The basic area formulas presented as reasoned methods rather than formulas to be memorized. Part 3 deals with how to find the areas of more complicated shapes and introduces the Surveyor's method.
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https://www.youtube.com/watch?v=bM5HYU2BdoU
Video lesson for Foerster's Precalculus with Trigonometry: Concepts and Applications, Chapter 1-1. See http://MathWithoutBorders.com for more information.
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https://www.youtube.com/watch?v=lfz1gwW1OUM
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
The Pythagorean Theorem appears in nearly every branch of mathematics. Here are several proofs drawing from algebra, geometry, and trigonometry.
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https://www.youtube.com/watch?v=GsgfP6KZHxg
Homeschool Highschool Math. This is an introduction to Math Without Borders Home Study Companion series which provides the equivalent of the classroom experience for homeschoolers and others who wish to self-teach the high school math curriculum.
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https://www.youtube.com/watch?v=QRoDqqgCa34
I was limited to a 3 minute presentation for a physics group, so I packed as much as I could about rainbows into a 3 minute video. This version has a few notes added for clarity.
https://mathwithoutborders.com (look under the Bonus Topics tab).
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https://www.youtube.com/watch?v=MuK2YaCQYZ0
The basic area formulas presented as reasoned methods rather than formulas to be memorized. Part 4 shows the derivation of the surveyor's method for finding the area of an arbitrary polygon or an arbitrary curve that can be approximated as a polygon.
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https://www.youtube.com/watch?v=uKHIkvU5BXI
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