Math - Page 2

All of us widely use calculators to perform mathematical operations. Obviously, these machines were invented by people, who determined their work according to the certain algorithms for quick count. In this article, we’re going to tell you about one of such algorithms. We’ll also show how you can extract square roots in column and you’ll see that the result of this operation can be received with arbitrary precision; we can find any digits number in its decimal representation, even if it turns irrational. Continue reading →

Quite often students have some problems with understanding the concept of the vector space basis, the linear dependence and linear independence of the vectors. In this article, we’ll try to explain these terms through simple things and examples. If you still don’t know what the vector is or don’t know how to do simple operations with vectors we offer you to watch our introductory video tutorial and then continue reading this article. Continue reading →

Solving math problem, especially in the high school, requires using a wide variety of theorems, lemmas, their corollaries. However, quite often students face misunderstandings during the math lectures, which bring troubles with solving these practical exercises.  But how to remember all the math stuff? Here we’ll offer you one of the methods. This interesting and useful technique deals with the association of the difficult problems with the simple things. Continue reading →

Every day each of us listens to music, views images on the Internet, turns on a radio station or a TV channel. All these processes have a common feature; it is their implementation involving the use of the same mathematical tool – the Fourier transform. It’s not an exaggeration to say that this is one of the most widely used mathematical discoveries, which is widely known in optics and quantum physics, radio astronomy, X-ray crystallography, voice recognition and PET (positron emission tomography) or MRI (magnetic resonance imaging), etc. Continue reading →

Having noticed the name of this article, many of you have already guessed what it’s going to be about. Also, here are additional hints: this short but quite famous formula may be seen on the T-shirts or cups worldwide; mathematicians and physicists name it “the greatest equation” in some scientific polls. Actually, we’re talking about the Euler’s identity, named to honor the great Swiss mathematician Leonhard Euler. So what exactly is great about this formula? Continue reading →

Humanity has always wished to make the life easier. Initially, people invented the abacus (primitive counting board) for easy calculations, then there was a calculator, next appeared some huge calculating machines and finally have come the computers. Now, almost any gadget has a calculator and all the complex calculations are performed with the help of the built-in functions of the textual and spreadsheet editors. Continue reading →

Recently, the term “catastrophe” started to appear not only in the newspaper articles and TV news but also in… mathematics! The first signs of the catastrophe theory emerged in the early 70s and provoked a revolution in mathematics. This achievement is only comparable to the invention of integral and differential calculus. While Newton’s theory allows investigating smooth, continuous processes, catastrophe theory provides a universal “recipe” for the study of abrupt transitions, ruptures and sudden qualitative changes. Continue reading →