Affluent Savvy
Affluent Savvy
Photo: Mikhail Konetski
The number 1.618… goes by many different names. However, mathematicians mostly call it phi. Everywhere around us, we see this beautiful number.
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Learn More »As you can see in this image, the seeds of the sunflower grow in opposing spirals. Now, if you calculate the diameters of successive spirals and divide them, you will be left with phi! Quite brilliant isn’t it? Since we’re talking about spirals at the moment, let’s have a look at this marine animal called a nautilus. The nautilus has a very interesting shell, and if you look at the next two photos, you will understand what I mean: The left photo is how the nautilus looks on the outside. The nautilus doesn’t look very special when viewed from the outside. But when seen on the inside, you see a magnificent spiral pattern within its shell. What’s more, if you divide the diameters of consecutive spirals, like what we did with the sunflower, you will again obtain phi as the the quotient! Interestingly, the Golden Ratio is often showed in the following form: As you can clearly see in this image, if you divide the length of the bigger squares by the length of the preceding smaller square, you will be left with phi again. Very often, you will see this curve superimposed on images like that of the sunflower and nautilus we saw above. The Milky Way galaxy is really quite beautiful. The radiating arms of of the galaxy never cease to catch one’s eye. However, since it’s a spiral, like the other examples, do you think that dividing the diameters would yield phi? If you thought that, then you are are right! Indeed, the quotient that you obtain when you divide the consecutive diameters of the spirals in the galaxy is the Golden Ratio. No doubt, our ancestors would have been awestruck seeing this number everywhere and believed it to have been put there by God himself. Hurricanes are one of the most deadly natural disasters in the world. But, have you ever seen a satellite image of them from above? If you have, you would know that the hurricane looks like a spiral. And no doubt about it this time, if you divide the diameters of each spiral, you will be left with phi again. Seeing this number in nature so many times truly shows that the number is one of extreme beauty and elegance. In a beehive, it is a known fact that the female bees always outnumber the male bees. However, what’s truly special is that if you divide the number of female bees by the number of male bees, you will always be left with phi! Isn’t that amazing? The Divine Proportion can also be seen outside of nature, inside our own bodies! “Where?”, you may ask. Well, let’s have a look!
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Learn More »If you divide the length of your shoulder to your fingers by the length of your elbow to your fingers you obtain phi again! Similarly, dividing the distance of your hip to toes by your knee to toes, not surprisingly, you get phi again. There are multiple more examples of the Golden Ratio that can be seen within the human body. In the words of Robert Langdon in Dan Brown’s international bestseller The Da Vinci Code: My friends, each of you is a walking tribute to the Divine Proportion. Not surprisingly, after seeing the beauty of this number, a lot of different artists, architects and musicians began featuring this number in their works. From Da Vinci to Michelangelo, from Beethoven to Mozart, all of these people followed a strict adherence to the Divine Proportion. The number appears in many monuments like the Great Pyramids in Egypt, the Parthenon in Greece and even modern buildings like the headquarters of the United Nations in New York. Legend states that the famous violin making family, the Stradivari, used phi as the basis for marking the f-holes on their violins! With such legends using the Golden Ratio in their works, there is no doubt that phi is indeed the most beautiful number in mathematics.
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