Circle Definition and 1000 Threads

The (perfect) circle, defined in the Cartesian coordinates as the set of (x,y) pairs that fit the equation x^2 + y^2 = r^2 can "exist" as a mathematical abstraction, I have no problem with that. But can we have a perfect circle in the physical world? Particularly, can an object move in a...

Homework Statement Suppose a non-uniform circular motion where a particle of mass "m" is attached to a string, which rotates on a vertical plane. Once an initial velocity is provided to the particle at the lowest point of the trajectory, no further forces act on the particle. (Air drag is...

General formula of a line is ax+b=0 Similarly can we have a general formula of a circle ?

How I can show the following \int _{\mathbb{T}} \frac{1}{|1-e^{-i\theta}z|^2}dm(e^{i\theta})= \frac{1}{1-|z|^2} , where z is in the unit disc dm is the normalized Lebesgue measure and T is the unite circle.

Here's the problem. A point traversed half a circle of radius $R = 160 \text{ cm}$ during a time interval of $\tau = 10.0 \text{ s}$. Calculate the following quantities averaged over that time: (a) the mean velocity $\langle v \rangle$; (b) the modulus of the mean velocity $ |\langle {\mathbf...

hello. I have a MATLAB skeleton provided because i want to model a distribution with a circular geometry. all in all, i want the 3d graph of the code to be some type of cylinder. This is the code: % flat step condition for ii=1:nHi, for jj=1:nHj, if (X(ii)/R_P)<1 &...

Crazy Circle Illusion! | Showyou pNe6fsaCVtI

"A set in the plane is called a region if it satisfies the following two conditions: 1. Each point of the set is the center of a circle whose entire enterior consists of points of the set. 2. Every two points of the set can be joined by a curve which consists entirely of points of the set."...

Find the smallest possible area of an isosceles triangle that has a circle of radius $r$ inside it. I cannot seem to find the relationship between the circle and triangle. Any hints? I'm thinking similar triangles, but I want to know if they're any other approaches before I try that.

I know that some AWD vehicles used the gear ratio of a planetary or other transfer gear combined with a gear type torque biasing diff that would allow a natural mechanical advantage to apply more of the torque to the front or rear axle. Why not apply this to a rear diff for circle track...

Can someone show me how to resolve this question? A particular circle in the standard (x,y) coordinate plane has an equation of (x − 5)2 + y2 = 38. What are the radius of the circle, in coordinate units, and the coordinates of the center of the circle? radius center F. √38 ( 5,0) G. 19 ( 5,0)...

Theoretically it is said that, tangent touches to a single point on a circle. But If my circle is very big, and large enough, then i think, it should not be a just single point where my tangent is touching, though is will be a very small portion depending on how large is the circle. If i have...

[SIZE="4"]Definition/Summary A circle has many definitions, a classical one being "the locus of all points on a plane that are equidistant from a given point, which is referred to as the 'center' of the circle". [SIZE="4"]Equations Equation for a circle with it's center as the origin...

I have an object (A) at some altitude above the Earth ellipsoid, and a point (B) on the surface of the Earth. Since you're not confined to the surface of the Earth as you travel from A (at altitude), to B, I'm getting confused. If I were to create a (Cartesian) vector pointing from object...

Homework Statement Homework Statement [/b] The purpose of this lab is to determine the mass of a rubber stopper being swung in a horizontal circle. I made an apparatus that resembles the picture attached, with a string (with a rubber stopper on one end, and a weight on the other end) put...

Homework Statement I basically have the radius of the circle and its displacement from the origin, so ##(x-p)^2+(y-q)^2=r^2## And now I need to find a tangent to the circle at a given point ##(a,b)##. Or at least the slope of the tangent. How would one do that? Homework Equations...

Is the squaring of a circle just a riddle that when solved to a great degree of accuracy then that's it... riddle solved. Or there more to it then that?

Homework Statement there are 7 seats around a round table, and is labelled form A to G. Find the number of ways a committee of 3 teachers and 4 parents can sit around the table? (i ) there is no restriction my ans is 7!=5040 (ii) all teachers must sit together the ans is 1008. can...

