def. of circle in mathematics?
826387
A circle is the locus of a point which moves in a plane in such a way that its distance from a given fixed point is always constant.\n         The fixed point is called the centre & the constant distance is called the radius of the circle.\n           \n          A circle with centre O & radius r is denoted by C(O,r) !!!
392733
Divide the circumference of a circle its diameter.
831242
This is just the inside of the unit circle including its circumference.\nThe unit circle (circle at the origin with radius=1) is\nx^2 + y^2 = 1\nAnd you want x^2 + y^2 ≤ 1\nso its the circle plus its inside.\n( if it had been x^2 + y^2 ≥ 1 it would be the circle plus everything outside )\nIf you wanted x in terms of y, you just get |x| ≤ √(1-y^2) .
875889
There are no 3d circles because by definition circle is a 2d figure. The figure obtained by the revolution of a circle around its diameter is called a sphere which is 3-dimensional.\n\nOn the lighter side, if you want to call a 3d circle something, you can call it a "Non-Existant Circle"   :-)
665322
In Euclidean plane geometry, π may be defined either as the ratio of a circle's circumference to its diameter, or as the ratio of a circle's area to the area of a square whose side is the radius. Advanced textbooks define π analytically using trigonometric functions, for example as the smallest positive x for which sin(x) = 0, or as twice the smallest positive x for which cos(x) = 0.\n\nAll these definitions are equivalent, they amount to the following numerical value of π, truncated to 50 decimal places:\n\n3.14159265358979323846264338327950288419716939937510... \n\nThe digits can be up to 4 millions digits (http://www.zenwerx.com/pi.php )
383274
well that question cant be answered b/c only a circle has a radius nothing else
1172110
let circle =  x^2 + y^2 = r\nin xyz plane.\n\n1 line is y = ax ,   a is any real no,\n2nd is z axis
226433
The circle's center is at (4, -1).  Therefore its radius is sqrt((6-4)^2 + (3- -1)^2) or sqrt 20.\n\nSo its equation is (x-4)^2 + (y+1)^2 = 20\n\nThe reason we know the center is at (4, -1) [at least how I did it] is by calling the center (a,b) and writing three different but equal applications of the distance formula, one from each known point to (a,b), then taking two pairs of these three distances, making them equal, and solving for a and b.
1062497
What everyone has said is correct, but look at it this way: Consider a square. We know from the theorem of pythagoras that the ratio of the hypotenuese to the length of one side = sqrt(2) or, if you like, the ratio of one side to the hypotenuese = 1/sqrt(2). These constant ratios are independent of the size of the square. We have the ratio of the perimeter of the square to the hypotenuese = 4/sqrt(2) = 2*sqrt(2), which is independent of the size of the square.  Similarly the ratio of the circumference of a given circle to the longest chord(the diameter) has an exact value, and similarly this value is independent of the size of the circle. As has been mentioned, for any regular n-gon(square, pentagon, hexagon etc) the ratio of the perimeter to the length of the longest line segment that can be drawn within the n-gon will have a specific value depending on n, and this value can be determined. As we let n approach infinity, the n-gon approaches a circle and the ratio of the perimeter of the n-gon to the longest "chord" approaches a specific limit and this limit is pi, the ratio of the circumference to the diameter.  And, as mentioned above, analytic techniques can (and have) determined the value of the constant pi to a trillion or so digits.\n\nFootnote: SK, determining the limit of a series or even that the limit exists does not necessarily require calculus.\nFor example, the sum of a geometric series such as Sum[1/(2^n)] = 1/2 + 1/4 + 1/8+....+1/2^n is proved without calculus to be 1- 1/2^n and the limit of it (without calculus) as n---> inf. = 1. Check out the below link regarding pi.\n\n http://mathworld.wolfram.com/ArchimedesAlgorithm.html
39475
Diameter of a circle, I'm assuming?\n\nDiameter = 2 * Radius\nDiameter = Circumference / (2 * pi)\nArea = pi * (diameter / 2)^2
634060
The length of one side of the rectangle can be related to the Circumference of the circle.\nTo get the perimeter of a circle, called the circumference of the circle, one simply has to multiply 2 times pi (about 3.14) times the radius of the particular circle. \nThe circumference of a circle can be calculated from its diameter using the formula:\nc = πd\nOr, substituting the radius for the diameter:\nc = 2πr\nWhere r is the radius and d is the diameter of the circle, and π (the Greek letter pi) is the constant 3.141 592 653 589 793...
