Pencils and Envelopes (The Cardioid in your Coffee Cup, part 1)
Channel: Kevin's Mathematical Musings
Date: 2021-03-29

We define the mathematical concepts of a pencil and an envelope, and use them to solve a simple string art problem.

00:00 Intro
00:46 String art
01:51 Drawing a curve
02:20 Formula for a single string
03:33 Formula for a set of strings
04:02 Definitions of “pencil” and “envelope”
05:27 Finding the envelope of a pencil
07:36 Warmup problem - string art between straignt lines
09:09 Coming attractions

MUSIC

“Almost New” Kevin McLeod (incompetech.com)
Licensed under Creative Commons: By Attribution 3.0 License
http://creativecommons.org/licenses/by/3.0/

IMAGES

“Cardi B - Openair Frauenfeld 2019 02” Franz Schwichtenberg
https://commons.wikimedia.org/wiki/File:Cardi_B_-_Openair_Frauenfeld_2019_02.jpg
Creative Commons Attribution-Share Alike 4.0 International
https://creativecommons.org/licenses/by-sa/4.0/

“Confused Boy” j4p4n (altered)
https://openclipart.org/detail/286075/confused-boy
Creative Commons Universal Public Domain Dedication (CC0 1.0)
https://creativecommons.org/publicdomain/zero/1.0/

“Eagle String Art” Artist: Willie Bond
https://catalog.archives.gov/id/6361960
US Government work not subject to copyright protection

“Letter” vile_666
https://openclipart.org/detail/29821/letter
Creative Commons Universal Public Domain Dedication (CC0 1.0)
https://creativecommons.org/publicdomain/zero/1.0/

“Mary Everest Boole”
This work is in the public domain in the United States because it was
published or registered with the U.S. Copyright Office) before January
1, 1926.
https://commons.wikimedia.org/wiki/File:Mary_Everest_Boole.jpg

“Pencil” Jonathan Dietrich
https://openclipart.org/detail/37987/pencil
Creative Commons Universal Public Domain Dedication (CC0 1.0)
https://creativecommons.org/publicdomain/zero/1.0/

“Red Ball” chris_sharkot (altered)
https://openclipart.org/detail/3738/ball
Creative Commons Universal Public Domain Dedication (CC0 1.0)
https://creativecommons.org/publicdomain/zero/1.0/

All other material is original to the videographer.