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# Cheenta. Passion for Mathematics.

Pause for a moment. Let us divide letters by letters!

What if you wanted to divide the base by an exponent? This situation comes up quite often in Elementary Number Theory. Consider the following equation:

$$\displaystyle{ k! + 48 = 48 \times (k+1)^m }$$

Can you show that k divides m? The answer is hidden somewhere in our library articles.

#### 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.

# @Ramnath

a latex enabled social network for mathematicians of future!

## Test of Mathematics Solution Objective 401 – Trigonometric Series

Summing a sequence of trigonometric ratios can be tricky. This problem from I.S.I. Entrance is an example.

## Understanding Simson Lines

Simson lines arise naturally. Imagine a triangle as a reference frame. Let a point float on the plane of the triangle. How far is the point from the sides of the triangle?

## What if a Simson Line moves!

A beautiful curved triangle appears when we run along the circumference! A magical journey into the geometry of Steiner’s Deltoid.

## Dudeney Puzzle: A Tale from Pythagoras to Dehn – Part II

Remember the Dudeney puzzle introduced in the last post. We have ended with the question “Why four?”…We will be revealing the reason in this post.

## 2016 ISI Objective Solution Problem 1

Problem The polynomial $$x^7+x^2+1$$ is divisible by (A) $$x^5-x^4+x^2-x+1$$             (B) $$x^5-x^4+x^2+1$$ (C)   $$x^5+x^4+x^2+x+1$$          (D)   $$x^5-x^4+x^2+x+1$$ . Also Visit: I.S.I. & C.M.I Entrance Program Understanding the Problem: The problem is easy...

## Dudeney Puzzle : A Tale from Pythagoras to Dehn

" Take care of yourself, you're not made of steel. The fire has almost gone out and it is winter. It kept me busy all night. Excuse me, I will explain it to you. You play this game, which is said to hail from China. And I tell you that what Paris needs right now is to...

## Spiral Similarity of cyclic quadrilaterals

Pedal triangles lead to spirally similar cyclic quadrilaterals in any triangle. A half turn and dilation by 1/8 create the new quadrilateral.

## I(N)MO Camp 2018-19

30 sessions, 45 hours, a team of 6 faculty members. Cheenta is presenting a camp for Indian National Math Olympiad (leading to International Math Olympiad). We begin on 14th December 2018 and it will run up to 19th January 2019.

## Test of Mathematics Solution Objective 398 – Complex Number and Binomial Theorem

Try a beautiful problem from complex numbers and geometry. It is from I.S.I. Entrance. We have created sequential hints to make this mathematical journey enjoyable!

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.”