-5
votes
0answers
17 views

<html5> draw circle by arc and triangle [on hold]

I want if click the retacgle, draw a triangle around the circle. source code like this... but, triangle was not good each of positions.. How can i draw a triangle around the circle like attached ...
1
vote
1answer
48 views

Parametric equation of a circle given starting point.

Find the parametric equations of a circle with radius of $5$ where you start at point $(5,0)$ at $v=0$ and you travel clockwise with a period of $3$. So, I know that I require to have a $x(v)$ and ...
4
votes
2answers
648 views

The area of circle

The question is to prove that area of a circle with radius $r$ is $\pi r^2$ using integral. I tried to write $$A=\int\limits_{-r}^{r}2\sqrt{r^2-x^2}\ dx$$ but I don't know what to do next.
0
votes
1answer
32 views

The surface area of a ring: $\pi[(r+dr)^2 - r^2]$ or $2\pi r\,dr$?

I know this may be really simple but here it is nonetheless. Let's say that I have a ring with a radius of $r$ and width of $dr$. I'm trying to find the surface $dS$ of the ring. Isn't it $dS = ...
0
votes
1answer
42 views

Finding the points of intersection of the circles [closed]

How can you find the points of intersection of the circles $x^2+y^2-2x-2y-2=0$ and $x^2+y^2+2x+2y-2=0$?
0
votes
1answer
187 views

Maximum speed in a circular orbit?

Visualize two points:  $O\equiv(0\mid 0)$ and $D\equiv(d\mid 0)$.  The two are $d$ units apart.  Visualize a movable rod whose endpoints, $C_O$ and $S_O$, are a unit apart. $C_O$ always coïncides ...
1
vote
1answer
75 views

Area inside cardiod $r=2-2 cos (θ) $ and circle $r=-6cosθ$

I found the points of intersection $(3,2π/3)$ and $(3, 4π/3)$ but now I'm stuck and don't know how to continue. I don't know how to choose the range of numbers to integrate. The answer is 5π if it ...
0
votes
1answer
48 views

Finding the release angle for projectile

Hello. I would like to create an game application for android platform that is similar like projectiles. I called it snowball machine. As you know regular projectiles has to hit the ...
1
vote
2answers
51 views

Circle Area formula question

Take a peek at the following proof Everything makes sense but one thing: how did they determine that $\sqrt{\cos^2\theta}$ was positive and not negative? Thanks.
1
vote
1answer
90 views

Newbie: Find the intersection of a line and a circle and interpret geometrically

Find the points of intersection of the line $x+y+k=0$ and the circle $x^2+y^2=2x$. Show that there are two points of intersection if: $-1-\sqrt2<k<-1+\sqrt2$, one point of intersection if: ...
1
vote
1answer
215 views

Finding the radius, distance of the center of circle inscribed in the square

I am trying to solve this question but can't figure out the last part. I was able to get answers for part A and B but i don't know how to approach/solve part C. Any help will be appreciated. The ...
-1
votes
2answers
52 views

What is the equation of the circle which passes through P, Q and R? [closed]

In the diagram, the y-axis is a tangent to the circle. P has co-ordinates (0,2) and Q is (12,2), at angle PRQ it is 90 degrees. HELP PLEASE
2
votes
1answer
87 views

Optimization: A certain amount of wire to create a square and a circle, minimize area.

You have 4 feet of wire to create a square and a circle. How much wire should you spend on each shape to minimize the area. Also, why isn't the minimum area when you use all of the wire on the ...
1
vote
2answers
493 views

What is the equation for a line tangent to a circle from a point outside the circle?

I need to know the equation for a line tangent to a circle and through a point outside the circle. I have found a number of solutions which involve specific numbers for the circles equation and the ...
2
votes
1answer
468 views

Is *njwildberger* wrong about area and circumference of a circle?

