Notes in Mathematics

A Cheenta Newsletter

Hello friend,

Suppose there is a lion inside a round field (not at the center). The field has a boundary wall. You are standing outside the field. How can the lion catch you?

A running joke amongst mathematicians is this: the lion must invert!

**Inversion**is a very powerful geometric transformation. It converts lines into circles and vice versa.

Consider a circle with center O and radius 1. P be a point inside the circle. Draw OP and produce it toward P. Then the inverse of P, is a point P’ on the ray OP, such that OP*OP’ = 1. Clearly, if P is inside the circle P’ must be outside (OP*OP’ cannot equal to 1).

Learning about inversion quickly takes you to the world of Mobius Transformations. From a geometer’s point of view, this is the entry point of complex numbers. (Think about a complex number

**z**taken to**1/(conjugate of z)**).A fantastic introduction inversive geometry can be found in

**Yaglom’s Geometric Transformations.**

Price Change

Perhaps, most of you already know, that GST is commencing soon in India. We are aligning our course fee accordingly.

- Regular Mathematics Course (I.S.I., Math Olympiad, College):
**₹ 29,000** - Boot Camp:
**₹ 9000** - Informatics Olympiad / Physics Olympiad:
**₹ 29,000**

This fee structure is subject to change after 31st March 2017.

All the best!

Ashani Dasgupta

Cheenta

*vidya dadayati vinayam.*