Problems Plus 18: Finding the Center of a Polygonal Spiral
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
Related Videos:
Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .
------------------------------------------------------
SUBSCRIBE via EMAIL: https://mes.fm/subscribe
DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate
Like, Subscribe, Favorite, and Comment Below!
Follow us on:
MES Truth: https://mes.fm/truth
Official Website: https://MES.fm
Hive: https://peakd.com/@mes
MORE Links: https://linktr.ee/matheasy
Email me: contact@mes.fm
Free Calculators: https://mes.fm/calculators
BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm
Free Online Tools: https://mes.fm/tools
iPhone and Android Apps: https://mes.fm/mobile-apps
-
16:04
Math Easy Solutions
16 days ago $0.01 earnedLaboratory Project: Taylor Polynomials: Question 2: Approximation Accuracy
1421 -
LIVE
Steven Crowder
1 hour agoEXCLUSIVE: Murderer Groomed High School Girl into Sex in Jail; Massive Cover-Up
34,628 watching -
1:09:11
Graham Allen
2 hours agoPutin PLOTTING With Kim Jong Un?! + US On High Alert For Terror Threat!
6.16K43 -
LIVE
Wendy Bell Radio
5 hours agoThe Spin Cycle Is Working Overtime
10,914 watching -
18:33
Stephen Gardner
9 hours ago🔴BREAKING: NYC must STOP THIS now! | CNN tries to SHUT DOWN Tucker Carlson
10.9K117 -
LIVE
jeffahern
2 hours agoNever Woke Wednesday's (6am Pacific)
929 watching -
50:37
Edge of Wonder
20 hours agoGobekli Tepe: Evidence Found that Proves Noah’s Flood is Real
57.3K35 -
1:25:59
TheMonicaCrowleyPodcast
20 hours agoThe Unseen Power Plays of the Left
76K23 -
19:33
Producer Michael
20 hours agoTHE NEW JACOB & CO RELEASES WORTH MILLIONS!!
29K9 -
11:38
Fascinating Horror
1 day agoTrapped Underground: The Wellington Pit Disaster | Fascinating Horror
14.2K4