Philosophy
Time for some math. No, don't run away! I guarantee even the greatest of mathophobes among you are going to love this, not only because it's a new episode of the Doodling in Math Class series (narrated by the future mother of my children, although she doesn't know this yet), but because it's related to golden spirals and the Fibonacci sequence.
The mathematical properties of this sequence are easy enough to understand. The marvel comes from the fact that it is instantiated all over the place. You've seen a stunning animation of this phenomenon before, but why don't we put the idea to the test with some real-world examples:
As she said, there's nothing really mystical about the appearance of this number in these plants. If you consider this to be an engineering problem requiring the most efficient packaging solution, then it shouldn't be that surprising that the blind process of evolution should have eventually stumbled upon this pattern. For more, take a listen to this great discussion of the Fibonacci sequence and the golden ratio from In Our Time.
If you're still hungry for more, learn more about fractals from none other than Arthur C. Clarke, or how simplicity can give rise to complexity in The Secret Life of Chaos, with Jim Al-Khalili.
And don't forget to check out parts 2 and 3 of this awesome little series.
- Doodling In Math - Spirals, Fibonacci And Plants - 3
Ok, so now that you've learned how the beauty and elegance of the golden ratio and Fibonacci sequence are instantiated all over the natural world (parts 1 and 2), you're probably wowing all your friends and thinking this is the coolest thing ever......
- Doodling In Math - Spirals, Fibonacci And Plants - 2
This girl is so cool I may soon have to create a tag on this blog just for her awesomeness. Last time we saw her, she gave us a nice introduction to how the Fibonacci sequence can give rise to the kinds and numbers of spirals we find in many plants. Now,...
- Bach Visualized Through Math
You've no doubt heard the claim that some of the greatest musicians of all time had an intuitive sense for mathematical proportion and harmony. It's no coincidence, for instance, that the musical scale was invented by that most eccentric of mathematicians,...
- Nature By Numbers - Fibonacci And The Golden Ratio
Among the pre-Socratics, it was Pythagoras who hypothesized that the most basic constituent of the universe wasn't some material substance but rather numbers. The idea must have seemed strange to most of his contemporaries, but over two thousands...
- Mother Nature's Fractals
This variant form of cauliflower is the ultimate fractal vegetable. Its pattern is a natural representation of the Fibonacci or golden spiral, a logarithmic spiral where every quarter turn is farther from the origin by a factor of phi, the golden ratio....
Philosophy
Doodling in Math - Spirals, Fibonacci and Plants - 1
The mathematical properties of this sequence are easy enough to understand. The marvel comes from the fact that it is instantiated all over the place. You've seen a stunning animation of this phenomenon before, but why don't we put the idea to the test with some real-world examples:
As she said, there's nothing really mystical about the appearance of this number in these plants. If you consider this to be an engineering problem requiring the most efficient packaging solution, then it shouldn't be that surprising that the blind process of evolution should have eventually stumbled upon this pattern. For more, take a listen to this great discussion of the Fibonacci sequence and the golden ratio from In Our Time.
If you're still hungry for more, learn more about fractals from none other than Arthur C. Clarke, or how simplicity can give rise to complexity in The Secret Life of Chaos, with Jim Al-Khalili.
And don't forget to check out parts 2 and 3 of this awesome little series.
- Doodling In Math - Spirals, Fibonacci And Plants - 3
Ok, so now that you've learned how the beauty and elegance of the golden ratio and Fibonacci sequence are instantiated all over the natural world (parts 1 and 2), you're probably wowing all your friends and thinking this is the coolest thing ever......
- Doodling In Math - Spirals, Fibonacci And Plants - 2
This girl is so cool I may soon have to create a tag on this blog just for her awesomeness. Last time we saw her, she gave us a nice introduction to how the Fibonacci sequence can give rise to the kinds and numbers of spirals we find in many plants. Now,...
- Bach Visualized Through Math
You've no doubt heard the claim that some of the greatest musicians of all time had an intuitive sense for mathematical proportion and harmony. It's no coincidence, for instance, that the musical scale was invented by that most eccentric of mathematicians,...
- Nature By Numbers - Fibonacci And The Golden Ratio
Among the pre-Socratics, it was Pythagoras who hypothesized that the most basic constituent of the universe wasn't some material substance but rather numbers. The idea must have seemed strange to most of his contemporaries, but over two thousands...
- Mother Nature's Fractals
This variant form of cauliflower is the ultimate fractal vegetable. Its pattern is a natural representation of the Fibonacci or golden spiral, a logarithmic spiral where every quarter turn is farther from the origin by a factor of phi, the golden ratio....