Footsteps of pi
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Footsteps of pi
1–10 of 38 posts
Re: Footsteps of pi
#2I always wondered if some hidden pattern would be exposed when visualising numbers in unconventional ways in numbers with no known pattern such as Pi or prime numbers. A sort of multi-dimensional rendering that suddenly reveals a hidden pattern.
Re: Footsteps of pi
#3Would be nice to make not just a decimal direction picture, but one for other bases as well. Binary won't work as you just move back and forth along a single line, but ternary should work, and as the minimal base for 2D directions, is less arbitrary than decimal. Then I'd look at bases 4,5,6,7, and octal as well to see whether the picture depends more on the number or on the base.
Another choice is whether to use absolute directions, or relative to the current direction, as in Logo.
Re: Footsteps of pi
#4I wonder if the path stays consistent in other (maybe very high) number bases, or if that general path is random and unique to base-10
Re: Footsteps of pi
#5Would be nice to make not just a decimal direction picture, but one for other bases as well. Binary won't work as you just move back and forth along a single line, but ternary should work, and as the minimal base for 2D directions, is less arbitrary than decimal. Then I'd look at bases 4,5,6,7, and octal as well to see whether the picture depends more on the number or on the base. Another choice is whether to use abs…
for binary, introduce a constant down step, and then let the line run back and forth in that space.
Re: Footsteps of pi
#6[deleted]
Re: Footsteps of pi
#7> I originally created this image in early 2020 to impress and woo my now-girlfriend, who I adore.
Dating gurus hate him for this one weird trick.
Re: Footsteps of pi
#8I always wondered if some hidden pattern would be exposed when visualising numbers in unconventional ways in numbers with no known pattern such as Pi or prime numbers. A sort of multi-dimensional rendering that suddenly reveals a hidden pattern.
This is sort of how Fermat's last theorem was solved by Andrew Wiles (forgive me if I misrepresent this proof, my math is a few years rusty) - by creating a different kind of representation of elliptic curves, it was possible to compare them to modular forms in a way that created a contradiction that proved the theorem correct.
Re: Footsteps of pi
#9I always wondered if some hidden pattern would be exposed when visualising numbers in unconventional ways in numbers with no known pattern such as Pi or prime numbers. A sort of multi-dimensional rendering that suddenly reveals a hidden pattern.
Well some numbers expose patterns when written as a continued fraction. In particular e becomes pretty regular.
You can modify the continued fraction slightly to make pi regular as well, but the normal continued fraction sequence doesn't give much of an insight. Other than the fact that 3 + 1/(7 + 1/16)) is a damn good approximation (7 digits, pretty good for something that can be written using only 4 digits total: [3;7,16]).
Re: Footsteps of pi
#10I saw one that was similar except that it used triplets of pi digits (3.xyzxyzxyz..) and drew line segments with direction (x,y) and magnitude z.