Question Of The Week: How Does Light Travel?

May 15, 2009

Ever wondered how light travels? Or how many diagonals are present in a 100-sided polygon?!



Curious Topper readers posed these questions in Topper's Ask The Expert section, and received an answer within three working days.



Subject: Mathematics


Q. Please tell me the number of diagonals in a hundred sided polygon.


Posted by: Rakesh1994


A. For 'n' sided figure, if you join each point to every other point you will have total number of line segments given by[n(n-1)]/2]

We are dividing by 2 because line segments get repeated while counting. eg if we are counting a line segment from a point say A to another point C, then the same line segment gets counted when counting the number of line segments from C.


Also, this number contains all the sides along with the diagonals.

So the number of diagonals = total number of line segments - the number of sides = [n(n-1)/2]-n

For a quadrilateral, n = 4

So number of diagonals = [4(4-1)/2]-4 = 6-4 = 2

For a pentagon, the number of diagonals = [5(5-1)/2]-5 =10-5 = 5

Similarly, for n =100 number of diagonals = [100(100-1)]/2]-100 = 4850.





Subject: Chemistry


Q. Explain how water is purified.


Posted by: Sasha14


A. Water purification is the process of removing contaminants and other harmful micro organisms from a raw water source to make it suitable for various specific purposes like drinking and domestic consumption. There are various methods of purification of water like ultraviolet light, filtration, water softening, reverse osmosis, ultrafiltration, deionisation and powdered activated carbon treatment.