65537-gon Construction (Most Accurate Version)
Автор: Doggo's Science
Загружено: 2024-12-15
Просмотров: 11284
Please check out the files below if you want to go into more detail about this construction.
List of steps:
https://drive.google.com/file/d/1KJj7...
List of point values:
https://drive.google.com/file/d/1HSQH...
List of just the point formulas (not mine, credits to Ken Brakke):
https://kenbrakke.com/RulerAndCompass...
This is the more accurate version of the 65537-gon construction animation. My previous one was full of mistakes, like Carlyle circles that don't intersect the X axis. I have fixed 99.99% of the visual bugs, so this version should be the most accurate. This will be the last 65537-gon attempt I will upload.
The 65537-gon is the last polygon in the series of Fermat prime polygons (3-gon, 5-gon, 17-gon, 257-gon, and 65537-gon). This makes it the largest constructible polygon with a prime number of sides. Fermat primes are defined as a prime number in the form of 2^2^n+1, with 65537 being 2^2^4+1. We currently have not found any Fermat primes higher than n=4.
Stats:
1142 Carlyle circles (including the first circle)
86308 Arcs
2283 Lines (excluding the ones in the polygon)
2029 Points (excluding the ones in the polygon)
91,762 Steps
84,910 Steps (combining the steps for perpendicular bisection)
h253 is the smallest point (-0.0009058899072389437)
b1 is the largest point (-154.93745120206825)
tier j contains the most points (745)
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