Circle Definition and 1000 Threads

Exercise #27 from a textbook called Kiselev's Geometry / Book I. Planimetry: Using only compass, construct a 1 degree arc on a circle, if a 19 degree arc of this circle is given.Please, check my reasoning on this one. I just want to make sure that I'm getting it right. My solution: Using a...

A textbook shows a circle with a line drawn through the centre and advises that the line represents the diameter of the circle, ok with that, but what happens if the circle was a pipe and the pipe had a hole drilled into it, so the pipe now has an outer diameter of 10 but the hole inside the...

say I have a circle with a diameter of d and there is a point at the top of the circle, p. I want to know the distance from point p to any other point on the perimeter and the angle θ from the tangent line of p. is there a function that will describe this? I will try to put up a picture to...

Homework Statement A small light is 22.0 cm below the surface of a liquid of refractive index 1.50. Viewed from above, the light appears to illuminate a circle on the surface of the water. What is the diameter of the circle? cm Homework Equations Snell's Law n1sin(θ)1 = n2sin(θ)2...

I keep reading that a random vector (X, Y) uniformly distributed over the unit circle has probability density \frac{1}{\pi}. The only proof I've seen is that f_{X,Y}(x,y) = \begin{cases} c, &\text{if }x^2 + y^2 \leq 1 \\ 0 &\text{otherwise}\end{cases} And then you solve for c by integrating...

Homework Statement Sketch modulus((z+1)/(2z+3))=1 on the complex plane where z=x+iy Homework Equations The Attempt at a Solution I know it is a circle but i need help simplifying the equation into the form of a circle. i'm stuck at 0= 3x^2 + 3y^2 + 10x + 8 I usually...

Find the center and radius of the circle using the equation: x^2 + y^2 + 2√2x - 4√5y = 5 I just can't seem to solve this equation into the form (x-h)^2 + (y-k)^2 = r^2 in order to get the center and radius. Any help would be appreciated

Centroid of a "TILTED" Semi circle! Guys, could anyone help me out how to solve the centroid of these "tilted" semicircle. I really don't have any idea how to get its centroid since it's tilted..Please I really want to understand so kindly do it step by step, Thanks.. Just Find the x-bar and...

I know I should keeps this short, but I need to explain it a little. So, please have patience with me :) Given a standard ellipse, and its eccentricity and position on screen, is there some clever way of calculating how much a regular circle needs to be tilted in (angles) in a perspective...

Ok, so I'm trying to plot the unit circle using the chebyvhev metric, which should give me a square. I am trying this in MATLAB, using the 'pdist' and 'cmdscale' functions. My uber-complex code is the following: clc;clf;clear all; boundaryPlot=1.5; % Euclidean unit circle for i=1:360...

What is the equation of the circle with a center point of (10, -14) when the circle is tangent to x=13? D = √(13-10)^2 + (0-(14))^2 D = √(3)^2 + (14))^2 D = √9+196 D = √205 Radius = √205 (x-10)^2 + (y-(-14))^2 = √205^2 (x-10)^2 + (y+14)^2 = 205 But how am I suppose to graph this?

Homework Statement The problem is attached as TheProblem.jpg and the answer is A. Homework Equations Geometry rules. The Attempt at a Solution The triangle which has angles of 30deg and 10deg also has an angle of 180deg-30deg-10deg = 140deg and the other side of the line intersection...

I want to show that if the complex variables ζ and z and related via the relation z = (2/ζ) + ζ then the unit circle mod(ζ) = 1 in the ζ plane maps to an ellipse in the z-plane. Then if I write z as x + iy, what is the equation for this ellipse in terms of x and y? Any help would be...

Homework Statement -8\int^{3}_{0}\sqrt{9-x^2}dxHomework Equations The Attempt at a Solution am i right in thinking this the area of a circle in the first quadrant so my answer is-8(\frac{9\pi}{4}) = -18\pi Thanks for reading?

Hi all, I have a seemingly simple linear algebra problem which I have trouble with and I would like to ask for some advice how to solve it. Here is the problem: Here are my thoughts about this: It is clear that a solution is not always defined for the whole range of \nu and that for...

Homework Statement I would like to ask how to find the mass of a circle with equation x^2+y^2=4 given its density=xy^2 by not using polar coordinate but use dxdy or dydx ( cut the circle into pieces parallel to x-axis or y-axis ) Homework Equations x^2+y^2=4 xy^2 The...

