Circles Definition and 307 Threads

Do the formation of auroras always occur in circles/ovals/ellipses?? What causes the shape of their formation?

Homework Statement What is the next radius outwards of this Apollonian gasket? R = radius of outer circle = 5 r1 = radius of largest inner circle = 3 r2 = radius of second largest inner circle = 1 a = unknown radius Homework Equations C = 2πr A = πr2 d = 2r The Attempt at a Solution Make a...

3. A(a,b), B(-a,-b), and C is plane XOY. P moves along with curve C. If the multiplication product of PA's and PB's gradients are always k, C is a circle only if k = ...? 4. The radius of a circle which meets X-axis at (6,0) and meets the curve $$y=\sqrt{3x}$$ at one point is ... 5. A circle...

The article below is tainted with the silliness of woo, but the phenomenon is quite natural - and way cool. It's a tropical verson of an ice circle. I found ice circles hard to believe at first, but I watched a small-scale simulation on an artificial river with just the right flow rate and...

A minha pergunta é na divisão 10800/1110 My question is in the division 10800/1110 ?

I'm working on the following fun problem. I have a circle of a given radius, R0. (Green circle in the image). I want to be able to supply a radius of the first circle that is to fit into this large circle. Let's say R1 is 0.75 * R0. Following this I find the best position of R2 (to maximise...

Hi How can i prove that the set if circles does not form a vector space AXIOMATICALLY . ( i am not considering a circle lives in xy-plane ( subset ) as a subspace of xy-plane

Supposed 2 circles ##C_1 : x^2 + y^2 + {f_1}x + {g_1}y + h_1 = 0## and ##C_2 : x^2 + y^2 + {f_2}x + {g_2}y + h_2 = 0## through two points. A family of circles can be constructed as ##x^2 + y^2 + {f_1}x + {g_1}y + h_1 + k(x^2 + y^2 + {f_2}x + {g_2}y + h_2) = 0##. By altering the k, an...

Is there a shorter way to get the answer, the polar equation of a cardioid, directly? My solution involves some tedious work and doesn't give the polar equation directly: The equation of the member curves (circles) is ##f(x, y...

Hi, Not sure how to categorize/title this question. I was looking at the Coriolis Effect and was considering the straight-line motion of an object wrt the background stars/masses and this question occurred to me: Except for the fact that they are traveling nowhere near fast enough to trace out...

http://arxiv.org/pdf/1510.06537v1.pdf I found this semirecent paper about CCC's concentric circles prediction for the CMB. Is this just another piece of the debate, or is its significance enough to increase the plausibility of Penrose's model? Thank you in advance for your answers, and please...

Homework Statement In a specific area of the space, an electrical potential is given as: \begin{equation} V(x,y,z) = A(2x^2 - 3y^2 - 3z^2) \end{equation} where A is a constant. a.) Determine the electrical field E for any given point in the area. A test charge q_0 is moved from the point...

Hello, I VAGUELY recall reading, some many years ago, a statement to the following... "The Greeks were obsessed with circles. Had they relaxed this obsession, they may have seen the significance of modeling curves with small straight lines, and thereby anticipated the Calculus." Is there any...

Draw a large number of concentric circles with constant radii increment (i.e.: 1m, 2m, 3m...). Assign each with a serial number counting from the centre. (i.e.: innermost: 1, second innermost: 2, etc.) Divide all the circles into segments, the number of segments for each circle is equal to its...

Because a triangle comes out to 180 degrees, and yet it can only have three sides. A circle has 360 degrees, but its number of "sides" are uncountable. Can someone explain this?

Obviously, they exist as mathematical concepts, and those concepts are real, but in physical reality, everything is made up of subatomic particles and, if the theory is ever verified, strings. So if you try to construct a curve, circle or sphere, you are necessarily stacking a bunch of subatomic...

I recent came across this paragraph by David Hume. Although he is considered a philosopher, he tried to make comments on math as well. I find this one interesting, but I have no idea what it means and what he is getting at. Out of pure curiosity, does anyone else know what this means?: "The...

Homework Statement A small conducting spherical shell with inner radius a and outer radius b is concentric with a larger conducting spherical shell with inner radius c and outer radius d. The inner shell has total charge -2q and the outer shell has charge +4q. a) calculate the electric field...

