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Based on the paper Sometimes Newton's Method Cycles, we first asked ourselves if there were any Newtonian Method Cycle functions which have non-trivial guesses. We encountered a way to create functions that cycle between a set number of points with any initial, non-trivial guesses when Newton's Method is applied. We exercised these possibilities through the methods of 2-cycles, 3-cycles and 4-cycles. We then generalized these cycles into k-cycles. After generalizing Newton's Method, we found the conditions that skew the cycles into a spiral pattern which will either converge, diverge or become a near-cycle. Once we obtained all this information, we explored additional questions that rose up from our initial exploration of Newton's Method.
A Latex template for ASEE conference proceedings. This template is not affiliated with the American Society for Engineering Education and comes with no warranty or guarantee.
ASEE provides a list of formatting requirements on its website.
This is a template for the 2016 AES Brasil congress article.
I do not own this template, nor have designed it. I just downloaded from the official website and uploaded here on overleaf
In this experiment, we attempt to better understand how materials properties are tested. We tested a number of simple beams of different materials under a stress. The bending of the materials allowed for us to calculate the Poisson's Ratio and elastic moduli for each material. From this, we were able to not only compare materials but also methods of measuring elasticity. Despite some error in our results, which can be explained by the scale of our measurements in relation to the stiffness of certain materials, we find both strain gauges and equations of cantilever to be appropriate measurement techniques for measuring the elastic modulus of simple beams.
Stephen Yonke
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