Problems of modern mathematics and mechanics

 

Nowadays mathematics becomes more and more important in a man’s life. Modern world brings new technologies, new way of thinking, new ideas, which are all based on the principles of mathematics. People may not even notice it, but a successful person will not be able to live in the society without any knowledge in Mathematics. So it is very important to understand which way mathematics is developing at that moment. I’d like to tell about the rapidly developing branch of geometry, which now has a lot of unsolved problems in spite of being widely used.

At the end of the last century it was developed the branch of geometry which deals with the fi nite sets of points in the plane. This is a problem of alpha-shapes.

In 1970s, the planar convex hull algorithm was generalized; it found the shape of a finite point set. This algorithm was based on the pivoting the line segment and sometimes this approach caused the mistakes. However, the difference between the logic structure of algorithm and the numerical evaluation of its geometric primitives makes difficult to turn the algorithm into correct software. Any mistake causes geometrical constructions which do not exist. Thus there are a lot of cases, for example, three collinear points, and all of these cases must be examined.

The main important structures in this branch of geometry are the Voronoi diagram and the Delaunay triangulation, named after two Russian mathematicians. A great number of algorithms of their constructions are known today, but it’s very important and difficult problem to find faster and more efficient method. These two structures are very useful and have a high significance value. In climatology, Voronoi diagrams are used to calculate the rainfall of an area, based on a series of point measurements. In epidemiology, they can be used to correlate sources of infections in epidemics. One of the early applications of Voronoi diagrams was implemented by John Snow to study the 1854 Broad Street cholera outbreak in England.

A great result in this sphere has been already achieved, but still there are directions that remain largely unexplored. Finally, there are ideas of creating shape spaces from alpha complexes which have yet unrealized potential. Today the range of application and development of this branch is very wide: pattern recognition, digital shape sampling and processing, structural molecular biology. It is applied in ecology, materials science, chemistry and even in mathematical statistic.

 

 

 

The art in man’s life

When we talk about art what we imagine? Probably we remember such names as Picasso, Dali, Chopin or Tchaikovsky. And if we think about technology we imagine maybe a smartphone or a computer. Throughout history, technology has provided artists with new tools for expression. Nowadays, these two disciplines are interlinked more than ever, and technology becomes a fundamental force in the development and evolution of art. Naturally entirely new art forms are evolving as well. More and more artists are pushing the boundaries of art, looking outside of what's perceived as " traditional" to incorporate other aspects into their work. Art is becoming less static, taking up many new different shapes. Artist Ollie Palmer has created a machine to control the way synthetic pheromone directs ants - hoping this way to stage an 'ant ballet'.

Digital technology and modern techniques have had the strongest impact on the art of painting and drawing. In the past, painting and drawing depended on the artist’s skills in using his traditional tools - the brush, the pencil or pastels. The artist, through conventional and calculated steps, was in control of the density of color, different hues, the realism or abstraction of his work of art. Artists today operate with clicks of the mouse, video tools and digital colors. Contemporary art has been greatly influenced by the astonishing progress in the introduction of new, more attractive and convenient materials that artists could work with. Artist could focus more on contents of theirs works, creativity and developing delightful ideas. In other words, artists today have an enormous variety of techniques. Possessing this vast quantity of tools and potential must be accompanied by a comprehensive and in-depth knowledge of every detail of these tools and their capabilities, so as to enable the artist incarnate all his fantasies via the designated tool, using the best and the shortest way which is possible. Therefore artists need to improve their skills and understand these techniques well in order to use all opportunities they offer.

But on the other hand there are many people who think another way. One young artist from Japanize writes, that she is still learning the aspects of Digital painting and she thinks, painting digitally makes any Art work easy, efficient, fast and convenient, due to Undo / Redo commands and effects which you cannot use in traditional painting. In addition, you can paint digitally almost everywhere. But as I think digital painting is not easy as it seems, it is not just pressing any button or using a command. A digital artist must have deep knowledge in art in order to create painting comparable to traditional art.

Apparently digital technologies are changing the art very much. Firstly throughout history and until recently, the public was merely a passive observer. Today, in our modern world, everyone can create something. Digital painting tutorials are all out on the internet. You can find them easily and start your new hobby, digital painting. They are presented through a video where each step is demonstrated. All you have to do is to carefully watch the video and remember the steps and strategies that are showed by the expert. A lot of people don’t understand that it is not enough to make a really art. However, because it is now easier to create, we see a lot of strange things being created and exposed. A huge problem is that, as a result of so many new tools and techniques, we may lose our sense and ability to evaluate what is great art. But today, technology, and especially computer technology, develops and there will always be those who will experiment.

 

⇐ Предыдущая12345Следующая ⇒

Поделиться: