Category Archives: Math

10 Awesome Theorems & Results

Posted on February 13, 2011 by lorg

When I look back at various mathematical courses I took, most have at least one theorem that I really liked. Usually I like it because the proof has a surprising trick, sometimes it’s because of the unexpected conclusion, or maybe … Continue reading →

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Posted in Cryptography, Math | Tagged , | 12 Comments

Visualizing Data Using the Hilbert Curve

Posted on April 17, 2010 by lorg

Some time ago, a coworker asked me to help him visualize some data. He had a very long series (many millions) of data points, and he thought that plotting a pixel for each one would visualize it well, so he … Continue reading →

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Posted in Fractals, Graphics, Math, Programming, Python | Tagged , , , | 2 Comments

Fast Peak Autocorrelation

Posted on October 14, 2009 by lorg

So, I was at geekcon. It was a blast. There were many interesting projects, and I didn’t get to play with them all. I did get to work a bit on the Lunar Lander from last year, and this year … Continue reading →

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Checking the ulam spiral

Posted on September 17, 2009 by lorg

In the following post, the Ulam spiral is described. It’s a very simple object – write down consecutive natural numbers starting from 41 in a square spiral. Curiously, the numbers on the diagonal are primes: Reading this post, I immediately … Continue reading →

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Posted in Math, Programming, Python | Tagged , , , , | 4 Comments

Computing Large Determinants in Python

Posted on March 25, 2009 by lorg

Story: For my seminar work, I had to calculate the determinant of a large integer matrix. In this case, large meant n>=500. You might say that this isn’t very large and I would agree. However, it is large enough to … Continue reading →

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Posted in Algorithms, computer science, Math, Programming, Python, Research | Tagged , , , , , | 2 Comments

Fractal Memory Usage and a Big Number

Posted on June 12, 2008 by admin

In a previous post I said I’d talk about 4**(4**(4**4)). First, about the number. I first saw it mentioned in a math lesson back in high-school, when the teacher wanted to demonstrate estimation abilities. He wrote it on the board, … Continue reading →

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Posted in Algorithms, computer science, Fractals, Math, Programming, Python | Tagged , , , | 1 Comment

PyKoan – The Logic Game

Posted on June 1, 2008 by lorg

As you can probably tell, I’m back from my undeclared hiatus. I’ve got lots of stuff to talk about, and I’ll be starting with PyKoan, one small project I’ve been working on lately in my spare time. A few weeks … Continue reading →

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Two Mathematical Bugs

Posted on March 8, 2008 by lorg

A few days ago, I discovered I had at least one, maybe two mathematical bugs. The first bug is in the line clipping algorithm. Here’s a quick reminder of what’s going on there: There are six points of interest: the … Continue reading →

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Posted in Algorithms, Geometry, Math, Programming, Python | Tagged , , , , | 2 Comments

Solution for the Random Selection Challenge

Posted on February 23, 2008 by lorg

A few days ago, I wrote up two small Python Challenges. Several people have presented solutions for the first challenge, and I also posted my solution in the comments there. However, the second challenge remained unsolved, and I will present … Continue reading →

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Fun with Matrices

Posted on February 20, 2008 by lorg

I’ll let the code speak for itself: In [81]: m = Matrix(array([[1.0,1.0],[0.0,1.0]]))   In [82]: def my_sqrt(x, num_iters): ….: r = 0.5*x ….: for i in xrange(num_iters): ….: r = 0.5*(r+x/r) ….: return r ….:   In [83]: m*m Out[83]: … Continue reading →

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Posted in Math, Programming, Python | Tagged , , | Leave a comment