Circle Definition and 1000 Threads

How do you construct the arc of the circle as a straight line by geometry not by an equation? Thank you

I'm working on an assignment that is due in roughly two weeks and I'm stuck on a problem. I have what I believe may be a solution but am unsure whether or not it is 'complete'. Here is the problem: "Let C be a circle or a straight line. Show that the same is true of the locus of points...

Homework Statement A spring with an unstretched length of 20 cm and a force constant of 100 N/m is attached to a 2-kg mass with a charge of 3.0 C. The mass is swung in a circle in a zero gravity environment, so that the spring is perfectly horizontal and is parallel to the radius of the...

consider a pendulum. The mass 'm' is hung and now we are interested in finding the velocity so that it completes one circle. Clearly we can do it easily by conserving energy. Now my problem is with the top most point. Clearly the tension is minimum at this point so that string becomes slack...

Homework Statement A car with a horn making a frequency of 'f' Hz is driven in a circle with a radius of 'r' m. The uniform velocity of the car is v ms-1. Draw graphs showing the frequency observes by the observer who is standing on; a) Position A b) Position B (Position B is very far...

I'm having some difficulty with this question. Can anyone help me out, please? Many thanks. Homework Statement A circle of radius length \sqrt{20} contains the point (-1, 3). Its centre lies on the line x + y = 0. Find the equations of the 2 circles that satisfy these conditions...

Hi, Homework Statement A circle of radius r is as shown in the attached diagram. I am asked to first express X as a function of θ, then to compute E(X). It is also stated that θ obeys U[0,2π]. Homework Equations The Attempt at a Solution Through simple trigonometry I have found X...

Homework Statement A variable line ax+by+c=0, where a,b,c are in A.P (arithmetic progression), is normal to a circle ##(x-\alpha)^2+(y-\beta)^2=\gamma##, which is orthogonal to circle ##x^2+y^2-4x-4y-1=0##. The value of ##\alpha+\beta+\gamma## is equal to A)3 B)5 C)10 D)7 Homework...

This is a tiny part of a presentation I am giving Friday, any and all help is appreciated. Homework Statement Suppose we have a circle centered on O. We are looking for the distribution of the points generated by the following method: We choose a random radius of the circle, and then choose...

Homework Statement derive/create an equation for a "great circle" route r(t) from a given point A to a given point B along the surface of the sphere with center (0,0,0) and radius = 15 test point 1: A=(2,10,11) to B(14,5,2) test point 2: A=(10,5,10) to B(0,-12,9) Homework Equations...

Homework Statement The uniform quarter-circular sector is released from rest with one edge vertical as shown. Determine its subsequent maximum angular velocity. The distance b is 560 mm. Homework Equations The Attempt at a Solution I know that I need to use: T1 + V1 + U'1-2...

A friend's homework problem (Prove any five points in the plane determines a possibly degenerate conic section) led us to a different problem that we found more interesting. We can identify a circle with three points on the circle, or six parameters $(x_1,y_1,x_2,y_2,x_3,y_3)$ where, keeping...

Hi, I am conducting an experiment and i am displaying diffraction images of light through 2 pinholes on a DSLR camera. I get a good image with lasers but when I capture images of chromatic light i only get the top half (semi circle) image. can someone explain to me why this occurs? I think...

Points A, B, C, D are on a circle with radius R. |AC| = |AB| = 500, while the ratio between |DC|, |DA|, |DB| is 1, 5, 7. Find R.

Homework Statement A uniform rod moves in a vertical circle .Its ends are constrained to move on the track without friction.Find the angular frequency of small oscillation .Homework Equations The Attempt at a Solution Suppose the rod of length L moves in a circle of radius R . Let the...

Homework Statement A 100g (0.1kg) rock is attatched to a 1.0m rope and spun around in a circle with a period of rotation of 1.0s. What is the Radius of the circle that it forms? Homework Equations Fc = (mV^2) / r V= (2∏r/T) LCosθ = r The Attempt at a Solution Im quite stick...

So how does the topology of R^n minus the origin relate to that of the (n-1)-dimensional sphere? I would think the topology of the former is equivalent to that of an (n-1)-dimensional sphere with finite thickness, and open edges. But I suppose that is as close as one can get to the...

