For centuries, symmetry has remained a theme that has fascinated philosophers, astronomers, mathematicians, artists, architects, and physicists. The ancient Greeks were directly obsessed with it. And even today, we tend to stand on the side of symmetry in everything from the layout of our furniture to the styling of our hair. No one knows why this is so, or why mathematics is behind it, why it seems to be in everything around us. The examples below prove this to be the case. And once you are aware of this, you will most likely have an uncontrollable desire to look for symmetry in everything you see.
Sunflowers boast radial symmetry, an interesting kind of numerical symmetry known as the Fibonacci sequence. The Fibonacci sequence is 1, 2, 3, 5, 8, 13, 21, 24, 55, 89, 144, and so on (each number is formed by adding the previous two numbers together). If you take the time to count the spirals in sunflower seedlings, you will find that the spirals are actually the Fibonacci sequence. In fact, a large proportion of plants (including Roman broccoli) produce petals, leaves, and seeds in the Fibonacci sequence, which shows why it is so difficult to find four-leaf clover. Counting spirals in sunflower can be difficult, so if you want to test this principle for yourself, try counting spirals for bigger things like cones, pineapples, and artichoke. But why do sunflowers and other plants follow mathematical rules? Like the hexagonal models in the hive, it's all a matter of efficiency.
You may have walked past Roman broccoli at the grocery store and assumed it was some kind of genetically modified food because of its unusual appearance. But this is actually just one of many cases of fractal symmetry in nature - albeit striking. In geometry, a fractal is a complex pattern where each part of something has the same geometric shape as the whole. So in Roman broccoli, each flower represents the same logarithmic spiral as the entire head. In essence, the whole plant is a large spiral composed of small, conical buds, which are also mini-spirals.
Honey-producing bees also seem to have a sense of geometry. For thousands of years, humans have wondered at the perfect hexagonal figures in wax cakes and how bees can instinctively create a shape that humans can reproduce only with a ruler and a compass. The honeycomb is a case of symmetry, where a repeating pattern covers a plane (eg terracotta floor or mosaic). How and why do bees yearn for hexagons? Well, mathematicians think this is the best form to allow bees to store as much honey as possible while using as little wax as possible. Another shape, such as circles, for example, will leave a gap between the cells as they do not fit together exactly. Other observers who have less faith in the ingenuity of bees consider the shape of hexagons to be an "accident." In other words, bees just make round cells and the wax naturally breaks down into a hexagon. Anyway, everything is a product of nature and it's damn impressive.
In addition to plants, in some animals, such as the cephalopod nautilus, the Fibonacci sequence is also observed. A "Fibonacci Spiral" is found in the nautilus shell. The spiral is due to the tendency of the shell to retain the same shape, growing proportionally outwards. This pattern of growth allows it to retain its same shape throughout its life (unlike people whose bodies change in proportion, depending on age). There are exceptions, but in general in all nautilus the shells adhere to some kind of logarithmic spiral. And before we start thinking that these cephalopods can shine through a math class, remember that they are not consciously aware of how their shells grow, but simply take advantage of an evolutionary design that allows the mollusc to grow without to change my shape.
Most animals have bilateral symmetry, which means that they can be divided into two corresponding halves with one midline. Even people have bilateral symmetry, and some scientists believe that facial symmetry is the most important factor in whether or not we find ourselves physically beautiful. Animals can be considered to have taken all the attractive symmetry. An example is the peacock. Apparently peacocks have various adaptations to attract ladies, including bright colors, large size and symmetry in their body shape and in repetitive patterns in the tail feathers.
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Sunflowers
Sunflowers boast radial symmetry, an interesting kind of numerical symmetry known as the Fibonacci sequence. The Fibonacci sequence is 1, 2, 3, 5, 8, 13, 21, 24, 55, 89, 144, and so on (each number is formed by adding the previous two numbers together). If you take the time to count the spirals in sunflower seedlings, you will find that the spirals are actually the Fibonacci sequence. In fact, a large proportion of plants (including Roman broccoli) produce petals, leaves, and seeds in the Fibonacci sequence, which shows why it is so difficult to find four-leaf clover. Counting spirals in sunflower can be difficult, so if you want to test this principle for yourself, try counting spirals for bigger things like cones, pineapples, and artichoke. But why do sunflowers and other plants follow mathematical rules? Like the hexagonal models in the hive, it's all a matter of efficiency.
Roman broccoli
You may have walked past Roman broccoli at the grocery store and assumed it was some kind of genetically modified food because of its unusual appearance. But this is actually just one of many cases of fractal symmetry in nature - albeit striking. In geometry, a fractal is a complex pattern where each part of something has the same geometric shape as the whole. So in Roman broccoli, each flower represents the same logarithmic spiral as the entire head. In essence, the whole plant is a large spiral composed of small, conical buds, which are also mini-spirals.
Honeycomb
Honey-producing bees also seem to have a sense of geometry. For thousands of years, humans have wondered at the perfect hexagonal figures in wax cakes and how bees can instinctively create a shape that humans can reproduce only with a ruler and a compass. The honeycomb is a case of symmetry, where a repeating pattern covers a plane (eg terracotta floor or mosaic). How and why do bees yearn for hexagons? Well, mathematicians think this is the best form to allow bees to store as much honey as possible while using as little wax as possible. Another shape, such as circles, for example, will leave a gap between the cells as they do not fit together exactly. Other observers who have less faith in the ingenuity of bees consider the shape of hexagons to be an "accident." In other words, bees just make round cells and the wax naturally breaks down into a hexagon. Anyway, everything is a product of nature and it's damn impressive.
Nautilus
In addition to plants, in some animals, such as the cephalopod nautilus, the Fibonacci sequence is also observed. A "Fibonacci Spiral" is found in the nautilus shell. The spiral is due to the tendency of the shell to retain the same shape, growing proportionally outwards. This pattern of growth allows it to retain its same shape throughout its life (unlike people whose bodies change in proportion, depending on age). There are exceptions, but in general in all nautilus the shells adhere to some kind of logarithmic spiral. And before we start thinking that these cephalopods can shine through a math class, remember that they are not consciously aware of how their shells grow, but simply take advantage of an evolutionary design that allows the mollusc to grow without to change my shape.
Animals
Most animals have bilateral symmetry, which means that they can be divided into two corresponding halves with one midline. Even people have bilateral symmetry, and some scientists believe that facial symmetry is the most important factor in whether or not we find ourselves physically beautiful. Animals can be considered to have taken all the attractive symmetry. An example is the peacock. Apparently peacocks have various adaptations to attract ladies, including bright colors, large size and symmetry in their body shape and in repetitive patterns in the tail feathers.
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