An Interesting Story about Snowflakes

    Apart from the fact that no two snowflakes are alike, there is a great symmetry in all snowflakes. The scientific world has not been able to understand scientifically that snowflakes have such a symmetry. When mathematicians examined the snowflakes under the microscope, all snowflakes under the microscope differed. The first studies about snowflakes date back to 1611's. Johannes Kepler was talking about a six-symmetrical shape of snow crystals in one article. 20 years later, Rene Descartes made a more detailed study and mentioned that hexagons also have different shapes.

    American Wilson Bentley, the first scientist to work on snowflakes in a microscopic environment, illustrated the following 800 different models as a result of the examination of the whole sample of snowflakes. Although Wilson Bentley is referred to as an American photographer, in three books he wrote - all of which depict the unique state of snowflakes - he mentions that snowflakes have a symmetrical structure. But a situation like this occurred. Wilson Bentley devoted his life to this question.

 “Can snowflakes have any other match? Does a snowflake have no other equivalent in the universe? "

    Bentley's life, unfortunately, was not enough to understand this. He studied many snowflakes, but they all had a different shape. But in 2006, scientists examined snowflakes falling with special microscopes in the city of Norwich, in the study, which was funded by the State and had a budget of 20 million pounds (46 million TL). Scientists, who started their studies in 2006, finally managed to detect a snowflake on December 3 that was exactly the same as the "Bentley snowflake". Just as follows….

    His words showed how he was affected by the snowflakes.

“I discovered under the microscope that snowflakes are miraculously beautiful. It is a great loss that this beauty is not seen by others and not given the necessary importance. Every crystal is a wonder of design and no design is ever repeated.

Apart from snowflakes, Bentley also photographed all forms of water such as clouds and fog. Called the snowflake man, Bentley was the first American to record raindrop sizes and also one of the first cloud physicists.

    The fractal geometry structure found in snowflakes is one of the most important evidences that show us the mathematical structure of snowflakes. Snowflakes are designed to maintain the Chaos theory according to the "Koch Order". These intertwined snowflakes that stretch forever. 

    The way snowflakes are formed is a branch of interest in chaos theory. Mathematically, each snowflake is formed by a fractal pattern of hexagonal shapes defined as n and r nested. Here n is the number of hexagons and r is its width. American Physics Professor Kenneth Libbrecht is another scientist doing research on this magnificent structure of snow crystals. Working at the California Institute of Technology, Libbrecht took real photographs of snowflakes, revealing the flawless beauty of God's art of creation.

 Exponential coronavirus growth

In these days of emergency for Covid-19 we are bombarded with conflicting news: alarmist messages on the one hand, hymns to normality on the other.

Coronaviruses are a large family of respiratory viruses that can cause mild to moderate illnesses, from the common cold to respiratory syndromes. The virus responsible for the current pandemic is a new strain of coronavirus never previously identified in humans. The contagiousness of this virus can be described through a statistical factor called R0.

The R0 value, or the "basic reproduction number", indicates the average number of infections directly caused by each infected individual since the beginning of the epidemic.  If R0 is 2 it means that on average each infected person will infect two people, so the higher the R0 value, the higher the risk of spreading the virus. If R0 is less than 1 (ie each infected infects less than one person), it means that the infection will tend to extinguish naturally because the number of infected will progressively decrease.

Initially, the spread of the virus could be described by an exponential function.

Exponential growth occurs when the growth rate of a mathematical function is proportional to the present value of the function. It appears initially characterized by a rather slow trend which then undergoes a sudden acceleration.

However, the type of growth previously illustrated do not accurately describe the trend of the situation as they are far from a realistic model.  A logistic function describes a curve whose growth is initially almost exponential, then slows down, becoming logarithmic, to reach an asymptotic position where there is no more growth.  Through this type of function it is in fact possible to observe how, in the case of an epidemic, the presence of healed and deaths decreases the R0, contributing to the slowdown, stabilization and resizing of the phenomenon analyzed.

In concrete terms, it is the behaviors that determine the changes. If lockdowns and restrictive measures had not been implemented, the peak of infections and the number of deaths would have been higher.

The graphs have helped to raise awareness of the extent of the phenomenon and also highlight the progress made by the company over the past few months.