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

  • Thread starter Thread starter Adam Kohnle
  • Start date Start date
  • Tags Tags
    Mathematical
Adam Kohnle
Messages
21
Reaction score
5
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.
 
  • Like
Likes Dadface
Mathematics news on Phys.org
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
Back
Top