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Equipartioning of angle using Flexica curve
Posted:
Sep 26, 2010 5:17 PM


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 EulerBernoulli 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.



