I see mathematics as an absolutely separate world, with its own rules and laws. A lot of people believe that just knowing the rules is enough to be successful in this world. However, in my opinion, it is necessary to understand these rules to be really successful.
What I am trying to say, is that the knowledge of mathematical formulas can make you good in maths and you will be able to solve the standard problems. But just like in our world, sometimes there may occur problems which you cannot solve by using a template. That’s where your logic and understanding of the problematic area make all the difference.
In this article I will try to briefly explain the meaning of the Pi value. Pi is widely used in mathematical formulas. Circles, spheres, angles etc. Everyone knows, that its approximate value is 3,14. But where did this value come from? What does it mean?
Pi – is an amount of radians in 180 degrees. 1 radian is 180/Pi, which is approximately 57,3 degrees. Actually Pi is a half of a circumference of a circle with radius 1. So, by using this value we can show absolutely any angle.
For example:
180 degrees = Pi
90 degrees = Pi/2
360 degrees = 2Pi
We can use Pi in trigonometric equations as well. For example:
sin (Pi/6) =1/2 (Pi/6=180/6=30 degrees)
tan(Pi/4) =1 (Pi/4=180/4=45 degrees)
Why cannot we just use degrees? Well, it is fine to use degrees, if you are working with angles; however there are some aspects where it is easier to use Pi, but let’s skip them for now. The thing I would like to discuss is the usage of Pi in formulas of the circle and sphere – these are the most frequent situations where we meet this value.
In a circle Pi is a ratio of circumference to diameter. So, we can determine Pi as c/d, where c is circle’s circumference and d is its diameter. Let’s go through the simplest formula.
The formula of circumference is 2*r*Pi (r is a radius). 2 radiuses is nothing but a diameter, so we get a formula d*Pi. I have already said, that is Pi=c/d. If we put this equation to our formula, that’s what we get: d*c/d and as a result only c is left, which is a value of circumference.
The explanation of the circle area, the surface area of sphere and volume of sphere formulas takes a bit more space and time, but it is not too difficult.
The great advantage of understanding all of these formulas is that even if you do not remember one of them, you still can reproduce it by using your logic and understanding.
