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:
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.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTWpKP588CfE79bDc8ZlZkBUJLi0jWiVUXqB1T6A0xFYr84jSqsdo2qR9HrDKHcjhxJ3oaFBEb7G97ZX83LLm8BWSLtnuRNdIghTt4H6lhlM0pAcuPYTtD8DhKOABQGV0OjzQlPn4cKTWc/s320/golden+spiral.png)
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.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZw9M0b7aHZcxkcqC0SMRjRSCGt73DTEe0MqQVs-i2NYI-HFDLCYHlCCu29rl3Nb4mgyQQIS8jdIwJ_vpS5odM-kGh-TILXktp19V-eDe_Nnu-uFMWVC1Uk61lyBF7A-aa2_jTpTFQhHgv/s320/200w_MATH_P_DVMON.jpg)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifH0BsbB1VMw89UaTajvHTQt0rlIPSncDgCoh8rqq7f1tgzId6hedKdFwoXNrcKyCijOyx1KfXSt5JmsPCyf4-KsB69FaQNhYE7vDtqpYjZWTN6sGYCvCVdMnYd7OQnZtoIo9GUNyTUNQi/s320/parthenon2.jpg)
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.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDMnjv11nbzzW7zpndg8wAXCJT-BKKWls5bL5LyFmCACVq-pxu0FrtXtDkuWnWnxvKvlOpJoyYmCmYsgn3amMB3RGwvqotIhmBDKZst7C_RPASo0kxthwWpxrr4NM9mnK1pwNJItQ8H3UZ/s320/golden+mean+flower.jpg)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_3W-cs1ZaWaJJ8KE2mPpvDSwmrFfDRjvOqTaO2laz7FeqClUbQYO7lkHn6cet5smRG8SWXgAEMMKqzFtyX-E39meEvk2U83LDtMJUZMRkplOZ3FFeYUnItrtSpIFv2Bto4HieRghr_ofd/s320/nautilus.jpg)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgegDzSbO5pKXI2qivbca1pbxf66KJE1z3K6weaWn1IyYsaGPJpsGgWWMi5pKgGObTFREowsBI5Hx2NtC04nqLJr8pF1ovuRwjRiBFIoNRYZNUyNVAKm4SY-gA0dG0QAM-2RLxC5-CjorRa/s320/fib_apple_1.jpg)
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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