Life is a peephole…

Here’s a nice quote that I found at the beginning of a book I was reading. I found it rather profound and wanted to share it here.

Life is a peephole, a single tiny entry onto a vastness — how can I not dwell on this brief, cramped view I have of things?

Yann Martel, Life of Pi

Also relevant:

That’s your dose of philosophy for the day, internet.

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Linux/Programming Snippets – Wave 2

Here’s some more useful things I’ve found myself using lately. Yeah, they’re trivial, but I’m putting them here so they will be easy to refer back to.

how to do simple arithmetic in a bash script
$((1+1)) does 1+1
$(($i+2)) does the variable i + 2

how to alias something in bash
alias youralias=’the command to run’
example: alias ls=’ls -l’

to print the nth line of a file
cat yourfile | sed -n 2p

basic git commands

  • git add yourfile – adds yourfile to the repository
  • git commit – add a commit message, commits the file changes for all “added” files
  • git push origin master – pushes the changes to github
  • git pull – pulls down the most recent changes into your local repository

Fibonacci Square Updates

So as I noted back in this post, I’ve got more fun things to share about this curious sequence. I got the idea from this video here, and decided to test it out on my own sequences. My “fibonacci grids” are similar to what is shown in the video, but in mine, you can see that at the beginning of each line, I retain the first number in my sequence on each line.

The basic premise of the video was that if one picks out a space of 2×2 numbers on this Fibonacci Grid, (he proceeded to write the original sequence and carry over no numbers, however) the determinant of the resulting “matrix” can be predicted cleverly by simply looking at the last number on the first line. What I’ve noticed is interesting because mine seems to rely on the parity of the starting number. My conjectures are as follows. I have not completed proofs as yet, but wanted to get this idea out there.

Conjecture 1. For the first and second values in a Fibonacci-like sequence (denoted here as f, s. respectively) in a 4 by r fibonacci square (using Nelson’s modified rules as noted in the original post), where f \equiv 1 \mod 2, then the determinant of any 2 by 2 square is (s*f)*(s+f)*r, where r is the starting “row” of the fibonacci square.

Conjecture 2. For the first and second values in a Fibonacci-like sequence (denoted here as f, s respectively) in a 4 by r fibonacci square (using Nelson’s modified rules), where f \equiv 0 \mod 2, then the determinant of any 2 by 2 square is f*(s+f)*r, where r is the starting “row” of the fibonacci square.

Now if only I were better at proofs…all the same, thought this was neat! Need to extend it to include arbitrary row lengths.

Return of the Blarg!

I know it’s been quite a while, but life happened and I got lazy about this blog. But I have returned, and have a new set of things to talk about. I’m now in Week 4 of my Clemson REU, and although its been stressful, its been good fun as well.

I’ve made some more progress with the “Fibonacci Squares”  problem, which I will elaborate on in a further post. In addition, I’ll post an overview of the problem I’ve been focusing on here at the REU. Finally, I gave a short talk on Introduction to P and NP today and I’ll be posting that here as well.

The maths shall return! Stay tuned…

Where all the magic happens…