1
vote
1answer
33 views

2 pi term in sinusoidal signal

My intuition is that the $2\pi$ term in the sinusoidal signal equation: $$x(t) = \sin(2\pi\,f\,t)$$ Is indicative of the fact that this signal can be described as movement around a circle, is that ...
0
votes
2answers
73 views

How $\pi$, $3.1415…$ and $180^o$ are adaptive together?!

I planed following to compute the circle's circumference. The circle's circumference finally can computable from: $$\lim_{\alpha\to0}{\frac{360^o}\alpha d} = 2\pi r$$ I don't want to follow above ...
12
votes
10answers
499 views

How is the value of $\pi$ ( Pi ) actually calculated?

When I was a child I was taught $\pi$ (Circumference/Diameter) is an irrational number and can be approximated to $22/7$ but $= 3.(142857)(\ldots)$. But where does this value comes from? In ...
5
votes
2answers
263 views

Proofs without words of some well-known historical values of $\pi$?

Two of the earliest known documented approximations of the value of $\pi$ are $\pi_B=\frac{25}{8}=3.125$ and $\pi_E=\left(\frac{16}{9}\right)^2$, from Babylonian and Egyptian sources respectively. ...
0
votes
2answers
41 views

calculating various cuts of a circle

im trying to find some sort of formula to calculate lines within a circle. I need to find the length of the various lines within the circle from which I only know the diameter. Is there some sort ...
6
votes
1answer
279 views

How exactly do you measure circumference or diameter?

I am absolutely confused about trying to calculate circumference. And I do not mean using the math formula, I mean back in old days when people had very primitive tools, and had to make the ...
20
votes
4answers
730 views

Did Euclid prove that Pi is Constant?

Pi is defined the ratio of the circumference of a circle to its diameter, but of course different circles have different circumferences and diameters, so in order for it to be well-defined we need to ...
0
votes
0answers
34 views

Overlapping Circles Area [duplicate]

I have searched but could not find the exact question. Two circles with radii 5 intersect such that the center of one circle lies on the circumference of another. What is the area of the overlapping ...
0
votes
1answer
75 views

“Aera” of square if “aera” of circle is passage in upper decimal

A circle with a radius of $5$ has an aera of $50$. What will be the aera of the square with a width of $10=2\times 5$? Do we need a ratio of diagonal/width to find this?
5
votes
3answers
233 views

Why is $\pi r^2$ the surface of a circle

Why is $\pi r^2$ the surface of a circle? I have learned this formula ages ago and I'm just using it like most people do, but I don't think I truly understand how circles work until I understand why ...
5
votes
2answers
297 views

Geometric Identities involving $π^2$

Are there any known geometric identities that have $π^2$ in the formula?
-1
votes
2answers
2k views

Are “perfect” circles mathematically impossible (and do irrational numbers exist)? [closed]

It occurred to me that while $\pi$ is an irrational number, it is nevertheless the ratio between the circumference and diameter of all circles. This seems like a contradiction. Thinking about it ...
2
votes
2answers
168 views

Is the value of $\pi$ in 2d the same in 3d? [closed]

I am starting with my question with the note "Assume no math skills". Given that, all down votes are welcomed. (At the expense of better understanding of course!) Given my first question: What is ...
2
votes
2answers
724 views

How do I find the area of a circle inside a square?

In the figure above, the circle with center $O$ is inscribed in square $ABCD$. What is the area of the shaded portion of the circle? (A) $\pi/4$ (B) $\pi/2$ (C) $\pi$ (D) $3\pi/2$ (E) $2\pi$
1
vote
1answer
348 views

Relationship between the sides of inscribed polygons

In my math textbook there's a demonstration for the calculus of the circumference of a circle that involves regular polygons inscribed in the circle, but I don't get it. The book gives the following ...
5
votes
1answer
119 views

A rope and Pi's irrationality

Here is a question which has been puzzling me for some time. You have a thin rope of an integer length $L$. You can bend it to create a rectangle of perimeter $L$. Fine so far. Next, through some ...
3
votes
1answer
166 views

What does Spivak want me to do?

This goes on in Chapter 8, on least upper bounds and related topics. I have proven $(a),(b),(c)$. The sketch is. $(a)$ If $\{a_n\}$ is a sequence of positive terms such that $$a_{n+1}\leq a_n/2$$ ...
-2
votes
3answers
554 views

What will be the shape of circle if it has no pi (π) [closed]

I not so good with mathematics I like to know if there is no pi (π) existed in this world what will happen to a Circle. What will be the shape of it
2
votes
1answer
321 views

Generating a random point on the unit circle

I'm trying to figure out a way to generate a random point on the unit circle in an application I am developing (I'm a programmer). So far I have the following (in pseudo-code), where Z is a random ...
5
votes
4answers
1k views

Calculate $\pi$ precisely using integrals?

This is probably a very stupid question, but I just learned about integrals so I was wondering what happens if we calculate the integral of $\sqrt{1 - x^2}$ from $-1$ to $1$. We would get the surface ...