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# Cheenta. Passion for Mathematics.

Pause for a moment! Think…

Suppose ABC be a triangle with side lengths 3, 4, 5.

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We are building a beautiful seesaw. It has three seats at A, B and C respectively. The fulcrum of the seesaw is at incenter of the triangle.

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What masses should we put at A, B and C to balance the seesaw?

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#### What is Cheenta?

Cheenta delivers outstanding programs in Mathematics for Olympiads, I.S.I. & C.M.I. Entrance and College.

Since 2010, we have worked with hundreds of students from India, United States, UK, Australia, Singapore and Middle East

All of our classes are delivered exclusively live and online. Our main center in Calcutta (India) office hosts a reading facility for advanced learners.

#### Who are Teaching?

We have ex-Olympians and outstanding researchers who teach out of love for the subject.

In India: Indian Statistical Institute, Chennai Mathematical Institute, IISER, TIFR, Calcutta University, IIT KGP

Outside India: the University of Wisconsin Milwaukee (USA), University of North Carolina (USA), St. Louis University (USA), IMPA (Brazil), E’Cole (France)

Admission to a Cheenta program is highly selective. The prospective student must first go through a trial class.

Our courses are significantly more intense than regular school or college programs. Apply only if you are thrilled by the beauty of mathematics.

Math Olympiad, I.S.I. Entrance and College Mathematics candidates form the core student body of Cheenta.

## A Proof from my Book

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...

## ISI BStat 2018 Subjective Problem 2

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 of $$\triangle QOS$$ and $$\triangle POR$$ By the...

## ISI BStat 2018 Subjective Problem 1

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. The picture looks...

## Napoleon Triangle for Math Olympiad – Cheenta Open Seminar

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

## A Math Conversation – I

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 discussion between...

## The 3n+1 Problem

This 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...

## The Dhaba Problem

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...

## The Organic Math of Origami

Did you know that there exists a whole set of seven axioms of Origami Geometry just like that of the Euclidean Geometry? The Origami in building the solar panel maximizing the input of Solar Power and minimizing the Volume of the satellite Instead of being very...

## Excursion in Geometry – INMO 2019 Problem 1

A beautiful journey in geometry through sequential hints! We take a (very) slow walk in Indian National Math Olympiad (INMO 2019) first problem.

An advanced program in Mathematics for brilliant school students. Taught by ex-Olympians and active researchers in Mathematics.

By the way, are you interested in the fourth dimension? Here is a beauty to behold! Tetracube created the beautiful image of the Omnitruncated tesseract.

# Training brilliant minds.

Since 2010.

Cheenta has worked with brilliant maths and science olympiad students from over 6 countries. Our courses are specifically geared toward students with an exceptional interest in Mathematical Sciences.

Outstanding mathematics program for deserving school students.

For children who are starting out in Mathematics and Science.

#### I.S.I. & C.M.I. Entrance

For B.Stat and B.Math entrance at Indian Statistical Institute, B.Sc. Math at C.M.I. & KVPY.

#### College Mathematics

For I.S.I. M.Math, Mathematics Subject GRE, TIFR; Groups Analysis, Topology and more

# I.S.I. & C.M.I. Entrance

B.Stat, B.Math Entrance at I.S.I. and B.Sc. Math Entrance at C.M.I. require special training in Number Theory, Geometry, Combinatorics and Algebra (apart from regular High School topics).

Problems from standard topics such as Calculus, Trigonometry or Coordinate geometry can significantly tricky.

Number Theory, Combinatorics, Algebra, and Geometry at Olympiad standard are both necessary and useful components of this course.

#### Regular High School Topics

Advance problems from Calculus, Trigonometry, Coordinate Geometry and Algebra are bread and butter for handling more complicated ones.

# College Mathematics

An advanced program for College Students as well as adults interested in modern mathematics. This program is useful for I.S.I. M.Math Entrance, Subject GRE, IIT JAM and similar entrances.

We work on Groups, Rings, Fields, Linear Algebra, Analysis, Topology and other advanced topics. As usual problem solving remains the driving force of the program.

The hyperbolic 3 space may come up in this course. Behold this beautiful Hyperideal Honeycomb created by Royce3 (under creative commons).

#### Continuing Education

Many adults, who are pursuing jobs or industry, have taken this program. A curious mind, coupled with a determination to take up challenges is sufficient.

This program is for the true math fanatic, who yearn to understand the anatomy of ‘reason’ a little better. Advanced problem-solving session every week!

# What is Torsion?

Geometry is everywhere. Enjoy this bit.

# Testimonials…

“a wide range of mathematical topics, and every lesson is packed with insights and methods. We are extremely pleased with the difference he has been making. Under his tutelage Sam has secured several gold awards from the UK Mathematics Trust (UKMT)and Scottish Mathematical Council (SMC).”

Jayanta Majumdar

Glasgow, UK

“Shuborno has been studying under Ashani from last one year. During this period, we have seen our son grow both intellectually and emotionally. His concepts and approach towards solving a problem has become more mature now. Not that he can solve each and every problem but he loves to think on the tough concepts. For this, all credit goes to Ashani, who is never in a hurry to solve a problem quickly. Rather he tries to slowly build the foundation..”

Shubrangshu Das

Bangalore, India

“Our experience with Cheenta has been excellent.  Even though my son started in Middle School, they understood his Math level and took personal interest in developing a long-term plan considering his strengths and weakness areas. Through out the semester courses they have nourished him with challenging problems and necessary homework.  His guidance has helped my son to perform well at competitions including USAJMO and others. He has grown more confident in his math abilities over the past year and half and is hoping to do well in the future.

I am impressed with their quality and professionalism.  We are very thankful to Cheenta and hope to benefit from them in the coming years.  I would strongly recommend them to any student who wants to learn Math by doing challenging problems, specially if they are looking for Math than what their school can offer.”