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Science Forum

  1. 17 May '17 13:57
    assuming that a DNA is a perfect cylinder and the nucleus is a perfect sphere. Prove mathematically that that DNA can fit into a nucleus.
  2. Standard member DeepThought
    Losing the Thread
    18 May '17 18:51
    Originally posted by wormer
    assuming that a DNA is a perfect cylinder and the nucleus is a perfect sphere. Prove mathematically that that DNA can fit into a nucleus.
    Suppose a cylinder of radius a and length 2h just fits inside a sphere of radius r. The cylinder touches the sphere to form two circles of radius a with formulae x^2 + y^2 = a^2, z = +/- h. So we can use Pythagoras' theorem to relate a, h and r. Imagine the triangle formed by the origin, the point h on the z axis and a point on the circle of contact. We have that:

    r^2 = h^2 + a^2

    So the cylinder will fit in the sphere if:

    h < √(r^2 - a^2)

    and

    a < √(r^2 - h^2)

    The length l of the cylinder is 2h so we can write these conditions as

    l < 2√(r^2 - a^2)

    and

    a < √(r^2 - (l^2)/4)