Funkcja logarytmiczna

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logarithmic function

A lot of things that surround us in the world we believe to be totally normal and not having links with the complex science. People are thinking so to a large error, and simply to take a normal snail who has shell.

Snail is animal, which belongs to the molluscs. He also called stomachfoot. Apart from the antennae, an exploratory feature of nearly every worm is its shell (of course, not every individual has it). Shell has a protection function and its owner is like a cozy cottage. However, whether such a shell may have links with mathematics and more specifically with logarithmics? It has and is very high.

When we cut shell along, we can easily notice that the chambers are wrapped in a regular manner. The further from the center of the shell, the fragments of cells (resembling parts of districts) are becoming a larger radius, and are making more and more simple. That description more understandable for people who have not yet known the logarithmic spiral. These chambers coincide with a flat curve, which intersects at an angle of equal standing and all the outgoing ray from inside the shell. On the same basis there is a logarithmic spiral said earlier.

In the logarithmic spiral, which is called the center of the shell, here called spiral pole. Please specify more abovementioned property geometric spiral. A few sentences ago was mentioned, is that, in a further spiral loops are becoming more erect and this shows that successive loops, are becoming increasingly distant from the pole. It is also worth mentioning that this distance is growing exponentially. Another feature of this spiral is that the curve of the road from any point on it to the pole is proportional to the distance from a pole, and inversely proportional to the cosine of angle, which it determines the spiral. Going from a specific point on the spiral in the direction of its expansion, its pole goimg to infinite number of times, never reaching it. The reason for this that we will always be away from the pole.

Besides the shell snails, logarithmic spiral occurs in very many places in our world. Starting with little, after the larger and ending with huge. Such as the creation of small flying insects have a relationship with the logarithmic spiral, as the insect flying into the light, keeps constant angle between the flight path, a light source. The television often hear about disasters, which led to tropical cyclones or hurricanes. But perhaps few who know that their arms are arranged on the spiral shape of log. The shapes of these take the spiral arms of spiral galaxies.

In order to guess what is the gateway connecting the logarithmic spiral from the logarithmic function, simply look at the same design spiral. There is also a symbol of "e", which is the foundation of the natural logarithm. For the logarithmic functions, logarithms are values. The function of this we define as follows: function f(x) = logax, where a>0 and x>0 .

Logarithmic function has many properties. An important one is that for each and belonging to R/{1} the function of a continuous basis in the collection of R. Another important property of functions is as follows: for each and belonging (1; infinity) is a growing feature in the collection of R , while in the (0,1) is decreasing in the collection of R.

On such a simple, they are snails, which communicate with the logarithmic function, you can show that many things can explore and discover these you will never end. Never we think, but that does not benefit may be associated with the other, because it suggests to us an instinct. To find the logarithmic spiral first mathematician had to watch the shells snails, or watch a galaxy, or look at the phenomena of nature such as cyclones. The proposal raises a simple, always worth learn from all fields of science and look at the things that we are not important. Looking at the tiny part of the world know not go to the end, not knowing the rest.