An experiment to teach percentage arithmetic, Euclidean geometry, rational and irrationals and computational software tools in an interdisciplinary manner. We extensively used GeoGebra and plan to use Python later in this sequence of discussions. The exposition is conversational (in the spirit of Tarasov's Pre-Calculus). As a method of pedagogy, dialectics is subtly employed to enhance student's grasp of the subject.
A.M.- G.M. Inequality can be used to prove the existence of Euler Number. A fascinating journey from classical inequalities to invention of one of the most important numbers in mathematics!
RMO 2018 Tamil Nadu Problem 3 Sequential Hints and Solution. A number theory problem with a pinch from diophantine equation.
RMO 2018 Tamil Nadu Problem 2 Sequential Hints and Solution. A polynomial problem with seasoning from geometric progression.
RMO 2018 Tamil Nadu Problem 1 Sequential Hints and Solution. A beautiful geometry problem that uses properties of cyclic quadrilaterals.
Regional Math Olympiad (Tamil Nadu Region, 2018) Problems, Sequential Hints and Discussion.
The golden ratio is arguably the third most interesting number in mathematics. We explore a beautiful problem connecting Number Theory and Geometry.
Parity and divisibility are two interesting tools of elementary number theory. Coupled with an estimation with AM-GM inequality, we have excursion into the queen of mathematical disciplines.
This post contains RMO 2018 solutions, problems, and discussions. RMO 2018, Problem 1: Let \(ABC\) be a triangle with integer sides in which \(AB < AC\). Let the tangent to the circumcircle of triangle \(ABC\) at \(A\) intersect the line \(BC\) at \(D\). Suppose \(AD\) is also an integer. Prove that gcd\((AB,AC) >1\). RMO 2018, […]
A convex polygon \( \Gamma \) is such that the distance between any two vertices of \( \Gamma \) does not exceed 1. Prove that the distance between any two points on the boundary of \( \Gamma \) does not exceed 1. If X and Y are two distinct points inside \( \Gamma \), prove that […]
This is a beautiful problem from ISI MSTAT 2019 PSA problem 11 based on basic counting principles . We provide sequential hints so that you can try .
This is a beautiful problem from ISI MSTAT 2019 PSA problem 6 based on basic counting principles . We provide sequential hints so that you can try .
Try this beautiful problem from Geometry based on lengths of the rectangle from AMC-10A, 2009. You may use sequential hints to solve the problem.
Try this beautiful problem from AMC 10A, 2003 based on Probability in Divisibility. You may use sequential hints to solve the problem.
This is a beautiful problem from ISI MSTAT 2019 PSA problem 4 based on basic counting principles . We provide sequential hints so that you can try .
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1988 based on function. You may use sequential hints.
Try this beautiful problem from the Pre-RMO, 2017, Question 23, based on Solving Equation. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1988 based on Fibonacci sequence.
This is a beautiful problem from ISI Mstat 2019 PSA problem 17 based on limit of a function. We provide sequential hints so that you can try this .
This problem is a very easy and cute problem of probability from ISI MStat 2019 PSA Problem 18.