Homework Statement Given a circle with a set diameter, how does one calculate the area of the segment below? Homework Equations The only information available is the diameter (in this particular example it is 14"), You may not use angles. Only the chord length. Thank you for your reply. Miguel

Hi all, Please help. I am stuck with the question below and I have no clue how to solve: Thanks for the help.

Homework Statement A small circular metal ring of radius r is concentric with a large circular metal ring of radius 10r. Current in the outer ring flows counterclockwise due to an unpictured power supply. By adjusting the power supply, you can adjust I, the current in the large ring. The graph...

In my textbook, its given that the equation of family of circles touching a given circle S and line L is ##S+\lambda L=0## So to find the equation of family of circles touching line L at point P(p,q), can i use the same equation taking S to be a circle of radius zero and center at P? That is...

If the image we obtain from Cherenkov light is actually the projection of a continuous wave front (Fig. 1) on a vertical plane, orthogonal respect to the direction of propagation of the incident particle, why we just see a ring (Fig. 2), instead of a full circle? Is it because Cherenkov light is...

Homework Statement My class is working through chapter 2 of Newman's Analytic Number Theory text (on partitions). We have come to a part where he states that "elementary geometry gives the formula" (for the length of arc A) 4r\text{arcsin}\frac{\sqrt(2)(1-r)}{\sqrt(r)} We are attempting to...

Two circles lie in a plane. The circle of radius 1 meter overlaps the circle of smaller radius $r$ in such a way that their points of intersection are separated by distance $2r$. Show that the area inside the small circle and outside the large circle is largest when $r=(1+(2/\pi)^2)^{-1/2}$...

Decided to make a new thread so it wouldn't be jumbled up with the other thread I posted about this particular problem. Question: Find the area of the region which is inside both $$r = 2$$ and $$ r = 4sin(\theta)$$ So solving, I know that $$sin\theta = \frac{1}{2}$$. I also sketched a picture...

Suppose you have a square, and you simply start increasing the number of vertices and edges proportionally, all the way to infinity. What, exactly, distinguishes this infinitely sided polygon from a circle? Logically, an infinitesimal edge would be like a point on a circle, although I...

Homework Statement Find the meridians and circles of latitude of a surface of revolution ##X(t, \theta) = (r(t)cos(\theta), r(t)sin(\theta), z(t))##. Homework Equations The Attempt at a Solution I honestly just need a definition of what these concepts are. My book, as an aside for...

Homework Statement Consider two unshaded circles ##C_r## and ##C_s## with radii ##r>s## that touch at the origin of the complex plane. The shaded circles ##C_1,C_2...C_7## (labeled in counterclockwise direction sequentially) all touch ##C_r## internally and ##C_s## externally. ##C_1## also...

Homework Statement Let C=\lbrace(x,y) \in R^2: x^2+y^2=1 \rbrace \cup \lbrace (x,y) \in R^2: (x-1)^2+y^2=1 \rbrace . Give a parameterization of the curve C. The Attempt at a Solution I'm not sure how valid it is but I tried to use a 'piecewise parameterisation', defining it to be...

Hello all, I've been trying to work out this problem I came across yesterday when a professor mentioned it in a math education course. It states, "Take a circle and put two dots on the circle then connect them with a cord. How many sections of area does the cord split the circle into?" Of...

Homework Statement In ##\mathbb{R}^2##, draw a unit circle for taxicab distance ##(d_t)##, euclidean distance ##(d_e)##, and max distance ##(d_s)##. Homework Equations ##d_e = \sqrt{(x -x_1)-(y-y_1)}## ##d_s = \text{max}\{|x-x_1|,|y-y_1|\}## ##d_t=|x-x_1|+|y-y_1|## The Attempt at a...

My textbook says : "The friction force on a car turning a corner does no work." I agree somewhat. However, if there is no work, there is no change of speed, aka no change of kinetic energy. How can a car in a real-life stop if it is doing perfect circles with forces pointing towards the...

Hello all I am hoping someone could help shed some light on a surveying problem I am having. The problem is this:- • A circle is centered at point B with Known co-ordinates (X2,Y2) • The circle has a radius which is known (R). • Point A lays outside of the circle with known...

