In this video I go over another example on graphing Polar Coordinates and this time look at the family of curves r = 1 + c sin ϴ which are known as Limaçons, which is a French word which translates to “cochlea” which is derived from the Greek and Latin words for “snail shell” or “screw”. This gets the name Limaçons because the curves do in fact look somewhat like a snail’s shell, for some values of the constant c. I once again use the amazing Desmos calculator to illustrate how the shape changes as we change c. The shapes change from a circular shape with a loop inside it for large values of c, to a cardioid at c = 1, then to a circle at c = 0; and a mirror image of the results for negative values of c. I may go over an “analytic” proof to these properties in a later video so #StayTuned!
Also in this video I take a side quest into learning more about the “cochlea” which is a snail-like structure as part of the human inner ear. It is filled with fluid and thousands of hair cells which transfer the sound vibrations as nerve signals to the human brain. What’s interesting is that prior to the 17th century, the “cochlea” was used in reference to any spiral objects such as a spiral staircase and the famous Archimedean screw. The Archimedean screw (or Archimedes’ screw) is a very interesting piece of engineering ingenuity and comprises of a screw like structure that moves fluid or other objects across the length of the screw by rotating it. I also get side tracked in this video and discuss “dimples” which are indentations on the human body, like dimples on a smile, so hope you enjoy the random topics I cover!
Anyways like always, play around with the Desmos calculator and let me know what other amazing shapes you can discover!
You can play around with the graph that I created in my video here: https://www.desmos.com/calculator/mhxsxtyt5p
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvROaAz3hEliI-MHpQ
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/video-notes-polar-coordinates-example-11-limacons-cochlea-archimedean-screw
Related Videos:
Polar Coordinates: Example 10: Graphing r = sin(8ϴ/5):
Polar Coordinates: Graphing With Polar Curves with Desmos Calculator:
Polar Coordinates: Example 9: Cardioid: Part 4:
Polar Coordinates: Example 9: Cardioid: Part 3: Question B:
Polar Coordinates: Example 9: Cardioid: Part 2: Question A:
Polar Coordinates: Example 9: Cardioid: Part 1: Slope Formula & Trigonometric Algebra:
Polar Coordinates: Tangents to Polar Curves:
Polar Coordinates: Symmetry:
Polar Coordinates: Example 8: Four-Leaved Rose:
Polar Coordinates: Example 7: Cardioid:
Polar Coordinates: Example 6: Part 2: Polar Circle to Cartesian:
Polar Coordinates: Example 5: Straight Lines:
Polar Coordinates: Example 4: Circle:
Polar Coordinates: Example 3: Cartesian to Polar
Polar Coordinates: Example 2: Polar to Cartesian:
Polar Coordinates: Cartesian Connection:
Polar Coordinates: Example 1:
Polar Coordinates:
Parametric Equations and Polar Coordinates: .
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I don’t always go graph Limaçons but when I do I usually get sidetracked and look up the Cochlea, Archimedean screw, and even dimples ;)
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/video-notes-polar-coordinates-example-11-limacons-cochlea-archimedean-screw
Nice video @mes
Hi there, I was curating your post for steemstem and I found that the content of your post is not original because it was already posted on this link: https://www.bitchute.com/video/PpuIjjyRHGrU/
Steemstem only votes original content, sorry
But that is my original content! That link is from my BitChute channel!! I also post on YouTube too.
I would suggest posting it on steemit first and then on your website, at least write something different in your post compared to the description of your videos. The description of your video matches 100% the content of your post which means not original content.
Hmmmm ohh okay. I have a database of all my videos on YouTube which I am moving to Steemit and BitChute. I'll try to add some different text too. Thanks for the heads up!
No worries, if you decide to modify this post and add more info and original text, reply to this comment and I will curate it
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