The Golden Ratio and karmic vision
I love recursive ad infinitum arguments. I really do.. and that's why I've decided to write about something that is already very famous in the math world by the name "Golden Ratio". What is the golden ratio ? Its smply a number: = 1.61803399. Whats so special about it ? I won't go intricate math details here, but here's a nice definition from Stephen Wolfram's mathworl website:
"Given a rectangle having sides in the ratio 1:x , the golden ration x is defined such that partitioning the original rectangle into a square and new rectangle results in a new rectangle having sides with a ratio 1:x. Such a rectangle is called a golden rectangle, and successive points dividing a golden rectangle into squares lie on a logarithmic spiral."
The ratio is claimed to be most pleasing to the human eye, when present in geometrical and architectural structures. Indeed it is found in an overwhelming number of architectural contructs. However, its most astounding presence is in nature itself. Consider the following alternate definition of the golden ratio:
Notice the recursion ? It turns out that angles between successive whorls of leaves on a branch of any tree, or angles between successive petals in a flower are always exact multiples of the golden ratio. It help the plant o maximize received sunlight!
The golden ratio is also the ratio of successive terms of the fibonacci series: 1, 2, 3, 5, 8, 13, 21, 34, 55... in the limit that the number of terms tend to infinite. The number of petals on a flower is always a member of this series. The number of ancestors in the same generation in a family of bees is always a memeber of this series.
For me, the definition if the golden ratio has a new meaning. And yes, its recursive.
"To understand what recursion is, we first have to understand what recursion is".
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"Given a rectangle having sides in the ratio 1:x , the golden ration x is defined such that partitioning the original rectangle into a square and new rectangle results in a new rectangle having sides with a ratio 1:x. Such a rectangle is called a golden rectangle, and successive points dividing a golden rectangle into squares lie on a logarithmic spiral."
The ratio is claimed to be most pleasing to the human eye, when present in geometrical and architectural structures. Indeed it is found in an overwhelming number of architectural contructs. However, its most astounding presence is in nature itself. Consider the following alternate definition of the golden ratio:
Notice the recursion ? It turns out that angles between successive whorls of leaves on a branch of any tree, or angles between successive petals in a flower are always exact multiples of the golden ratio. It help the plant o maximize received sunlight!
The golden ratio is also the ratio of successive terms of the fibonacci series: 1, 2, 3, 5, 8, 13, 21, 34, 55... in the limit that the number of terms tend to infinite. The number of petals on a flower is always a member of this series. The number of ancestors in the same generation in a family of bees is always a memeber of this series.
For me, the definition if the golden ratio has a new meaning. And yes, its recursive.
"To understand what recursion is, we first have to understand what recursion is".
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