Here is a problem based on the area of triangle from ISI B.Stat Subjective Entrance Exam, 2018. Sequential Hints: Step 1: Draw the DIAGRAM with necessary Information, please! This will convert the whole problem into a picture form which is much easier to deal with. Step 2: Power of a Point - Just the similarity […]
Napoleon Bonaparte loved mathematics. Legend goes that he discovered a beautiful theorem in geometry. It is often called the Napoleon Triangle and has applications in math olympiad
Inspired by the book of Precalculus written in a dialogue format by L.V.Tarasov, I also wanted to express myself in a similar fashion when I found that the process of teaching and sharing knowledge in an easy way is nothing but the output of a lucid conversation between a student and a teacher inside the […]
The 3n+1 Problem is known as Collatz Conjecture. Consider the following operation on an arbitrary positive integer: If the number is even, divide it by two. If the number is odd, triple it and add one. The conjecture is that no matter what value of the starting number, the sequence will always reach 1. Observe […]
Suppose on a highway, there is a Dhaba. Name it by Dhaba A. You are also planning to set up a new Dhaba. Where will you set up your Dhaba? Model this as a Mathematical Problem. This is an interesting and creative part of the BusinessoMath-man in you. You have to assume something for Mathematical […]
Did you know that there exists a whole set of seven axioms of Origami Geometry just like that of the Euclidean Geometry? Instead of being very mathematically strict, today we will go through a very elegant result that arises organically from Origami. Before that, let us travel through some basic terminologies. Be patient for a […]
A beautiful journey in geometry through sequential hints! We take a (very) slow walk in Indian National Math Olympiad (INMO 2019) first problem.
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x. In the simplest case, the logarithm counts the number of occurrences of the same factor in repeated multiplication AMC 10A 2014 Problem 25 (or 12A Problem 22) is a […]
Natural numbers also have a natural geometry of their. This post is about how they look in practice.
Sometimes we are interested in the relative position of a point with respect to a triangle. Is it close to the vertices? Is it closer to one of the sides compared to the other sides? This brings home the notion of mass point coordinates or barycentric coordinates.