Homework Statement A circle is inscribed in a triangleHere is a picture Picture of circle inscribed in triangle, not necessarily to scaleWhich is larger: the circumference of the circle, or the perimeter of the triangle? Homework EquationsC=∏D (D=diameter of the circle, C=circumference of...

Homework Statement Show that the maximum possible area for a rectangle inscribed in a circle is 2r^2 where r is the radius of the circle.Homework Equations Pre-calc ! NO TRIG ! Doesn't matter if it's easier, it's supposed to be solved with algebra. The Attempt at a Solution I have no clue...

Hello Im wondering how to calculate the acceleration of a circle down an inclined plane (due to gravity). I am familiar with caclulating the acceleration of a body sliding down a inclined plane, but not a circle. How do you determine the acceleration of a circle (preffer rotation per second, if...

Homework Statement Find the equation of the circle whose centre lies on the x-axis and which passes through points A (6,0) and B (0,10). Homework Equations The Attempt at a Solution I drew a diagram of the circle and determined that the line AB has gradient 5/3. Its perpendicular bisector...

Homework Statement An equilateral triangle of side x is is inscribed in a circle. Express the area of the circle as a function of x. Homework Equations Anything non-trig. I suspect it's got something to do with the Pythagorean theorem. The Attempt at a Solution I tried getting the...

What does it mean when one says that "A circle and an ellipse with a focus at the circle’s center can touch each other only at the longer axis"? Can't you, by varying the size of the circle, make it intersect the ellipse in a variety of ways? Thanks! :)

This problem arose for me while working out a triple integral in spherical coordinates. Basicly I know that when we shift a parabola along the axis it is simply translated. I naturally assumed that if we shifted a circle in a similar manner that it would act the same. However when we shift...

So over the course of yesterday and the day before that I've spent a few hours thinking about these problems; 1. Given a circle, place n points arbitrarily* on the edge and connect every point to every other point with a straight line. How many intersections do you get? 2. Given the same...

Homework Statement The problem is attached Homework Equations P=F/A The Attempt at a Solution I did the question like this (got wrong answer though): Surface area of sphere=4∏r2=4×∏×0.252 Atmospheric pressure=1.01×105 Force=1.01×105×4×∏×0.252≈80000N Actual answer 20000N...

Homework Statement the figure is shown on the attachment. Find the area of the smallest part of the circle. Homework Equations area of circle, sector, segment The Attempt at a Solution I cannot use the said equations since the part of the circle is not with reference to the...

Homework Statement Find the position of the center of mass for a thin sheet and homogeneous, with sides R and 2R ,from which has been subtracted a half circle of radius R. [Xcm=(2/3)*R*(4-pi)]Homework Equations Rcm=(1/M)*∫rdm The Attempt at a Solution By symmetry we know Ycm=0. For de...

I thought this was a very interesting development in the Syrian situation: http://www.jpost.com/MiddleEast/Article.aspx?id=274828

Homework Statement Describe the locus and determine the Cartesian Equation of: \left|z-3-5i\right|= 2 Homework Equations \left|z-C\right|= r -----> formula for a circle on complex plane Where C = the centre z = the moving point (locus) (x-h)^{2}+(y-k)^{2}=r^{2} -----> Formula...

\int_{-\sqrt{r^2-x^2}}^{\sqrt{r^2-x^2}} \sqrt{r^2-x^2-y^2}dy I can calculate the above integral [part of a double integral] by the conventional way [somewhat long], however my book says that this integral equals to \frac {\pi}{2}(r^2-x^2) because the integral is actually the area of half a...

Hello again, I'm finding myself stuck on what is probably a simple question, but I believe I am taking the wrong approach. The section is "Volumes with infinite integrals," and the chapter is "Improper Integrals." The question, "Use calculus to find the circumference of a circle with radius...

Homework Statement The points P and Q divide a given interval AB internally and externally respectively in the ratio 1:λ. The point X lies on the circle with diameter PQ. Prove that AX:XB=1:λ Homework Equations None The Attempt at a Solution Basically, if we define the centre of PQ and the...

