The Collatz Conjecture is one of the Unsolved problems in mathematics, especially in Number Theory. The Collatz Conjecture is also termed as 3n+1 conjecture, Ulam Conjecture, Kakutani’s Problem, Thwaites Conjecture, Hasse’s Algorithm, Syracuse Problem. Statement: Start with any positive integer. • Halve it, if it is even. Or • triple it and add 1, if…

# February 2011

Topic Beta & Gamma functions Statement of Dirichlet’s Theorem $ \int \int \int_{V} x^{l-1} y^{m-1} z^{n-1} dx dy ,dz = \frac { \Gamma {(l)} \Gamma {(m)} \Gamma {(n)} }{ \Gamma{(l+m+n+1)} } $ , where V is the region given by $ x \ge 0 y \ge 0 z \ge 0 x+y+z \le 1 $ .…

In this article we will learn about the Lindemann Theory of Unimolecular Reactions which is also known as Lindemann-Hinshelwood mechanism. It is easy to understand a bimolecular reaction on the basis of collision theory. When two molecules A and B collide, their relative kinetic energy exceeds the threshold energy with the result that the collision…

Puzzle Two women were selling marbles in the market place — one at three for a Rupee and other at two for a Rupee. One day both of then were obliged to return home when each had thirty marbles unsold. They put together the two lots of marbles and handing them over to a friend…

In 1904, the french Mathematician Henri Poincaré (en-US: Henri Poincare) posed an epoch-making question, which later came to be termed as Poincare Conjecture, in one of his papers, which asked: If a three-dimensional shape is simply connected, is it homeomorphic to the three-dimensional sphere? Henri Poincare – 1904 So what does it really mean? How…

Cosmic Rays or Cosmic Radiation Soon after 1900 it was shown by scientists that the air in an ionisation chamber, which was completely protected against penetration of α , β and γ rays, by surrounding it with thick lead walls, was still conductive; and it was thought that the inns causing this conductivity were produced…

Lord Rayleigh made an attempt to explain the energy distribution in black body radiation, which was completed by Jeans in 1900. The results obtained by then are known as Rayleigh-Jeans’ Rules on Black Body Radiation. The law covering these rules is called Rayleigh Jean’s Law. The black body emits radiation of continuously variable wavelengths right…

Various workers tried to explain the problem of energy distribution in black body radiation and finally the problem was successfully solved by German Physicist Max Planck. Before him, German Physicist Wilhelm Wein and British Physicist Lord Rayleigh & James Jean have tackled this problem and have given important laws. In fact, the work of their…

Albert Einstein This name need not be explained. Albert Einstein is considered to be one of the best physicists in the human history. The twentieth century has undoubtedly been the most significant for the advance of science, in general, and Physics, in particular. And Einstein is the most illuminated star of the 20th century. He…

We all know that the derivative of $x^2$ is 2x. But what if someone proves it to be just x?

Consider a sequence of functions as follows:- $ f_1 (x) = \sqrt {1+\sqrt {x} } $ $ f_2 (x) = \sqrt{1+ \sqrt {1+2 \sqrt {x} } } $ $ f_3 (x) = \sqrt {1+ \sqrt {1+2 \sqrt {1+3 \sqrt {x} } } } $ ……and so on to $ f_n (x) = \sqrt {1+\sqrt{1+2 \sqrt…

This is one of the top mysteries of universe.