Home work help! Maths Project>>>>> circle and pi relationship
Please provide answers for the following questions:
(1)What is the relationship between the circumference of a circle and n (pi)?
(2)please state a few famous mathematical operations featuring pi.
The Greek letter pi is used to represent a universal constant that we come across many mathematical and scientific calculations. It is defined as the ration of the circumference of a circle to its diameter. Thus in the form of formula pi is defined as:
pi = (Circumference of a circle)/(Diameter of the circle)
This ration is same for every circle irrespective of the size of the circle. Approximate value of pi is 3.14159. However please note that value of pi is an irrational number and it cannot be expressed exactly as a decimal or as a fraction.
Pi is used in all calculations of quantities involving circular objects. For example:
Circumference of a circle with diameter d = pi*d
Area of a circle with diameter d = (pi*d^2)/4
Surface area of a sphere with diameter d = pi*d^2
Volume of a sphere with diameter d = (pi*d^3)/6
Also pi is commonly encountered in angles measured in terms of radians as 360 degrees of angle representing one complete rotation is equal to 2*pi.
Many formulas that describing physical phenomena contain pi. For example, formula for the motion of a pendulum or the vibration of a string include pi.
(1) The relation which describes the length of the circle, that means the circumgference is:
L = 2*pi*R, where L is the circumference, pi = 3.14... and R is the radius of the circle.
(2) First pi is the measure, in radians, of 180 degrees.
All relations concerning features of the circle are using the pythagorean number, pi = 3.14...
For example, the formula for finding the circumference of the circle, stated to the point (1) is using the number pi:
L = 2*pi*R
Another example is the calculus of the area of the circle:
A = pi*R^2
The features of all geometric figures are calculated depending on the pythagorean number pi.
The volume of a cylinder:
V = pi*R^2*h, where h is the generatrix of the cylinder.