Piston Extenders Follow-up: The Extension Sequence PROOF!

WATCH PART 1: https://youtu.be/t4iGp44WQ-U?si=xv-1xh-bgLnWVLu7
More about SoME3: https://some.3b1b.co/

Patreon: https://www.patreon.com/mattbatwings
Discord: https://discord.gg/V5KFaF63mV
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Piston Animations created by @Sloimay
Proofs:
https://imgur.com/a/o0km92o
https://imgur.com/a/doCovlx

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0:00 Part 1 in the description!
0:36 Better Extension Formula
3:39 Extension Optimality Proof
8:24 Extension Parallelization
9:19 Lower Bound Symmetry
10:21 Retraction Reversal
10:50 Retraction Parallelization
11:16 Subscribe!

Music (in order):
MDK - Jelly Castle https://youtu.be/oMoYbINoShc?si=0IGHq8ClhJxBe8a8
Harris Heller - Iridescent https://youtu.be/FWXzp8THOuc?si=PJKIOfsIOy8FTEd1
Harris Heller - Guilty Spark https://youtu.be/w9M1_ZoxP54?si=9UfDIIp8ltZbyWar
Harris Heller - Plethora https://youtu.be/4U3iFdSyNuI?si=c92QIZlad-nRz2Ia
Alexander Nakarada - Favorite https://youtu.be/FbjW1ttvTxw?si=F-caDgNQzyosQ0ah
Harris Heller - Path Less Traveled https://youtu.be/l_o56ny2aao?si=OTZkmVgQJOzsF7ut
Harris Heller - Tokyo Rain https://youtu.be/WtOcNctiLfY?si=41IFoGee2m5fH6yu
Harris Heller - Golden Age https://youtu.be/Ws205UM0GzM?si=71tmYZk9P4U3B4j2
Harris Heller - Manhattan Project https://youtu.be/s02K_ofVPJc?si=3C_li1QFX_2jncHX
Harris Heller - One More https://youtu.be/mghwa8toMgw?si=al7h8q-yaF7gGyvy
Harris Heller - Creator's Kingdom https://youtu.be/fhloSoaPMQQ?si=1RQa8y3-lQcQ5Pvg
Mellowind - Sleep https://youtu.be/Mx_OfT-wHZs?si=dGPi-WH-mg8ZcuqX

Видео Piston Extenders Follow-up: The Extension Sequence PROOF! канала mattbatwings