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Equi-partioning of angle using Flexica curve
Posted:
Sep 26, 2010 5:17 PM
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Using computer plot, a given angle can be divided into 3,5,11 etc.
number of equal parts using a Flexica curve difined by me earlier.
>From a mechanics of materials approach, a beam of constant section
and given length a, fixed at one end and an increasing bending moment
applied at the other, flexes with large deflections by Euler-Bernoulli
Law as per equation: r/a = sin(t)/t . Successive points look at the
instantaneous center of curvature subtending the same angle, a fact
used in this method for angular division.The large curve is
proportionately scaled into whatever number of subdivisions is
required. It uses a computer plot,so has no claim among "using only
ruler /compass" methods.Hope you find it interesting.
http://i54.tinypic.com/6qwu1w.jpg
Best Regards,
Narasimham
PS : I have in mind the conchoid of Nicomedes used for solution of
cubics and angle trisection, which is also not a ruler/compass curve.
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