Nature offers us the beauty of mathematics itself. Fractal geometry is also known as the geometry of nature. A geometric fractal is a pattern or pattern that repeats itself infinitely. The pattern repeats itself to an increasingly smaller size. Therefore, when we enlarge a part of a geometric fractal, it looks exactly like the original. Fern is one of the best examples of this.
When we look at a tree, we are actually looking at mathematical beauty. Plants and trees follow the Fibonacci sequence. Each number in the Fibonacci sequence is equal to the sum of the two numbers before it. For example: 1,1,2,3,5,8,13,21,… In order to recognize the Fibonacci sequence on a tree, we need to calculate the number of leaves and the number of turns until we encounter a new leaf in the direction of a leaf we have chosen.
We can cover any plane we want, like a mosaic, with just regular hexagons, squares, and equilateral triangles.
Their areas are equal; Hexagon is the hexagon with the smallest perimeter among the square and equilateral triangle. Bees create honeycombs from hexagons, so they do less work. The hexagonal shape is found in honeycombs, snowflakes, molecules, crystals and many other areas.
The shapes that are most pleasing to our eyes are those that comply with the golden ratio (golden ratio: 1.618). In fact, today credit cards, some books, and some items comply with the golden ratio or are very close to it. For example, credit cards are very close to a golden rectangle (the ratio of the long side to the short side). The length of the credit card is approximately 8.6 cm. Its width is approximately 5.4 cm. Long side/short side: 8.6/5.4=1.593. This ratio is very close to 1.618, or the golden ratio. In other words, credit cards actually have the rectangular structure that looks most pleasing to our eyes.
The shape of a soap bubble is determined by surface tension. Surface tension shrinks the area of the surface and the soap bubble contains less air. Surface area is minimized for a given amount of air. This explains why soap bubbles take a spherical shape. The edges of the soap bubbles meet at the triple intersection and form 120 degree angles.
When chairs or tables with four legs, one of which is short, swing; Why don't 3-legged stools with one short leg swing? Three points not on the same line determine a plane; That is, all 3 legs of a 3-legged stool always rest on a plane.
In traffic, when vehicles get caught at a red light, they usually get caught at the next red light as well. Have you ever thought what could be the reason for this? Distance=Speed×Time. In other words, the distance from the traffic light to the next traffic light divided by the average speed of the vehicles on that road gives the time. Generally, during this time, vehicles constantly come across a red light or green light as they come to the next traffic light. Sometimes vehicles speed up to avoid getting caught at a red light, and that's actually why they speed up.
Birds migrate in a V-shape. The reason for this is to ensure 60–70% energy efficiency.
When the birds in front of a flock flap their wings, they change the direction of the air flow up and down. In this way, the birds behind them can flap their wings without getting too tired, using less energy. Tired birds in front move to the back. A flock of birds follows this route, especially when migrating. When we look at the sky, the flocks of birds, which are very numerous, take a V shape; When looked at more generally, they are generally positioned in a hexagonal shape. The reason for this is to consume less energy. Because the hexagon has the smallest perimeter among hexagons, squares and equilateral triangles with equal areas, and thus, more birds can be together and the highest energy efficiency is achieved.
Mathematics is everywhere, we can gain new awareness by observing our environment, and nature actually knows what to do and creates the most harmonious forms thanks to mathematics.
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