This video lesson is from the Home Study Companion to Paul Foerster's Algebra and Trigonometry: Functions and Applications. See http://MathWithoutBorders.com for more information.
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https://www.youtube.com/watch?v=wHCIY0_ArY8
This is a demonstration of how a large planet, such as Jupiter, can repeatedly modify the orbit of a smaller object, such as a comet, in an interaction called the slingshot effect. I am using the online javascript program OrbitSimulator.com, which runs right in a browser. If you would like to play with the orbits and tweak the parameters, use the URL http://orbitsimulator.com/gravitySimulatorCloud/simulations/1568602188517_Comet%20Slingshot.html
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https://www.youtube.com/watch?v=Caj2r0sNunI
Positive feedback loops cause small displacements from equilibrium to grow exponentially, often with catastrophic effects. This demonstration with a sound system is just one example. This topic is especially relevant today to the understanding of how "climate change" can become "climate catastrophe."
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https://www.youtube.com/watch?v=BzqitY3nC7A
This video lesson is from the Home Study Companion to Paul Foerster's Algebra 1: Expressions, Equations, and Applications. See http://MathWithoutBorders.com for more information.
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https://www.youtube.com/watch?v=dcCP5-Z3jyg
This is a bonus topic for a calculus lesson on derivatives of inverse trigonometric functions. It turns out that such a derivative is part of the calculation of the angle of a rainbow. This bonus lesson is a nice mix of physics and mathematics. The graphics in this lesson are generated using Geogebra, which is available from Geogebra.org.
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http://mathwithoutborders.com
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https://www.youtube.com/watch?v=Lim7KbKT2zU
The conventional way to represent the Real Number system is to think of the numbers as corresponding to points along an infinite straight line. The problem is that in this representation there is no place for "infinity". Infinity is not a real number. This video shows an alternate visualization of the real number system that has a place to put the point at infinity.
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https://www.youtube.com/watch?v=O2IhQ5rV_iQ
This is a lesson from the Home Study Companion video series for Algebra 2 for the textbook Algebra and Trigonometry: Functions and Applications, by Paul Foerster. See http://MathWithoutBorders.com for more information.
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https://www.youtube.com/watch?v=QAnV_nQCeF8