What is the Collatz Conjecture and How Can High Schoolers Have Fun With It?

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SUMMARY

The Collatz Conjecture, also known as the Hailstone sequence, is a mathematical sequence that begins with any positive integer. If the number is odd, it is multiplied by 3 and then 1 is added; if it is even, it is divided by 2. This process is repeated, and it is conjectured that no matter the starting number, the sequence will eventually reach 1. High school students can explore this conjecture using large numbers, such as 294329058492458430950869839065893685930, with the help of online computational tools.

PREREQUISITES
  • Basic understanding of mathematical sequences
  • Familiarity with odd and even numbers
  • Knowledge of multiplication and division operations
  • Access to online computational tools for large number calculations
NEXT STEPS
  • Explore the mathematical implications of the Collatz Conjecture
  • Learn about Hailstone numbers and their properties
  • Investigate computational methods for simulating the Collatz sequence
  • Watch Numberphile's video on the Collatz Conjecture for visual explanations
USEFUL FOR

This discussion is beneficial for high school students, mathematics enthusiasts, and educators looking for engaging ways to introduce mathematical concepts and conjectures.

Adam Kohnle
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Hello everyone and I hope you had a happy Easter if you celebrate it and even if you don't, I hope you had happy day at least! I was wondering if anyone knew of any interesting or "fun" mathematical conjecture, equations or whatever that an inexperienced high schooler (me or anyone else curious) could understand and have fun with it. My twin told me of one where you multiply odd number by 3 but divide even ones by 2 and it will always eventually get 1. I could have remembered that wrong but either way it is interesting and fun to mess with by using numbers like 294329058492458430950869839065893685930. Thankfully for a number like that their are online resources that can do the math for you because that would take a while.
 
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