Uploaded July 2026 | Updated September 2026, 2 weeks ago
The Koch snowflake fits inside a tiny circle, so its area is finite - but its edge is infinitely long. Every construction step swaps each segment for 4 pieces that are 1/3 as long, multiplying the perimeter by 4/3 forever, so the perimeter blows up. The area does not: each step glues on 4 times as many bumps at 1/9 the area, and because 4/9 is less than 1, that makes a geometric series that settles at exactly 8/5 of the starting triangle. Same process, two ratios - one above 1, one below it. The edge is so crinkly it sits between a line and a plane, with dimension log(4)/log(3), about 1.26. That is what makes it a fractal.
This video was partially created using Manim.
Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information.
#shorts #fractals #brithemathguy
The Koch snowflake fits inside a tiny circle, so its area is finite - but its edge is infinitely long. Every construction step swaps each segment for 4 pieces that are 1/3 as long, multiplying the perimeter by 4/3 forever, so the perimeter blows up. The area does not: each step glues on 4 times as many bumps at 1/9 the area, and because 4/9 is less than 1, that makes a geometric series that settles at exactly 8/5 of the starting triangle. Same process, two ratios - one above 1, one below it. The edge is so crinkly it sits between a line and a plane, with dimension log(4)/log(3), about 1.26. That is what makes it a fractal.
This video was partially created using Manim.
Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information.
#shorts #fractals #brithemathguy
