Mathematics the basic subject which everybody have studied in their School and college days. There are many people in the world who dislike mathematics than people who likes it. There are many reasons for it. And when we talk about Science and Engineering there can be nothing may be very little without dealing with mathematics. Since everywhere we find the application of Maths. And in engineering without trigonometry nothing could be done.

Four-Basic-Mathematical-Proofs
 
I have seen most of the time using the parameters of a circle in mathematical applications. When I asked people about these I came to know that only few knows them. As these things are very basic which everyone should know so I decided to write this article.

Four Basic Mathematical Proofs :

1 .What is pi  and how its value was calculated?

Pi(π) which you might have come across many times ?  Did you ever think of why we were using it? How it is known?  How its value was found, about million digits after decimal according to modern computers?
The answer is simple …
 
In the beginnings the mathematicians
 
First  found the perimeter ( circumference) of a circle ( a Pipe )  by some mean like using a thread or tape and that perimeter value was divided by the diameter of the circle then it was found to be a constant value of 3.1415..
 
And it was verified with different sized circles and found the final value a constant as 3.1415…which later named as ‘pi’( Greek Alphabet). And thus pi came into existence.
 
To know something more about ‘pi’ click here .
 

»  Perimeter of Circle

From the value of     pi (π)   =  Circumference/Diameter  
             → Circumference    =  π * d(diameter) = 2πr

2. How area of circle was determined ?

Circumference is found in terms of a proportionality constant.

 
Area-of-circle-proof
 

Now for the Area they (Mathematicians) with a logical thought arranged the pieces of circles in such a way that it forms a rectangle and that rectangle one side would be  of length radius (r ). And remaining side was easily found by circumference. That’s all followed the procedure same as for a rectangle resulting in  

 

             Area of Circle  =  r *πr= πr2





And this was the story behind in finding the Area of Circle.

 

Also Check : The most amazing and unbelievalble facts ever know

3. How pi radians = 180º (πc=180º) ?

In this case once again we consider Circle. A radian mean an Angle subtended by an arc of length equal to the radius of the circle.

Then in circle

proof-for-pi-radians-equal-to-180-degrees
 
Arc length is proportional to the angle subtended by that arc
 
Let us consider  Arc Length of    πr/2   α 900  ( one- fourth of a circle )
                         Arc Length of      r       α 1c  ( One radian length )
 

  So by ratio we get πc = 1800

That’s the trick behind radians and degrees relation..

 

4. How trigonometric values are calculated ?

Generally in school days the beginning of trigonometry the pupil are taught the values of trigonometric ratios for only 300 , 450, 600, 900,..etc. As these angles can be achieved by adjusting equilateral, isosceles triangles…

 
Tigonometric-ratio-calculation
 

For example finding the Sin (300). We first consider a triangle of side ‘a’ where we can achieve 300. We get 300 in equilateral Triangle by dropping a bisector from one side.

 
Now by relation   Sin(θ)   =  Opposite side/hypotenuse
                             Sin(300)  =  ( a/2)/(a) = 1/2
 

But for finding trigonometric ratio for any angle, First a  triangle  of that angle is made with the help of protractor and ruler and the sides are measured respectively using any device may be a ruler or anything and their ratio is taken  to get the value of that trigonometric ratio. 

And this was the method used by the people who had created trigonometric values.. This was done very easily using a machine which can measure the side lengths easily and that is nothing but a programmed computer which can calculate ratios of any angles.

These are the Four most things which you might not know in your school days.

If you like this tell your friends which are very basic to know. Any doubt on any part don’t hesitate to comment…





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