calculus illusion ppt 97 version
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optical illusion calculus projectTRANSCRIPT
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By: Himali Rajakarunanayake, Jasmine Kriston, Jessica HoriPeriod 5
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An object or drawing which appears to have properties which are physically impossible, deceptive, or counterintuitive.
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Calculus definition: an optical illusion is created by having lines intersect a family of curves. In each case the lines appear to be curved.
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What is a Slope Field? – A graphical representation of the solutions of a differential equation.
-A differential equation determines the slope of the solution at any point.
Family of Curves: formed when slope field isshown. When constant (C) is given, the particular equation is shown.
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tch/10215
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(a) x2 + y2 = C2 ; x=3, y=4, C=5
x2 + y2 = 25 Implicit Differentiation: 2x + 2y(dy/dx) =0 dy/dx=(-2x/2y) Plug in x and y values: dy/dx= (-3/4)
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(b) xy=C ; x=1, y=4, C=4 xy=4 Implicit Differentiation: y + x(dy/dx) = 0 dy/dx= (-y/x) Plug in x and y values: dy/dx= -4
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The St. Louis Gateway Arch is an optical illusion because it appears to be taller than it is wide. However…
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However, the distances of the height and the width are both 630 feet. It is explained by this mathematical equation:
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y= 693.8507-68.7672 (( e 0.0100333x + e -.0100333x )) (2) dy/dx= -0.3449809739(e0.0100333x + e-.0100333x)
Initial condition f(0)= 625.0835
http://www.sciencefriday.com/videos/watch/10215
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Calculus of a Single Variable 8th
Edition by Larson, Hosteller, and Edwards (textbook)
CRC concise encyclopedia of mathematics by Eric Weisstein
Queen Mary University Of London Website: http://www.agenarisk.com/resources/probability_puzzles/St%20Louis%20Arch.shtml
http://www.sciencefriday.com/videos/watch/10215
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The End
We love math!