Today was more NES, more protests, more HC Verma electrostatics problems, and much more of Batch 1. We had our first class of module IV today, and our modules have grown much bigger, and much more comprehensive after the pattern change of JEE last year. The batch is a great mix of comedians, philosophers, time-passers and dominantly, geniuses.
We had our Physics-Mathematics today, and both teachers are excellent at explaining and entertaining, although the Physics teacher seems to overdo it a bit. But one thing has changed for the worse, and that is our Chemistry teacher.
Our last teacher, Mr. Purushottam, shared a great tempo with our batch. He is the best chemistry teacher at our centre. Ms. Monica, our new teacher, is difficult to adjust with (you can imagine our problems because she has to write 256 and 16 like class III children one below the other to add them). We demanded the authorities to change our teacher back to Mr. Purushottam, but they did not pay any heed. Then we decided to write a petition with signtures of about 15 students and fax it to Chennai (head office of Brilliant Tutorials). But I am apprehensive of their decision.
Back to the world of computers, check out this cool
mp3 which recites digits of pi. Also download
Celestia, with which you can explore the universe in a 3D simulation, and visit planets, stars, constellations, sattelites etc. A really addicting game called
Pocket Tanks which is based on projectile weapons and tanks is available
here.
Today I realized that LCM is defined not only for rational numbers, but also for irrational numbers. Here I quote the proof that (2)½ is an irrational number:
Let (2)½ be a rational number such that (2)½=p/q, where p is an integer, q is a natural number, and p/q is in its lowest form
or, p²=2q²Thus p² is an even number, so p is also an even numberLet p=2kthus, 4k²=2q²or, q²=2p²Thus q² is an even number, so q is also an even numberThis contradicts the assumption that p/q is in lowest form, since the common factor 2 exists.This completes the proof.No questions today either, so you'll have to wait till tomorrow. Till then, ciao.
Today's Formula:
Lowest common multiple of two rational numbers p/q and P/Q is given by
LCM(p/q, P/Q)=LCM(p,P)/HCF(q,Q)