How to Solve Cubic Equations
On the last Pythagorean Theorem Day (12/16/20), I was thinking about the solution of a Cubic Equation (the one in the picture). Do you know that they do not teach students how to solve the cubic equations whose formula has been known to us for about 500 years? But, do you know the reason? It is because it is not that simple to apply. It requires the knowledge of complex algebra. If you check online there is a lot of information, however it is all spread around in bits and pieces. In this article, I have shown how to derive the cubic formula, together with the introduction of basic complex algebra topic, and I present the solutions to several different problems by following a step by step procedure. In this regard, this will serve as a good source for those who would like to learn about the cubic formula and how to use it.
The link to the paper can be found on the
There are certain key steps that a young entrepreneur has to take so as to progress in the business world. Some of them may seem to be straightforward, yet still be overlooked. I would like to point out those which seem to be important to me based on my experiences in the business world.
With an intent to give you an extra motivation, I would also like to elucidate how STEM (Science, Technology, Engineering, Mathematics) Education can be beneficial to acquire these attributes of a young entrepreneur.
Physics in BUSINESS: IMPORTANCE OF CAUSE, COLLABORATION, COMMUNICATION, CONTINUITY
The curiosity of human mind set the foundations for the SCIENCE and the laws of physics emerged in our lives. With an endless eagerness and enthusiasm, we have observed EVERYTHING with an ultimate goal to unravel the secrets hidden within the recesses of the very UNIVERSE. And, we still and will always be in the quest for UNDERSTANDING what yet seems mysterious.
Speaking of Physics, it may be better to start off with elucidating the process of questioning, and understanding how physicists approach a problem. As opposed to the conviction of many people that great physicists like Isaac Newton, Albert Einstein, Paul Dirac, Richard Feynman, ... are great since they could solve very complex problems, they are actually great since they were able to see the easy-to-handle pieces within the most intricate structures. Great Minds in Physics always tend to explain the concepts with the most basic terms and in the end when you finish listening to their lectures and/or reading their books, you are amazed by how everything, which seemed quite complicated at a glance, turns into something easy to grasp.
If you can not see the SIMPLE, you can not handle the COMPLEX.
"If you can't explain it simply, you don't understand it well enough." Albert Einstein 
Here in this blog post, I present to you a complex-looking Physics Problem and solve it by following the SIMPLE -----> COMPLEX approach. I have created this particular physics problem so as to convey highly important messages (through analogies) to entrepreneurs, to physics and engineering majors who would like to pursue their careers in business, and to other avid readers.
See yourself what a Physics Problem can tell us more than expected!
Here is a very powerful example from real world which explains how and why teamwork works ...
It is so often that we disregard the importance of having a good team of dedicated employees in our business. Even in evaluating the performance of our staff, we only consider individual accomplishments and failures, lacking the assessment of the holistic structure. However, it should be remembered that the true culmination of a business can only be achieved through an efficient and effective workforce of a team. The power of a good team is actually superior to that of the sum of contributions from each individual forming that team. Here, I present a very enlightening real-life example which will definitely substantiate our assertion.
Physicist, STEM Enthusiast, Business owner with a great aspiration to learn from and share with everybody ...