The most beautiful equation in mathematics is: It is often attributed to Swiss Mathematician Leonhard Euler. Interestingly enough, this is nothing but a statement about rotation! 23 is a shorthand way of writing 2 × 2 × 2. But this is very very different from what means. Mathematicians use this trick over and over again. They overload notations. In fact is a […]
This is a video in which you would learn Graphing an Integral. This is the third part of the video. It is taken from ISI B.Stat 2005 Problem 2. Watch, learn and enjoy the video.
This is a video in which you would learn Graphing an Integral. This is the second part of the video. It is taken from ISI B.Stat 2005 Problem 2. Watch, learn and enjoy the video.
In I.S.I.'s B.Stat Entrance 2005, the following problem appeared: Problem: Let $$ f(x) = \int_0^1 |t-x|t dt $$ for all real x. Sketch the graph of f(x). What is the minimum value of f(x)? Here is the first installment of a discussion on that. Part 1 Part 2 [button url="https://cheenta.com/graphing-an-integral-part-2/" class="" bg="" hover_bg="" size="0px" color="" […]
In this post, let's learn about the multipole expansion of a potential with the help of a beautiful problem and find the constant.
TIFR 2015 Problem 7 Solution is a part of TIFR entrance preparation series. The Tata Institute of Fundamental Research is India's premier institution for advanced research in Mathematics. The Institute runs a graduate program leading to the award of Ph.D., Integrated M.Sc.-Ph.D. as well as M.Sc. degree in certain subjects. The image is a front […]
Let's learn the inductance of a toroid with the help of a beautiful problem. Show that the inductance of a toroid of rectangular cross-section is given by..
TIFR 2015 Problem 4 Solution is a part of TIFR entrance preparation series. The Tata Institute of Fundamental Research is India's premier institution for advanced research in Mathematics. The Institute runs a graduate programme leading to the award of Ph.D., Integrated M.Sc.-Ph.D. as well as M.Sc. degree in certain subjects. The image is a front […]
We have indicated the source of these problems. Do not look up solutions. It is fun to try it yourself or see others try them live! Let P be an interior point of triangle ABC and AP, BP, CP meet the sides BC, CA, AB in D, E, F respectively. Show that \( \frac{AP}{PD}=\frac{AF}{FB}+\frac{AE}{EC} \) […]
The brightest meteor shower of the year is here! From December 14th to 17th, look at the North-Eastern sky above the Gemini constellation. (It won't be prominent in Southern Hemisphere, so our students in Singapore and Australia will miss it). In India, try moving to a less polluted region (and also out of the glare zone […]