THE GOLDEN RATIO IN NATURE

When a Fibonacci number is divided by the number before it, it converges to the golden ratio, an irrational number (1.6180339887).

                                             

                               

The familiar logarithmic spiral appears when the golden ratio is applied as a growth factor.

Places where we see the golden ratio in nature

 When the spiral folds in the structure of snails are transferred to a piece of paper, a rectangle emerges. The ratio of the sides is equal to the golden ratio

this shape is called the " golden rectangle ".

When the number of female bees living in beehives is divided by the number of dronesn the golden ratio emerges.

     

Although snowflakes are generally too small to be seen, the proportion of various protrusions always gives the golden ratio in the short and long branches that make up the snow crystal.

No two snow crystals are a like. And all of them have hundreds of golden ratios.

HUMAN AND THE GOLDEN RATIO

 Like everything in nature, there is a golden ratio in the human body.

Thanks to the golden ratio, the human body is very large when viewed from an aesthetic point of view.

You will see that many organs in our body have values at or close to the golden ratio. When we look at the ideal human face used by sculptors or painters, we see these proportions everywhere.

            

* Fingers have three knuckles. When you look at the knuckles, the ratio betweenthe first two knuckles and the length of your finger is the golden ratio.

* The ratio between middle finger and little finger is the golden ratio.

* The ratio of the wrists from the elbow to the distance between the fingers is the golden ratio.

* There is a golden ratio between the length and width of the face.

* There is a golden ratio between mouth and nose width.

* The width of the nose and the width of the nostrils is the golden ratio.

* Golden ratio is the ratio of the distance between the eyebrows of the pupils to each other.

* There is a golden ratio between the width and length of the upper two teeth.

* Apart from these, the lengths of the trachea parts, which are divided into two as right lung and left lung, are not equal. It is shorter because of the heart on the left. When you compare the two, the golden ratio is revealed. This rate is encountered even when looking at the DNA structure.

                         
                                             

           

 INTERESTING INFORMATION

A cicada we often remember for their laziness!

What makes them mathematically interesting is that they know how to count numbers. Cicadas coexist and use prime numbers to avoid the risk of being easily preyed.

                                                                                                                          

The reason they instinctively organize their life cycles according to prime numbers is that 13 and 17 are prime, and the states of two separate insect groups that emerge at the same time are only possible once every 221 years, which is the common coefficient. 13 and 17.

So the prime numbers are directly related to the survival of the cicadas.

Plants and Math!

Plants use special angles for their leaves to receive maximum sunlight by dividing 360 degrees into two parts. Golden ratio (1.618):

Its wide angle is 222.5 degrees. (This number is also the number of days the planet Venus orbits the sun.)

Its small angle is 137.5 degrees. (This number is also

   Fine structure constant in physics with respect to impact.)

                         

        

                                                                    

büşra.ea/Şehit Emre Karaaslan Vocational and Technical Anatolian High School / Eda Acar / Bursa