Problems Plus 4: Limit of the Angle of a Spiraling Triangle Sequence
In this video I go over a sequence which involves rotating triangles around a point and determining the limit of the inner angle of the triangles. To solve this I first use the Pythagorean Theorem to determine the square of the distance of one of the sides of the triangles, and then simplify it by noting it includes a geometric sum. Given that the other triangle side keeps doubling, we can thus determine a formula of the inner angle. Using exact trigonometric ratios, we can determine that the limit of the angle approaches 60 degrees.
The timestamps of key parts of the video are listed below:
- Problem 4: Find the Limit of the Angle in the Triangle: 0:00
- Solution: 1:31
- Pythagorean Theorem for the Square of the Length: 4:14
- Geometric Sum: 10:37
- Finite Geometric Sum: 12:34
- Calculating the Angle: 17:14
- Exact Trigonometric Ratios: 23:40
- Angle Approaches 60 Degrees: 25:22
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 .
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