First of all, sorry for my long absentee, sorry to Brilliant.org and also to all who tried to contact me. I wasn't much active because of being a bit busy, but I think it had a good reason, and it's that now I can be more helpful to all...
This note is for all people who like solving problems from Math Olympiads, and many times find it difficult to notice the key property that solves a problem.
I want to start this thing about spreading bash, because when I started studying for Math Olympiads, books were really helpful, I even shared what I knew about them. It was books, that helped me reach till the IMO training camp of India.
But when I went to IMOTC 2015, I learnt a lot of things and one of them was
I learnt a lot many things from seniors at the IMOTC 2015, and one of them was the use of Bash! It's a really very very useful tool for all who want to appear to Math Olympiads.
Bashing is solving a problem by methods which are not generally expected, for example solving a pure geometry problem by Coordinate geometry.
For bashing geometry, several known and widely used techniques are Coordinate geometry, Barycentric Coordinates, Complex numbers.
The reason why people do not generally motivate you to bash is because it just makes a problem, an actual problem that requires brain into just equations and calculations.
This means by bashing, we are just reducing the level of intelligence and knowledge required for solving the problem, and obviously nobody would promote that!
But guys, you know what? Even if people do not promote bash, they have to give full credit to a bash, ! Even in the Olympiads!
Coordinate geometry is a tool known to almost all people who appear for Olympiads, and it is a very useful tool. But sometimes it gets too tedious because of the many many equations and calculations.
But Complex numbers are actually coordinate geometry in a disguise, a disguise which is much shorter, sweeter!
The following comparison might highlight the importance of the use of complex numbers in Olympiad geometry.
If the table seems not readable, here is the original image
This note is part 1 of the bash-training I intend to start for Olympiads.
This note is intended to be a conversation, so share your views.
If this topic interests you, I'll be posting examples and tricks in complex-bashing.
Make use of the notes for enhancing your skills and
Help in this thing by sharing the new things you know!
Thank you for reading and there will be more coming!
Happy Problem Solving...
Interested in learning further?
Here's the Part 2 of this note