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Taking Galileo, His Inclined Plane, Uniform Acceleration, and ‘Mean Speed Theorem’ to the 21st Century with Mathematica
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| Organization: | Sand Box Geometry |
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Wolfram Technology Conference 2015
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Champaign, Illinois USA
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The equation for free fall displacement from initial (0 momentum) to final velocity has two terms, a fixed value for specific mass/volume ratio causing surface acceleration curvature of M1, and time. I explore how Galileo determined the square of time is in direct proportion with accumulating (meter) of free fall using HS STEM physics and Mathematica. Then I will use the square of Pythagoras to construct a Plane Geometry Space and Time Square. I will use the Space/Time Square to validate ‘The Mean Speed Theorem’ proposed some 300 years before Galileo showing a fixed velocity will cover same space in same time frame as uniform rate of acceleration using curves. Having established plane geometry of gravity field potential held central by a Space/Time Square I demonstrate field control of M1 curving orbit motion of M2 and prove constructed motive space curves of Earth/Moon system using Sir Isaac Newton’s Inverse Sq. Law. Alexander
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| 1445520945.nb (3.9 MB) - Mathematica Notebook |
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