Significance of pi

[CALCULUS' GOD]

Why do the mathematicians want to find the value of pi up to millions of places of decimals?

 

[Deleted member 4993]

Why do the mathematicians want to find the value of pi up to millions of places of decimals?

Why do people want to climb Mt. Everest?

 

[Explorer]

Trying to find patters and understand PI better ???
Plus it is a challenge to find lots of digits of PI. So this may be another reason.

Why should we stop at 3 digits ???

 

[Explorer]

Why not...the bible stopped at 1 digit: 3 :cool:

Try this, Explorer:

find area of isosceles triange with equal sides = 1
and apex angle = 1 degree

multiply the area by 360

3.141433159...

Close

 

[Explorer]

Now try:
find area of isosceles triange with equal sides = 1
and apex angle = 1/2 degree

multiply the area by 720

The area of the triangle can be generally written as
A = sin(θ) / 2
Where θ is the apex angle.

Also considering a circumference of radius 1, π can be written as:
π = (L / 2) x (360 / θ)

Where L is the length of the arc corresponding to θ.

Now, for very small angles θ, sinθ converges to L.
Therefore, for very small θ, π can be written as
π = (sin(θ) / 2) x (360 / θ)

The smaller θ, the more precise the found value for π will be.

This explains why by making the apex angle smaller, you have to multiply the area by a greater quantity (which is 360/θ), and you find a more precise value for π.

Smart, Denis!

 

[Ishuda]

Now try:
find area of isosceles triange with equal sides = 1
and apex angle = 1/2 degree

multiply the area by 720

Just for grins and giggles
\(\displaystyle \pi\) ~ 360 (1 + 5 10^-5 d²) (A/d)
where A is the area of an isosceles triange with equal sides = 1 and apex angle = d degrees. In fact
\(\displaystyle \underset{d\, \to\, 0}{lim}\, \, 360\, (1\, +\, 5\,*\, 10^{-5} d^2) \frac{A}{d}\, =\, \pi\)