In this video, njwildberger says that the area and circumference of a circle are proof-less theorems. But I heard that we can derive both the area and circumference of a circle using calculus? So are ...
0
votes
1answer
36 views

What are the applications? [duplicate]

How can I show that a sequence of regular polygons with n sides becomes more and more like a circle as n→∞? In which fields this concept is applied?
5
votes
2answers
297 views

Geometric Identities involving $π^2$

Are there any known geometric identities that have $π^2$ in the formula?
1
vote
0answers
66 views

Is there a continuous version of $tan^{-1}(\frac{y}{x})$ for the entire unit circle?

The fact that $tan^{-1}(\frac{y}{x})$ only "works" for the upper-right quadrant makes some calculations (for a physics simulator) impossible. I of course use $atan2(y,x)$ in the code, that's not what ...
0
votes
1answer
128 views

How to find a point on the tangent line whos length is 1?

im trying to figure out a formula to find the point(x,y) on a tangent line whos length is between 0 and 1 while it rotates around the unit circle uniformly, so the point would either be right on the ...
1
vote
3answers
642 views

Center of Mass of a Circle

How would one find the center of mass of a circle? The center of mass of a rod is given by: $$\frac{1}{M}\int^{L}_{0}\rho x dx$$ So, for a sphere, it would be an area integral, such as: ...
2
votes
2answers
966 views

Is the tangent function (like in trig) and tangent lines the same?

So, a 45 degree angle in the unit circle has a tan value of 1. Does that mean the slope of a tangent line from that point is also 1? Or is something different entirely?
0
votes
3answers
3k views

How do I get the slope on a circle?

I have drawn a circle by doing this in Matlab: syms x; ezplot(cos(x),sin(x)) I get the tangent point at which I want my tangent to be by taking $x = \cos(3.1415)$, ...
22
votes
5answers
1k views

Trying to understand why circle area is not $2 \pi r^2$

I understand the reasoning behind $\pi r^2$ for a circle area however I'd like to know what is wrong with the reasoning below: The area of a square is like a line, the height (one dimension, length) ...
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 $$a_{n+1}\leq a_n/2$$ ...
25
votes
12answers
18k views

Calculus proof for the area of a circle

I was looking for proofs using Calculus for the area of a circle and come across this one $$\int 2 \pi r \, dr = 2\pi \frac {r^2}{2} = \pi r^2$$ and it struck me as being particularly easy. The only ...
7
votes
1answer
711 views

How to turn this sum into an integral?

I have been trying to find the closed form of this sum to no avail. It was suggested to me to try and turn this sum into an integral and solve it like that. However, I am confused as to how to do ...
4
votes
1answer
179 views

Why do derivatives of certain equations relating to circles yield other similar equations? [duplicate]

Possible Duplicate: Why is the derivative of a circle's area its perimeter (and similarly for spheres)? We all know that the volume of a sphere is: $V = \frac{4}{3}\pi r^{3}$ and its ...
1
vote
2answers
218 views

Area of a circle

I've tried to find as a personnal exercise where the formula $A=\pi R^2$ comes from. After drawing the problem, I've found that $A = 2\int\limits_{-R}^{R}\sqrt{R^2-t^2}dt$. How can I calculate this ? ...
7
votes
3answers
207 views

Is there a simple formula for this simple question about a circle?

What is the average distance of the points within a circle of radius $r$ from a point a distance $d$ from the centre of the circle (with $d>r$, though a general solution without this constraint ...
3
votes
1answer
128 views

circles tangent to exponential curve

Circle $C_1$ is tangent to the curves $y=e^x$ and $y=-e^x$ and the line $x=0$, and for $n>1$ circle $C_n$ is tangent to both curves and to $C_{n-1}$, how can I find the radius of any circle $C_k$? ...
6
votes
3answers
2k views

Definite integral: $\displaystyle\int^{4}_0 (16-x^2)^{\frac{3}{2}} dx$

The following integral can be computed using the substitution $x = 4\sin\theta~$ and then proceeding with $dx = 4\cos\theta~ d\theta~$, and evaluating the integral of $\cos^4\theta~$: ...
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 ...