0
In this video I construct an infinite series of right triangles rotated about a single point and show that the central angle diverges to infinity as the number of triangles approach infinity. To show this, I first construct a table determining the base lengths of each triangle using the Pythagorean Theorem to obtain a formula for the n-th triangle base. From this we can obtain the angle as a formula involving the inverse tangent trigonometric function. Applying the Limit Comparison Test with a diverge p-series, I show, using L'Hospital's Rule, that the angle series diverges, hence the angle approaches infinity as the number of triangles approach infinity. This means that the series of triangles makes infinitely many turns around the central point.
The timestamps of key parts of the video are listed below:
This video was taken from my earlier video listed below:
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
Comments:
Reply:
To comment on this video please connect a HIVE account to your profile: Connect HIVE Account