Name: Problems Plus 18: Finding the Center of a Polygonal Spiral
Uploaded: 2023-09-30T04:49:50+00:00
Duration: 29 min 25 s
Description: In this video I solve for the center of a polygonal spiral that is constructed by drawing a line connecting, at first, the midpoint points of the sides of a square and then connecting the midpoints of

2 years ago

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math calculus science stem education polygon stewart calculus problems plus mathematics amazing math fractals

In this video I solve for the center of a polygonal spiral that is constructed by drawing a line connecting, at first, the midpoint points of the sides of a square and then connecting the midpoints of the previous lines forming an infinite spiral. I then use mathematical induction to prove the given formula for the x terms, and do the same for similar y terms. Taking the limit as n approaches infinity, I show am able to determine the center of the polygonal spiral. Truly amazing stuff!

The timestamps of key parts of the video are listed below:

- Problem 18: Polygonal Spiral: 0:00
- Solution to (a): Equation for x terms: 2:24
- Using mathematical induction: 6:52
- Summarizing all the induction terms: 16:43
- Similarly, we can solve for the y terms: 19:45
- Solution to (b): Solving for the x coordinate at infinity: 23:00
- Solving for the y coordinate at infinity: 27:44
- Final answer: Coordinates at infinity: 28:58

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P