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Patterns Based on the Collatz Conjecture: BLACK-AND-WHITE VERSION
THIS IS THE BLACK-AND-WHITE VERSION OF MY BOOK. I also offer a full-color version for $8.99.
When we study the Collatz conjecture, our focus is usually on the specific numbers in a particular sequence. We might not be considering what’s going on “behind the scenes,” where there’s the creation of rows and additional numbers that will also lead to 1 .
This document doesn’t try to prove the Collatz conjecture; instead, I wanted to show some patterns created by the Collatz mathematics that might lead someone to a proof.
To identify any possible patterns, I created a chart where the conjecture is run in reverse. I started with 1 in the upper-right corner and computed some sequences, where this reverse sequence always moves left and down (never right and up, as the normal Collatz sequence would travel).
Anything we learn about the Collatz conjecture—whether major or minor—will likely get us closer to a proof (or a disproof).
When we study the Collatz conjecture, our focus is usually on the specific numbers in a particular sequence. We might not be considering what’s going on “behind the scenes,” where there’s the creation of rows and additional numbers that will also lead to 1 .
This document doesn’t try to prove the Collatz conjecture; instead, I wanted to show some patterns created by the Collatz mathematics that might lead someone to a proof.
To identify any possible patterns, I created a chart where the conjecture is run in reverse. I started with 1 in the upper-right corner and computed some sequences, where this reverse sequence always moves left and down (never right and up, as the normal Collatz sequence would travel).
Anything we learn about the Collatz conjecture—whether major or minor—will likely get us closer to a proof (or a disproof).
56 pages, Paperback
Published July 26, 2021
4 people want to read
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