrigued by science stuff, I can just imagine him explaining the Golden Ratio to his 3rd grade teacher this fall. You've left us wanting more.(I was reminded of a show hosted by John Clese, I think it was NOVA, and the topic was beauty. They may have discussed the Golden Ratio, and used those lines and triangles on faces. Quite interesting.)
My readers are smarter than I. This is not breaking news...certainly not to my readers!
The Fibonacci Sequence is the easier to explain. You get the next number in the sequence by adding the previous two. So you start with 1. 1 plus 0 is still 1. Then 1+1 is 2, 2+1 is 3, and so on. It ends up as 1, 1, 2, 3, 5, 8, 13, 21, 34, etc.The golden ratio is maybe a little harder. Start with a rectangle. Draw a line inside the rectangle that divides it into a square and a smaller rectangle. The golden ratio is the ratio of side lengths where the smaller rectangle is proportional to the larger one. A rectangle that has that ratio of sides is called a golden rectangle; the smaller rectangle formed is also a golden rectangle, ad infinitum.The two concepts are very closely related, and they appear very frequently in nature. The video mentioned pine cones, rose petals, the DNA helix, and galaxies, and I also know of things like nautilus shell chambers that naturally grow in that ratio.
I'm pretty sure all of the kids in this family band are homeschooled. Just sayin'....
Pretty amazing talent all in one family. I'm jealous and I repent ... mostly.Their latest DVD is in the mail and I'm very much looking forward to it.
What is the significance of these things beyond, "Oh neat!"?I hate to be a wet blanket, but how is this not like being excited that squares show up a lot in nature?Someone help me out here.
There is a delightful book, Fascinating Fibonaccis: Mystery and Magic in Numbers by Trudi Hammel Garland, that explains them well also. It does get deep in places, but even a novice can get the overarching principles. Caution: Ms. Hammel's view point does not lead one to think she believes in our Lord, but the believer can clearly see God's fingerprints throughout creation as he or she sees the ubiquitous nature of Fibonacci and the golden ratio presented in this book. Our Creator is a God of order and these numbers display that truth. (Can you tell I love these?) Another direction you could go (if you were so inclined) would be Mathematics: Is God Silent?, by James Nickel. Nickel is a believer and his book is quite extensive and thorough.
Brad,I didn't read your comment before I put mine up, but I will respond anyway. Good question! So many people believe that the world is chaotic and random. It is not and number patterns are one way that this can be seen. Learning about Fibonacci and the golden ratio will cause you to glorify our Creator.In addition to the places that Trogdor mentioned, other places (I am drawing these from the Fascinating Fibonaccis book) the Fibonacci and/or the golden ratios are found in growth patterns in plants, the genealogy of a male bee, regular pentagons, the chicken egg, an ivy leaf, the Norway spruce, a ram's horn, a sea horse's tail, an ocean wave, a growing fern, a dying poinsettia leaf, lots and lots of shells (see a nice display at this link). Fibonacci numbers are seen in piano keys and other musical instruments. Fibonacci vibrations and the golden ratio are pleasing to the ear and have been employed by composers in a bazillion songs—simple tunes, such as "Mary Had a Little Lamb", hymns, such as "Amazing Grace," and classical music, such as pieces by Beethoven, Brahms, and Bach.Fibonacci ratios are pleasing to the eye and have been used by artists and architects throughout history, from the Great Pyramid of Gizeh, the Parthenon, to the layout of beautiful paintings and the dimensions of Grecian urns.My favorite? The proportions of you: your face, your fingers, your entire body. The reason clock's are usually set at 10:10 or 8:20 for display is because the hands fit within the golden rectangle and retailers know that will attract the eye.These are just lists (incomplete lists) of a few examples. You have to read about them yourself to get the how and why details.Ask Professor Google. I am confident he has lots of information for you.
What timing, waiting in my mailbox was Pilgrims & Prodigals by the Annie Moses Band. It’s a DVD and CD set and can be had at their website, anniemosesband.com. I commend it to you.
Okay, who or what in the heck are they? I know nothing about them. I just went to their YouTube page and am watching this amazing bunch of snippets... but no "band." What's up with that?
Dude, that's funny because I first learned about them after you played one of their YouTube videos.
I love Fibonacci! It is also my birthday 11-23. Oh btw to the senior who did her thesis on it - I did my high school valedictory address on the second law of thermodynamics. How is that for nerd-tastic for you. And I would totally buy that Phi t-shirt.
Anna, the girl who did the Pibonacci paper was a National Merit Scholar. She is crazy smart.Brad, I think the Golden Ratio and the Fibonacci Sequence help us when discussing aesthetics with relativists. There is such a thing as real beauty and God defines it, in fact he ordered the sunflower seeds to display it. Relativism be damned.al sends
Okay (totally not a mathematical mind here but this is driving me crazy and I gotta know) how do certain clock hand positions fit inside a golden rectangle? Went to the youtube page too - not crazy about the older clips but Pilgrims & Prodigals sounds like something I should definitely think about ordering. Good stuff.
Awesome!!! Although I'm unfamiliar with the Golden Ratio, geometry was not only one of my best, but one of my favorite subjects back in high school. It is so neat to see our God's painstaking geometric precision in his creation!!
I just watched a really interesting clip on YouTube that has to do with the Golden Ratio and the human body. All the more glory goes to the Creator of the universe! :)http://www.youtube.com/watch?v=085KSyQVb-U&feature=related
Dan, did you check out their website? I found it here:http://anniemosesband.com/category/features/(Sorry I don't know how to make my words turn into blue-colored links...yet. Maybe someone will one day 'splain it to me.)And a good part of yesterday was spent online watching various Youtube clips explaining the Golden Ratio, and my son was drawing rectangles and spirals. Thanks again. : )
Does anybody know of some books for children that discuss this matter? I saw a couple of links to books, but the reviews said they are for high school ages and up. I have two boys, 6 & 8. Our eight year-old LOVES reading and math, and I think this would be something he would really sink his teeth into. He can read on about a 6-8 grade level, but not quite at high school level yet. Any help is greatly appreciated.
Check out the mathematical genius of God in this my favorite of his handiworks-The Nautilus!
Susan,Great video, thanks for posting it!Robert, I just did an Amazon search. It looks like there might be something there that would work. I wouldn't advise paying $143.50 for a paperback though. :)
I was above average with Matt in school, but I'm lost with this Math. I like it though, I think.
As the person who made the video, thanks for posting it here. I noticed a huge spike on the youtube Insight data, which is how I found your blog. To the user who posted that they would buy the Phi shirt, it's available on www.thinkgeek.com. I already own it ;)
My blog makes for a "huge spike."Heh.(c:
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