Using integral find the area of that part of the circle x^2 + y^2 = 16 which is exterior to the parabola y^2 = 6x.

Hello people of Physics Forums, In my research into transmission lines, I have come across the following function: x = ( a - i * b * tan(t) ) / ( c - i * d * tan(t) ) In the above equation x, a, b, c and d are complex and t is real. If my analysis is correct, varying t from -pi/2 to...

Homework Statement Erik’s disabled sailboat is floating stationary 3 miles East and 2 miles North of Kingston. The sailboat has a radar scope that will detect any object within 3 miles of the sailboat. A ferry leaves Kingston heading toward Edmonds at 12 mph. Edmonds is 6 miles due east of...

Homework Statement A small mass M attached to a string slides in a circle (x) on a frictionless horizontal table, with the force F providing the necessary tension (see figure). The force is then increased slowly and then maintained constant when M travels around in circle (y). The radius of...

Hello guys , Can someone explain me why color of central circle in transmission case is bright whereas it is dark for the reflection case? Thanks a lot,

Please help me find the standard equation of the circle passing through the point (−3,1) and containing the points of intersection of the circles x^2 + y^2 + 5x = 1 and x^2 + y^2 + y = 7 I don't know how to begin, I am used to tangent lines or other points, but I don't know what is visually...

please help me find the standard equation of the circles that have radius 10 and are tangent to the circle X^2 + y^2 = 25 at the point (3,4). the soln: (x-9)^2 + (y-12)^2 = 100, (x+3)^2 + (y+4)^2 = 100, i found the eqn that intersects the centre of the small circle and the larger one to be...

I have some noisy data (x-y coordinates) containing two distinct clusters of data. Each cluster is centred at an unknown point on the unit circle. How can I estimate these two points (green points in the diagram)? We can assume the noise is Gaussian and noise power is equal in x and y...

Homework Statement Tangents drawn from a point P(2,3) to the circle $$x^2+y^2-8x+6y+1=0$$ touch the circle at the points A and B. Find equation of circumcircle of the ΔPAB. The Attempt at a Solution The chord of contact is equal to -x+3y+1=0. This is also the radical axis of the given...

Homework Statement Sketch the curve C defined parametrically by ##x=t^{2} -2, y=t## Write down the Cartesian equation of the circle with center as the origin and radius ##r##. Show that this circle meets the curve C at points whose parameter ##t## satisfies the equation ##t^{4} -3t^{2}...

as a regular polygon increases in sides, it becomes rounder. As you increase the number of sides, the polygon will tend towards a perfect circle but never quite make it. you can only make the circle with an infinite number of sides - stopping at any other number but infinity you will only get a...

Suppose I have a smooth curve \gamma:[0,1] \to M, where M is a smooth m-dimensional manifold such that \gamma(0) = \gamma(1), and \hat{\gamma}:=\gamma|_{[0,1)} is an injection. Suppose further that \gamma is an immersion; i.e., the pushforward \gamma_* is injective at every t\in [0,1]. Claim...

I'm trying to figure out what this one symbol was I saw. I also have a guess that I would like to see if is correct. I saw a double integral with a circle connecting the two. What does this mean? Here is my guess. Is it used when dealing with Stoke's Theorem? Since ∫F°dS =∫∫ curl(F)°dS (Both...

Homework Statement The line \{z: y=t+x\} is mapped to a circle by the function f(z)=\frac{z-1}{1-zi} Find the equation of this circle. The Attempt at a Solution One method is to find mappings of three points on the line. These points will be mapped to the circles boundary. Then find...

Why is the characteristic function* of a ball in Rn continuous everywhere except on its surface?My lecturer said that a circle is a 'set of discontinuities' - what exactly does that mean? (some context: we're looking at how we can integrate over a ball. Previously we've only looked at Riemann...

Hello, this isn't a homework problem, so I'm hoping it's okay to post here. I would like to know the correct way to mathematically express the idea in my title. It is intuitively obvious that as the radius of a circle increases, it's curvature decreases. I looked it up and found that...

