Philosophy
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 years of research have led to the inescapable conclusion that the book of the universe really seems to be written in the language of mathematics.
One of the most famous and intriguing mathematical patterns found throughout nature is phi (also known as the golden ratio). The idea is simple: two numbers are said to be in this ratio if the sum of the two numbers to the larger of the two is equal to the ratio of the larger to the smaller (like in the rectangles above). You can also converge on this fraction by taking the ratio between any two consecutive numbers in the Fibonacci sequence (or in the Lucas series).
As the stunning animation below shows, the remarkable thing is that the Fibonacci series and the golden ratio seem to be beautifully manifested in various aspects of the natural world, from the spiral shape of the nautilus to the arrangement of petals in sunflowers and even the predatory flight of the peregrin falcon as it hones down on its unsuspecting prey.
Need more proof that the golden ratio is a thing of beauty? Behold!
And if this has whetted your appetite, take a listen to this episode on the Fibonacci sequence from In Our Time, with Melvyn Bragg.
Or you might also be interested in The Secret Life of Chaos, and how order can arise out or disorder.
.
- 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,...
- Doodling In Math - Spirals, Fibonacci And Plants - 1
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...
- 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....
- "time Travel" Poll
Do you believe that "time travel" is possible or just fiction? Possible...4 Fiction...5 Closer than I thought. I am not about to delve into the issue that much. For me it is great fiction. Conjectures under the guise of science [theoretical physics]...
Philosophy
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 years of research have led to the inescapable conclusion that the book of the universe really seems to be written in the language of mathematics.One of the most famous and intriguing mathematical patterns found throughout nature is phi (also known as the golden ratio). The idea is simple: two numbers are said to be in this ratio if the sum of the two numbers to the larger of the two is equal to the ratio of the larger to the smaller (like in the rectangles above). You can also converge on this fraction by taking the ratio between any two consecutive numbers in the Fibonacci sequence (or in the Lucas series).As the stunning animation below shows, the remarkable thing is that the Fibonacci series and the golden ratio seem to be beautifully manifested in various aspects of the natural world, from the spiral shape of the nautilus to the arrangement of petals in sunflowers and even the predatory flight of the peregrin falcon as it hones down on its unsuspecting prey.
Need more proof that the golden ratio is a thing of beauty? Behold!
And if this has whetted your appetite, take a listen to this episode on the Fibonacci sequence from In Our Time, with Melvyn Bragg.
Or you might also be interested in The Secret Life of Chaos, and how order can arise out or disorder.
.
- 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,...
- Doodling In Math - Spirals, Fibonacci And Plants - 1
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...
- 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....
- "time Travel" Poll
Do you believe that "time travel" is possible or just fiction? Possible...4 Fiction...5 Closer than I thought. I am not about to delve into the issue that much. For me it is great fiction. Conjectures under the guise of science [theoretical physics]...