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It doesn't take long for anyone to check how many coins of equal size can be placed around a central coin so that these touch the central coin and yet not overlap. "Only six. To
calculate how many coins would touch the one in the centre, think of
circles of radius r. Think of another imaginary circle drawn by joining
the diameters of all the circles around the central one. The radius of
this imaginary circle is 2r, since the radius of each circle is r and
the radius of the imaginary circle is got when we join the centres of
two circles. Its circumference is 2.piX2r=4.pi.r. To know how many
circles are around, we divide this circumference by the dia of each
circle (i.e. 2r), since the imaginary circle is created by joining the
dias of all circles. (4 X 22/7 X r) / 2r = 44/7 = 6.2857142`85 or 6, if
we take the integer part only," says Vimal Jit Kaur.
"However, if the spheres are placed in three dimensions, three spheres on each side can touch the central sphere, totalling the number of spheres to 12 (6+3+3), so that all these are touching the one in the centre." Viney Yadav and Dr Tarsem Lal agree with her views, but in Suhail's view, the number of spheres which can be placed around a sphere is 14. Each sphere subtends an angle of pi(2 - 3^(0.5)) steradians, and since the total solid angle about a point is equal to 4pi steradians,14 spheres can be placed around one sphere. After Halley had thrown
them out of his house, Newton and Gregory resumed this debate and soon
agreed that "six" was indeed the answer for coins. However,
they still disagreed on the second point. Gregory stated that in
three-dimensional space, the first layer surrounding a central ball
would contain 13 spheres, while Newton was more in favour of 12:
"Put one sphere on the bottom, then arrange five spheres in a
pentagon around the central sphere, just below its equator; place
another five spheres more or less in the interstices of the lower five
spheres (slightly above the equator of the central sphere), and finally
put the 12th sphere on the top." Only Imperial College, UK, has the
Newton papers and even it is silent on the question of cricket. Not
until the 1950s it could be proved that theoretically, there was space
for nearly 15 spheres around the central ball. Practically though, only
12 have been achieved. Think. (Write at The Tribune or adityarishi99@yahoo.co.in) |