Homework Statement Find the radius of a circle inscribed in a quadrant of a circle with radius 5 Homework Equations The Attempt at a Solution I worked this but I'm not sure if its correct. I looked at the first quadrant so a quarter of a circle with radius 5. I drew the radius...

Homework Statement Hello! I need to calculate a little fraction (dA) of the area of a circle (mass m and radius R and area A) and I have no idea how to do this. Homework Equations According to my textbook dm=\frac{M.dA}{A}=\sigma .dA and dA=R.dR.d\theta. The Attempt at a Solution Well, I tried...

This is not really a homework problem, I'm just doing it as an exercise puzzle. I think I'm on the right track, but at this point I feel a little exhausted and would love a hint. Homework Statement Let C be a unit circle: x^2+y^2=1 . Let "p" be a point on the circumference and "q" be a point...

This question is about circular motion in a vertical circle Question 1: would I be correct in assuming that the magnitude for tension is dependant on (a) the weight of the object (b) the position of the object with respect to the horizontal diameter of the circle So above the...

Homework Statement This question comes out of "Introduction to Topology" by Mendelson, from the section on Identification Topologies. Let D be the closed unit disc in R^2, so that the boundary, S, is the unit circle. Let C=S\times [0,1], and A=S \times \{1\} \subset C. Prove that...

imgur.com/kBTVm Hi, I understand that work done in a conservative field when a closed loop is followed is zero. The answer to this question I am sure is B. How do I explain to my colllegue that it is not zero when he thinks that the speed is constant and there is no friction and the force...

Situation 1: completely horizontal circle Imagine a ball being whirled in a completely horizontal circle. The only forces acting are tension and weight Would I be correct in assuming that in this situation NO WORK is done on the ball because the forces are directed (at all times)...

Hello, What would be the right approach to solve for a particle's wavefunction/ energy eigenvalues inside of a 2d cicrle with a potential V(r) where r is the radial distance of a particle from the center of the circle? V(r) is known and is some sort of a well potential going to infinity at R...

The question asks to look for a surface and a circle is the only function which meets the conditions. Is this still considered a surface?

I am becoming confused when I read in Wiki that the dimension of the circle in the plane is 1! It is said that the dimension of circle is 2 (in general )! I do not get it!

Homework Statement If you twirl a ball attached to a cord in a vertical circle, there would be a critical speed at the top for which the tension in the cord is zero. This is because the force of gravity supplies all the centripetal force necessary to complete the circle. How slowly would you...

Homework Statement Going over some old tests, I am asked to find the contour of the function: T = 100 - x^2 - y^2 at T = 100, T = 0, etc. I have a question regarding the contour at T = 100 Homework Equations The Attempt at a Solution Consider T = 100 100 = 100 - x^2...

I was thinking about how planets revolve around sun. Although they subscribe a elliptical motion, my question is very similar. A heavy body exerts a force on a point mass, say with an acceleration of "a". If we take the direction of this acceleration to be X, what is the linear uniform velocity...

As we know a circle view at an angle appears as an ellipse , as you see in the picture, the center of the camera aim to the center of the circle , the angle between the circle axis and the camera is ө, the azimuth between mojor axis(a) and the camera is ∞, the rotation of the camera is €...

Homework Statement Find the equation of a circle if the circumference is 18∏ and contains the point (2, 8) The Attempt at a Solution I know I can find the radius by setting 18∏=2∏r. r=9. the equation of a circle is (x-h)2+(y-k)2=r2 So I have 92= (2-h)2+(8-k)2 which becomes...

As we know a circle view at an angle appears as an ellipse, as you see in the picture, the center of the camera aim to the center of the circle , the angle between the circle axis and the camera is ө, the azimuth between mojor axis(a) and the camera is ∞, the rotation of the camera is €...

Homework Statement Consider the following parameterization of the circle: a) x1 (t) = (cost, sint) b) x2 (t) = (cos3t, sin3t) c) x3 (t) = (sint, cost) How long does it take point a particle to go from (1,0) to (0,1) for each parameterization. Homework Equations The...

Homework Statement Find the total area inside the circle r = 4 and below the line r=2csc\theta Homework Equations \int^{b}_{a} 1/2r^{2}\thetad\thetaThe Attempt at a Solution r=2/sin\theta\Rightarrowrsin\theta=2\Rightarrowy=2 r=4\Rightarrow=circle with radius 4 at center (0,0) Point of...