Notes in Mathematics
A Cheenta Newsletter
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.
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!
vidya dadayati vinayam.