Fibonacci-like sequences that converge to 0

1604 days ago

I was curious about whether Fibonacci-like sequences could converge to 0, with a proper choice of starting terms and the usual recurrence relationship:


It turns out that they can, if the ratio of the second term to the first is 7249246bfa7088a808ebe568b18dd326c782dc4c, or 1-φ, approximately -0.618.

I found this using the closed form for Fibonacci-like sequences

25e243f0a1759585683430bdfcc60e927f296abc and solving for 510842f7d1fc6a07b50c4521dd7ee6a633628623.

Here are the first few elements of the sequence:

Interestingly, the integer part are the Lucas numbers and the multiples of the square root are the Fibonacci numbers, and their ratio converges to the square root of 5, based on their closed forms.



cor: a sample correlation game

1611 days ago

If you know what sample correlation is, you might enjoy Cor: A Sample Correlation Game, which is available here



truecrypt on the BeagleBone Black (Debian)

1821 days ago

As I’m using Revision B, I ended up downloading source to a mount point on the sdcard (/mnt/sdcard) as it’s too easy to fill up the 2GB root device otherwise.

Download and unpack truecrypt-7.1a-source

Download and unpack wxWidgets

export SDCARD=/mnt/sdcard
cd ${SDCARD}
tar xvfz wxWidgets-2.8.12.tar.gz
export WX_HOME=${SDCARD}/wxWidgets-2.8.12/

Download PKCS11 headers

mkdir ${SDCARD}/pkcs
cd ${SDCARD}
wget '*.h'
export PKCS11_INC=${SDCARD}/pkcs

Build truecrypt

cd ${SDCARD}/truecrypt-7.1a-source
make NOGUI=1 WX_ROOT=${WX_HOME} wxbuild

Copy the binary to the system

sudo cp Main/truecrypt /usr/bin
chown bin.bin /usr/bin/truecrypt
chmod 0755 /usr/bin/truecrypt



MediaWiki and the Case of the Sporadic LaTeX Failure

2129 days ago

I recently upgraded to MediaWiki 1.21 for my personal wiki, and I was annoyed to see that LaTeX support was removed, though it and MathJax are available as extensions.

Once I installed it, I was vexed by sporadic failures in typesetting — texvc would succeed in producing an image about 20% of the time.

Eventually, I found out why — the memory limits on the wfShellExec call were set pretty low, and so most of the time it would fail to malloc the memory it needed.

Increasing the global default for shell calls in LocalSettings.php fixed this:

$wgMaxShellMemory = 402400;

If you’re having the same problem, give it a try.



Parsing sentences and words from sentences in java

2138 days ago

I think this is worth highlighting, because I’ve seen so many cases where programmers “parse” text using java tools like StringTokenizer or split() with a set of punctuation characters:

java already has a built-in, locale-aware method for getting sentences from text, and words from sentences:


Anything you write yourself to parse text will likely miss corner-cases and be un-prepared for other languages.

Since BreakIterator does the job, isn’t difficult to use and has been around jdk 1.2, why not use it?

odd punctuation like this, for example, when reading words.



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