1065850
(circle's formula) divided by (hexagon's formula)
1143102
Example - you'll need to apply it to your own endpoints.\n\nA circle is described on the line joining (-2,5)and(3,4) as diameter, find its equation:\n\nThe equation for a circle is:\n(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius\n\nIt is easiest to find the center first. it is the midpoint of the line and the slope is constant:\nh = x1-[(x1-x2)/2] = 3 - 5/2 = 1/2\nk = y1-[(y1-y2)/2] = 5 - 1/2 = 4.5\n\nNow, find the radius using the distance formula to find the distance between the center and the endpoint or by using a right triangle where dx and dy are the lengths of the legs. I prefer the latter, but they are pretty much the same:\ndx^2 + dy^2 = r^2\nr^2 = (5/2)^2 + (1/2)^2= 26/4 = 13/2\nBy substituing back into the equation for a circle:\n(x-.5)^2 + (y-4.5)^2 = (6.5)^2 = 42.25
370884
The 16th letter of the Greek alphabet. \n\nMathematics. A transcendental number, approximately 3.14159, represented by the symbol, that expresses the ratio of the circumference to the diameter of a circle and appears as a constant in many mathematical expressions.
461233
In Euclidean plane geometry, π may be defined either as the ratio of a circle's circumference to its diameter, or as the ratio of a circle's area to the area of a square whose side is the radius. Advanced textbooks define π analytically using trigonometric functions, for example as the smallest positive x for which sin(x) = 0, or as twice the smallest positive x for which cos(x) = 0.\n\nAll these definitions are equivalent, they amount to the following numerical value of π, truncated to 50 decimal places:\n\n3.14159265358979323846264338327950288419716939937510
615830
I may be misunderstanding your question - the information you give does not describe a circle. However, I can walk you through the integral.\n\nS 1 + sqrt(9 - x^2) dx\nS dx + S sqrt(9 - x^2) dx\n\n3sin(u) = x\n3cos(u) du = dx\n\nx + S sqrt(9 - 9sin^2(u)) 3cos(u) du\nx + S sqrt(9(1 - sin^2(u))) 3cos(u) du\nx + S sqrt(9cos^2(u)) 3cos(u) du\nx + S 3cos(u) 3cos(u) du\nx + S 9cos^2(u) du\nx + S 9 (1 + cos(2u))/2 du\nx + 9/2 S 1 + cos(2u) du\nx + 9/2 (u + sin(2u)/2)\nx + 9/2 (u + 2sin(u)cos(u)/2)\nx + 9/2 u + 9/2 sin(u)cos(u)\n\nIf sin(u) = x/3, then cos(u) = sqrt(9 - x^2)/3 and u = arcsin(x/3).\n\nx + 9/2 arcsin(x/3) + (9/2)(x/3)(sqrt(9 - x^2)/3)\nx + 9/2 arcsin(x/3) + (x sqrt(9 - x^2)) / 2\n\nNow, we plug in 0 and -3, and subtract the results.\n\n0: 0\n-3: -3 + (9/2)(-pi/2)\n\nArea: 3 + 9pi/4\n\nI hope this helps! =]
293949
Here is one condition:\n\nR1^2  +  R2^2  =  AB^2 (Pythagorean theorem),\n\nwhere R1 and R2  are the two intersecting circles radii and AB is the distance between their centers (AB < R1 + R2)