This is proof from my book - my proof of my all-time favorite true result of nature - Pick's Theorem. This is the simplest proof I have seen without using any high pieces of machinery like Euler number as used in The Proofs from the Book. Given a simple polygon constructed on a grid of […]
Advanced mathematics classes now have an add on - Cheenta students will have access to One-on-One mentoring (apart from regular group classes).
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 […]
The solution will be posted in a sequential hint based format. You have to verify the steps of hints. Sequential Hints: Step 1: Solution set of sin(\(\frac{x+y}{2}\)) = 0 is {\({x + y = 2n\pi : n \in \mathbb{N}}\)} - A set of parallel straight lines. Step 2: Solution set of |x| + |y| = […]
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 […]
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.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2000 based on Algebraic Equation.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2000 based on Arithmetic and geometric mean with Algebra.
Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2000 based on Sequence and fraction.
Try this beautiful problem from the American Invitational Mathematics Examination, AIME I, 2000 based on Logarithms and Equations.
Try this beautiful problem from the American Invitational Mathematics Examination, AIME I, 1996 based on Finding the smallest positive Integer.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1996 based on Amplitude and Complex numbers.
Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 1996 based on Roots of Equation and Vieta's formula.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Tetrahedron Problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1995 based on Triangle and integers.
Try this problem from Singapore Mathematics Olympiad, SMO, 2018 based on Functional Equation. You may use sequential hints if required.