Marla is running clockwise around a circular track. She runs at a constant speed of 3 meters per second. She takes 46 seconds to complete one lap of the track. From her starting point, it takes her 12 seconds to reach the northernmost point of the track. Impose a coordinate system with the...

Homework Statement Find the points of tangency to a circle given by x^2+y^2=9 from point (12,9). Homework Equations dy/dx=-x/y (what I've been able to come up so far) The Attempt at a Solution Taking the derivative I got dy/dx=-x/y Let the unknown point of tangency be (a,b)...

Homework Statement Calculate ##\int _Kz^2exp(\frac{2}{z})dz## where ##K## is unit circle.Homework Equations The Attempt at a Solution Hmmm, I am having some troubles here. Here is how I tried: In general ##\int _\gamma f(z)dz=2\pi i\sum_{k=1}^{n}I(\gamma,a_k)Res(f,a_k)## where in my case...

I'd love it if someone could verify whether or not I did this problem correctly. A stained-glass window is a disc of radius 2 (graph r=2) with a rose inside (graph of r=2sin(2theta) ). The rose is red glass, and the rest is blue glass. Find the total area of the blue glass. So I set...

Homework Statement |zi - 3| = Pi Homework Equations Well, it clearly has to do with a circle but I do not believe there is a general equation for what I am asking about. The Attempt at a Solution There is no general solution not trying to solve anything. I want to know exactly...

Homework Statement Question: A mass m attached to a light string is spinning in a vertical circle, keeping its total energy constant. Find the difference in the magnitude of the tension between the top most and bottom most points. The Attempt at a Solution So for this one I've worked...

So for starters the area of an entire circle has 360º,right? So we can say that: ##1∏r^2## is ##\equiv## to ##360º## So by that logic ##0.5∏r^2## is ##\equiv## to ##180º## And finally ##0.25∏r^2## is ##\equiv## to ##90º## Divide both sides by 9, and you get : ##0.25∏r^2/9## is...

Imagine that a single bead has a hole in it. It is passed inside a " vertical " circle with no friction. Imagine that the "vertical"circle moves by spinning around its vertical axis and that the bead is, AT THE BEGINNING, on the bottom of the vertical circle. We had another problem related to...

Find the curve coordinates of the point nearest to P in the circle x2 + y2 = 16 P(0,6) as the former ( see a gift ) x2 + (y-6)2 = 16 (1) solving for y = y2 = 16- x2 introducing en 1 x2 +(16-x-6)2 = 16 x2 +100-20x + x2 = 16 derivating 4x -20 and x = 5 y = sqrt ( 16-25) and i...

Homework Statement Find the largest circle centered on the positive y-axis which touches the origin and which is above y=x^2 Homework Equations equation of a circle: r^2=(x-a)^2+(y-b)^2 equation of a circle centered on the y-axis: x^2+(y-b)^2=r^2 equation of a parabola: y=x^2 The...

I am interested to see if there is a way of creating a metal ring which has a variable diameter, the only way I imagine that this can be done is using segments which come together to form a circle, once pulled away the diameter changes however, the problem I face is that when the segments are...

Homework Statement Given that the line ##y=mx+c## is a tangent to the circle ##(x-a)^{2} +(y-b)^{2} =r^{2}##, show that ##(1+m^{2}) r^{2}=(c-b+ma)^{2}##Homework Equations Quadratic discriminant, sum and product of rootsThe Attempt at a Solution I substituted y=mx+c into the equation of the...

Hey guys, I'm new here. I got a problem from my professor that is different from any other problems we have done. I'm stuck and need a little help.Homework Statement r(t) = <cos(t), t, 2sin(t)> Find parametric equations for the circle of curvature at (0, pi/2, 2)The Attempt at a Solution I...

Thank you for taking time to read my post, I hope I am putting into the correct area of the physics forum. I am working with a programmer to complete a project that involves 2 intersecting vectors and a circle. The vector coordinates are known, we are trying to solve the circle equation...

What is the Rate of change of area of circle in respect to radius when radius is 3in I know that that dA/dr is equal to the circumference of the circle But where does that come from? Also the formula for the circumference of the circle is 2(pi)r But the answer is 6 (pi)in^2/in. I understand...