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13 Sep 2023 03:57:26 UTC
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Problems Plus 5: Fractal Snowflake Curve
In this video I go over calculating the area of an infinite snowflake curve constructed by adding a triangle to every side of the previous shape, and starting with an equilateral triangle of side length 1. Although the total length of the shapes approach infinity, the actual area approaches a finite number. When we determine the area of each consecutive shape, we obtain a convergent Geometric infinite series, which we can then plug in our earlier formula for the area. The area of the snowflake approaches exactly a 60% increase as compared with the original triangle area. Truly epic stuff!

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

- Problem 5: Snowflake Curve: 0:00
- Solution to Part (a): 2:59
- Solution to Part (b): 9:08
- Solution to Part (c): 10:14
- Determining a series for the area: 14:30
- Geometric Series: 21:36
- Calculations: 30:16

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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