Length of Altitude in a right angled triangle

Find the length of the altitude of a right angled triangle where the sides are given by 'a' and 'b'.

Solution:: There are many ways to solve this problem....
Method :1 Similar Triangles Concept

Method 2 :: Trigonometric Approach

Method 3 :: Pythagoras Theorem

Method 4 :: Straight Lines Approach

Method 5 ::  Area of Triangle Approach

Division of a Circle

Divide a circle into 'n' parts and what is the geometry of each part?

Solution:: Suppose if a line is drawn through the centre of a circle then it will divide it into 2 equal parts and if you draw 2 lines at right angles passing through the centre then it will divide into 4 equal parts...and for 3 lines at 60° each then 6 parts and it goes on...

For odd number of parts what we have to do??

It's simple as it sounds because initially we used angle concept.. The same can be applied here also.. If we want 3 equal parts then the angle at the centre should be divided by 3 , for 5 parts the angle at the centre is divided by 5 and so on..

If you want to divide into 'n' parts then the angle at the centre is divided by 'n'.
The angle of each part is (360/n)° and all the parts are sectors with equal area.

Let's see this diagrammatically...

Concept of Relative Motion

What is relative velocity and how can we understand it in a easy manner.

Relative Motion of two bodies :: Suppose if two bodies are in motion and are separated by a  distance then the concept of relative motion is useful.

Relative Velocity:: Suppose A and B are two objects which are moving with velocities 

X m/sec and Y m/sec then we can apply relative velocity of the two bodies . we can analyse the motion of the bodies.

Even we have to look for the motion of the objects A and B whether they are travelling in a straight path (1-d)or not(2-d / 3-d).

In 1 - D plane the explanation can be understood like this...

Suppose if A and B are approaching each other then the distance between them decreases as because their relative velocity is more compared to their original velocities.

Suppose if A and B are travelling in the same direction then the distance between them increases or decreases depending upon the velocities X and Y.

The whole situation can be viewed as

Connecting Six Dots

Suppose 6 dots are given to you and can you draw different possible orientations using the dots.

Answer :: First thing which comes to your mind is circular arrangement......
                  Then any other different orientations you can think off...
                   Yeah you got one more right i.e.. A linear orientation
                   Common let's start thinking differently
                   Now the possible ways are to be identified.. I have some ways
                 

Along with this you can think of placing the dots in different planes 

SQUARE PLANAR STRUCTURE

Even we can think of this 3 dots in one plane and 3 dots in other plane

i.e., Triangular PRISM

General Physics :: Trajectory of a bomb dropped from an aeroplane

General Physics :::
Suppose a bomb is dropped from a plane onto a target will the bomb goes in a straight path or a curved path?? and why??

Answer :: The path travelled by the bomb is not straight but it is a curved trajectory because the motion has to be understood clearly before arriving at a conclusion.
 First as the bomb is dropped from the plane it has only velocity in the x- direction and acceleration due to gravity in the downward direction i.e.. y- direction.
 Now the motion is in 2 directions which are perpendicular to each other.
 Along x- direction the velocity doesn't change as there is no acceleration in that direction
 Along y-direction the velocity initially is zero and it goes on increasing with time because it behaves as a freely falling body.

 As the velocity is present in 2 perpendicular directions and one component of velocity keeps on increasing then the resultant velocity acts from a situation where it is closer to horizontal component to a point where it is shifting towards vertical component.

Viewing Angle of an object

Viewing angle of an object ::
                                                     In display technology parlance, viewing angle is the maximum angle at which a display can be viewed with acceptable visual performance.
                                                             (OR)
                                                    The maximum angular distance from in front of a screen to looking from the side without a change of brightness or colors.
                                                              (OR)
                                                     Viewing angle is directly related to contrast ratio.
Contrast ratio is defined as the ratio of the brightness of a white image to the brightness of a black image.

Normally from the centre of a monitor or TV viewing angle is 140°,Contrast ratio 250:1
If you are displaced 70° from the centre then the contrast ratio becomes 10:1 or 5:1
(70° from the centre means move aside from centre to one end where you can view the screen).

Viewing angle for an eye can be understood from the following picture

How to think better and why it is needed

Let's start like this.

What is the reason that we are being educated? How the education help us in achieving better things??

The reason we learn many things every day in and day out is that when we learn about the inventions or discoveries then our brain starts ticking and the process of learning kick starts. When you are fascinated with an idea or an approach that led to the evolutions then you think what am I going to do after I grow big? How should I live and how can I create something big and useful to the people.

Suppose if a scientist thinks that after sending a rocket into space is enough then we cannot have this kind of visual experience to our eyes what's going on around the world each and every second, Even if a chemist is satisfied after finding a cure to a diseased tissue in the body then all so we face a problem because there are many tissues in the body and whenever a particular tissue is hurt we need to cure that one...so..

When we desire something then we can become something. If not then we will be remaining as we are and what we are. We have to aim and achieve big then atleast our desires will be fulfilled. We are living in a society where we interact with different kinds of people every day.

The amount of work we do is directly related to the amount of problems we come across in our lives and is some way its related to number of things we want to simplify.

LET'S GROW BIG AND THINK BIG.