Still thinking about the spirituality of math.
Consider the golden ratio, for instance. Two quantities are said to be in the golden ratio ( φ ) if the ratio between the larger and the smaller quantities is equal to the ratio between the sum of the quantities and the larger one. Put differently: the following two line segments (a and b) are in the golden ratio because the ratio between a and b is the same as the ratio between (a + b) and a.
We can represent this mathematically as:
If we rewrite the right side of the equation as a=bφ, we can substitute bφ for a, giving us:
Canceling b give us:
Multiplying both sides by φ and rearranging the terms gives us a quadratic equation:
Now we can solve for φ by completing the square:
The golden ratio, then, is 1: 1.6180339887...
The line segments of a star shape are in the golden ratio (the green to the red, the purple to the blue); a spiral that gets wider by a factor of φ for every quarter turn it makes is called a golden spiral.
Now for the profound so what: Human beings tend to find designs that follow the golden ratio aesthetically pleasing. Their proportions strike us intuitively as balanced, harmonious, elegant. It's a beautiful number. Leonardo Da Vinci knew this. So did the ancient architects who designed the Parthenon.
But here's the really mysterious thing: these artists didn't invent this as an aesthetic principle. It's more like they discovered it. For some reason, the golden ratio actually occurs all over God's world: from the spiral arms of galaxies to the star-shaped seed pod of an apple. Many flowers have a petal-to-pod ratio of 1.618... spiral sea shells expand in the golden ratio ... so do the spiral formations of sunflower seeds... and pine cones. 1.6180339887... , it seems, is one of the beautiful numbers that the all-wise artist of the universe used in designing his beautiful creation.
Balanced. Harmonious. Elegant. Not that the Psalmist had this in mind when he sang, but the beautiful math of the creation surely charges his exulting cry with new wonder: ""How many are your works, O Lord; in wisdom you made them all!"
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