The centers of three circles are situated on a line. The center of the fourth circle is situated at given distance d from that line. What is the radius of the fourth circle if we know that each circle is tangent to other three. Please give me a hint, if you can. Answer: d/2.

Homework Statement Let A, B, C, D be distinct points on a circle with centre O. If there exists non zero real numbers x and y such that ##|x\vec{OA}+y\vec{OB}|=|x\vec{OB}+y\vec{OC}|=|x\vec{OC}+y\vec{OD}|=|x \vec{OD}+y\vec{OA}|##, then which of the following is always true? A)ABCD is a trapezium...

Okay! Earlier today I was thinking about potential energy and how it is related to an orbiting object, O, around a centre, C, from which force emanates if the object O is traveling at radius r from this centre, we conclude that the force given by the change in direction must be equal to the...

Homework Statement In a circle we can place k numbers. The numbers can range from 1 to n. One position in the circle is fixed, say by 1. We have to place the other k-1 places with numbers in the range 1 to n such that no adjacent numbers are equal. Homework Equations The Attempt at...

[SOLVED]Trig problem: max square cut from circle Since this one is homework related, ill ask this as a procession so that I can make sure that I am grasping the logic. the question is that with a round log with a diameter of 16cm, what is the strongest log that can be cut where the strength =...

I have a grid and want to determine whether a point lies within (our outside of) a circle. The grid cells simply have integer coordinates, e.g. x = 5, y = 7. The circle's radius is known, and also an integer value. I wrote a program that can place points in a (quantized) circle using...

Question A thin nonconducting rod with a uniform charge distribution of positive charge Q is bent into a circle of radius R. The central perpendicular axis through the ring is a z axis, with the origin at the center of the ring. What is the magnitude of the electric field due to the rod at...

Homework Statement Consider a random walk on a circle of N points, labeled {0,1,...,N-1}. Let the initial state be X = 0 and define T to be the first time all points have been visited at least once. Show that the distribution of X[T] (i.e. last unique position visited) is uniform over...

Homework Statement Find the Arc Length from (0,3) clockwise to (2,sqrt(5)) along the circle defined by x2 + y2 = 9 Homework Equations Arc Length formula for integrals The Attempt at a Solution I have the correct answer at 3arcsin(2/3), but I tried to do this without calculus the first time...

Homework Statement A crate (35 kg) is located in the middle of the flat bed of a pickup truck as the truck rounds an unbanked curve in the road. The curve may be regarded as an arc of a circle of radius 80.0 m. If the coefficient of static friction between crate and truck is 0.410, how fast...

Homework Statement Plane stress in xy-plane. Use Mohr's Circle to find σx1 σy1 and τx1y1 if the XY axis is rotated counterclockwise θº I want to do my HW problem myself so I'll just put some sample values. If i know how to get this one, i'll know how to do the HW problem(s). (Units won't...

A truck with a width of 2,40 and height of 3,41 is driving through a tunnel that is formed like a half circle and has the radius of 3,60. Will it work? Now, this is a very pathetic question because this is junior high level geometry. I could blame the incapacity to solve this question on...

Homework Statement A 68.8 g steel ball is attached to the end of a string. The ball is swung in a vertical circle 86 cm in diameter. (a) What is the minimum speed the ball must have at the top in order to complete the circle without falling? (b) If this speed is constant, what will be the...

i tried hard to solve this question but i got a complicated answer any hint ? http://www.gulfup.net/uploads/13634557771.gif thanks

Homework Statement (see attachment 1) In this problem, we have a row of circles placed on a line. All points of tangency are distinct. The circle ##C_n## is uniquely determined. Homework Equations The Attempt at a Solution Here's the sketch I drew for the problem. Radius...

Homework Statement I would like to use the Weierstrass M-test to show that this family of functions/kernels is uniformly convergent for a seminar I must give tomorrow. H_{t} (x) = \sum ^{-\infty}_{\infty} e^{-4 \pi ^{2} n^{2} t} e^{2 \pi i n x} . Homework Equations The Attempt at a...

