# Tagged Questions

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### 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 ...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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 ...
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### 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 ...
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 ...
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### 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 ...
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### “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?
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### 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 ...
297 views

### Geometric Identities involving $π^2$

Are there any known geometric identities that have $π^2$ in the formula?
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### 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 ...
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### 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 ...
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### 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) $2\pi$
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 ...
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### 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 ...
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### 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 $$a_{n+1}\leq a_n/2$$ ...
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### 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
### 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 ...