Homework Statement Consider a family of circles passing through two fixed points A(3,7) and B(6,5). Show that the chords in which the circle ##x^2+y^2-4x-6y-3=0## cuts the members of the family are concurrent at a point. Find the coordinates of this point. Homework Equations The...

Homework Statement The circumference of a circle is increasing by 4 inches per second. What is the rate of change of the diameter with respect to time if the radius is 2 inches? Homework Equations C = 2∏r = ∏d. The Attempt at a Solution dC/dt = 4 = ∏dd/dt. dd/dt = 4/∏ Is this it? It...

Homework Statement Is there any direct formula for calculating the direct common tangent of two circles without having to go all the trouble of using y-y1=m(x1-x2) to derive it for two separate tangents t1 and t2. If there is could anyone explain to me how it is derived? Homework...

I've been wondering how to calculate the area of intersection of two overlapping circles in terms of their radii. There's two cases I'm interested in: The easier case: Suppose there are two circles of radius R and r (R > r). The center of the larger circle is at the origin, and the center...

I am reading an article about Minkowski space (as a vector space, which is why I am putting my question in this rubric) which is poorly translated from the Russian, and have come across several notational curiosities, most of which I have been able to figure out. However, there is one that I do...

In a paper translated from the Russian, the author refers to "m-m" and "n-n" circles (including Minkowski circles) and orbits. When I first came across "n-n", I thought it was "non-negative" until I came across the "m-m". In one of the references I went to a diagram referred to, and saw an arc...

Hi -- Thinking about the problem, where I have three circles in a closest possible packing inside an equilateral triangle. So two circles on the floor, adjacent to each other touching and a third circle placed on top so that the distances off their centers from each other are all 2R, R=Radius...

Homework Statement I have this picture http://i.imgur.com/ek2N1dL.png I have to find the electric field at the point inside 2 semi circles. The left semi circle has a charge of -3 micro Coulombs and the right one has +3 micro coulombs. The radius between the point and the circle is 0.2...

I have six 2x2 complex matrices from the group SL(2,C). Each line is a matrix: first row, second row. \left( \begin{array}{cc} \left\{\frac{1}{\sqrt{1-k^2}},\frac{k}{\sqrt{1-k^2}}\right\} & \left\{\frac{k}{\sqrt{1-k^2}},\frac{1}{\sqrt{1-k^2}}\right\} \\ \left\{\frac{1}{\sqrt{1-k^2}},\frac{i...

Homework Statement [FONT="Courier New"]Two circles with radii 12 cm and 10 cm respectively have their centers 14 cm apart, find the area common to both circles. (note : This is in radians.) Homework Equations Area of a sector = 0.5r2θ - 0.5r2sin θ The Attempt at a Solution None. :confused:

Homework Statement Q)A circle C whose radius is 1 unit touches the x-axis at 'A'.The centre Q lies in 1st quadrant.The tangent(other than x-axis) from origin touches the circle at T and a point P lies on it such that OAP is a right angled triangle with right angle at 'A' and its perimeter is 8...

Hi, I would very much like someone to help me solve the area of intersection between to intersecting circles (one with the radius r, and one with the radius 1). Tangents at the intersecting point form a 120 degree outer angle. 1. Homework Statement , 2 Relevent equations Here is a...

Meissner et al just posted a paper where they see those circles in the high res. microwave sky of Planck. Who knows if this is real, or what it would mean if it were confirmed? Meissner has a followup paper in preparation with Penrose and others. Either way I think it's pretty interesting...

Homework Statement Homework Equations The area of a circle: A_c = \pi r^{2} The Attempt at a Solution I know that the diameter of the oval shape is 10m since the problem says that it touches the circumference of the center of each circle. I am not sure how to approach the problem...

With this question, I have worked out the correct answers (see the section bordered by BBB), but my original approach was to go by the 1st attempt (bordered by AAA). In the 1st attempt, the h/ k equation results in a single centre, rather than the 2 required to form the 2 separate circle...

Homework Statement Use a double integral to find the area of the region enclosed within both circles of r=cosθ and r=sinθHomework Equations The Attempt at a Solution I begin by finding the region in polar co-ordinates. For r=\cos\theta 0\leq r \leq\cos\theta...