We typically have z=r*e^(i*theta). But let's say I want a circle centered at 2i. Is it valid to write z=r*e^(i*theta)+2i ? I ask this because I don't want to have abs(z-2i)=r; I want to solve for z.

My curiosity was piqued by another poster who's trying to find the area of a lune using calculus. I wanted to do this now. So I don't highjack his thread, I'm making a new post about it. First, the geometric picture of a lune that constitutes my basic plan of attack. First I want to solve a...

a metric on the plane determines an action of SO(2) on is unit circle by rotation. Suppose one starts with a free transitive action of SO(2) on a circle. When does this come from a metric? Always?

Homework Statement There are two circuits in the XY plane: one is a square (side 0.2 m in length) centered on the origin. The second is circle or radius r also centered on the origin. The circle is smaller than fits inside) the square. By assuming the radius of the circle is small compared...

I seem to recall when taking college Trigonometry my professor saying that the unit circle and sinusoidal curves were basically a mathematical represention of a slinky in that the unit circle was the view of a slinky head on, so that what you saw in the two dimensional sense was a circle, and...

arg(\dfrac{z}{z-2}) = \dfrac{\pi}{3} sketch the locus of z and find the centre of the circle I've sketched the locus of z but I can't seem to find the centre of the circle. Is there a way to do it algebraically? I've attempted to use z = x + iy, but to no avail.

Homework Statement Find the center of mass of a 5kg circle with a radius of 4m with a circle that has a radius of 2m cut out from it. Homework Equations The Attempt at a Solution To be completely honest, I do not know where to start. I do know how to find the center of mass when...

Hi, how can I prove that a circle it is not homeomorphic to a subset of R^n I can somehow, see that there isn't any homeomorphic application, for example between a circle in R^2 to a line, but how can I prove it? Thank you

Homework Statement Solve: ∫(-ydx+xdy)/(x2+y2) counterclockwise around x2+y2=4 Homework Equations Greens Theorem: ∫Pdx + Qdy = ∫∫(dQ/dx - dP/dy)dxdy The Attempt at a Solution Using Greens Theorem variables, I get that: P = -y/(x2+y2) and Q=x/(x2+y2) and thus dQ/dx =...

Given a circle centered at the origin, how can one prove that the limit of the quotient of the number of lattice points on the circle over the radius goes to zero as radius goes to infinity?

What is the theory behind mapping of the latitude and longitude of the sphere in the Poincare Circle to the polarization of the TEM wave? That is, why: 1) Linear polarization when ε=0 deg? 2) Circular polarization when ε=+/- 45 deg? 3) Elliptical when ε is not 0 or +/- 45 deg? 4) RH rotation...

Homework Statement What is the area of a right triangle whose inscribed circle has radius 3 and whose circumscribed circle has a radius 8? Homework Equations The diameter must be the hypotenuse of the circle The Attempt at a Solution The answer is 57, but I do not know the...

Homework Statement I solved this problem. I just have a general question at the very end. A current flows in a wire that has straight sections on either side of a semicircular loop of radius b. Find the mag and direction of the magnetic field B at point P(center of loop). ......... periods =...

Homework Statement I was looking at the following tutorial http://mathworld.wolfram.com/Circle.html Homework Equations equations 31-34 o the link The Attempt at a Solution My question is just whether this means that for 31-34, the answers are determinants of 3x3 matricies...

Hi, everyone. I am just trying to do some practice problems on finding volume. So this is the one I'm working on: 1. "Find the volume of the solid described below: The solid lies between the planes perpendicular to the x-axis at x=6 and x=-6. The cross-sections perpendicular to the axis on...

This may sound like a dumb question, but... For the equation of a circle with a radius of 1, the equation is: x^2 + y^2 = 1 But if we rearrange that to be: y= √(1 - x^2), then it's only a semicircle... Why is that? Why is it now a semicircle just because it got rearranged? Thanks!

Hey guys, I hope someone can give me some pointers with this because it should be really easy but I am just not getting it! I want to show that for a triangle inscribedin a circle an equilateral traingle gives the maximal perimeter. I've tried a few things and just get bogged down in algebra...