![]() Electrical - Electrical units, amps and electrical wiring, wire gauge and AWG, electrical formulas and motors.add a comma separated list with the sizes of the smaller circlesĪn array with the maximum number of smaller circles within the larger circles will be created.add a comma separated list with the sizes of the larger circles.an array with multiple smaller and larger circles.Calculate Maximum Number of Smaller Circles in Larger Circles Iteration 6 indicates that the outside diameter of the bundle of pipes is approximately 9.65 inches. The iterative process can be done like this: Iteration No. Example - Outside diameter of a bundle with 30 pc. ![]() Tip! - the calculator above can be used to approximate the outside diameter of a bundle of pipes by inserting the small pipe diameter and do an iterative changing of the outside pipe diameter until the number of pipes calculated fits the number of pipes in the bundle. Make a Shortcut to this Calculator on Your Home Screen?.Advantage of the `square' pattern is that you could maybe fit things in the gaps, which are larger than in the hexagon pattern. % of square covered by circles = ($\pi$/4) x 100 = 78.5% (rounded) This means that you could fit more cylindrical cans in a container using the `hexagon' pattern. % of hexagon covered by circles = (3$\pi$/10.38) x 100 = 90.8% (rounded) Notice how not using exact values for the height of the triangles in the hexagon calculation means this is 0.1 cm 2 off - a type of rounding error introduced by rounding off numbers before the answer. radius of circle = 1cm so area = $\pi$ cm 2 and area of 3 circles = 3$\pi$ cm 2 There are 3 whole circles in each hexagon. We worked out the percentage of each plane covered by circles, by dividing the two patterns into hexagons and squares (see the diagrams above) We worked out the percentage of each hexagon covered by circles and the percentage of squares covered by circles.Ī hexagon is 6 triangles area of 1 triangle: base = 2cm height = 1.73cm so area of 1 triangle = 1.73cm 2 and the area of the hexagon is 10.38cm 2. Here is another method for Circle Packaging from Suzanne and Nisha of the Mount School, York: The hexagon touches the circle at the midpoints of its sides, the distance between the midpoints of opposite sides is $2$ units, the lengths of the sides of the hexagon are $1/\sqrt$. In the other case the packing of the plane can be produced by a tessellation of hexagons (like a honeycomb). ![]() Therefore the proportion of the plane covered by the circles is $\pi/4 = 0.785398\ldots = 78.5\%$ to 3 significant figures. The area of the circle is $\pi$ and the area of the square is $4$ square units. ![]() Let us say that the radius of the circle is $1$ unit. In either case the calculation of areas is the In one case it could be a tessellation of squares, either surrounding the circles or formed by joining the centres of the circles. To find the percentage of the plane covered by the circles in each of the packings we must find, within the original pattern, a shape that tessellates the plane and in each case this can be done in different ways. ![]() James of Christ Church Cathedral School, Oxford and Alexander from Shevah-Mofet School, Israel sent very good solutions to this question. ![]()
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