Computational Physics Basics: How Integers are Stored

Unsigned Integers Computers use binary representations to store various types of data. In the context of computational physics, it is important to understand how numerical values are stored. To start, let’s take a look at non-negative integer numbers. These unsigned integers can simply be translated into their binary representation. The binary number-format is similar to […]

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String Art and Heart Curves

In my childhood, my parents would take us to the seaside for the summer holidays. One thing, other than the sun and the beach, that I distinctly remember were the nautic decorations in the cafes. One particular image was an abstract picture of a sailboat made from some nails hammered into a wooden board and pieces of string that were tied around those nails. It always fascinated me, how this simple arrangement of straight lines could create such a beautiful and dynamic image. Around the same time, in primary school, we used a similar technique in art class, with needle and thread and a piece of cardboard, to create an image of a snowflake.

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Interactive Data Visualisation in Schnek

Back in the old days computer were simple devices. When I got my first computer it was a Commodore 64. There were some games you could play but most of the fun to be had was in programming the device. Ever since those days I was fascinated with using maths and physics to create computer images. This is what ultimately drove me into computational physics. I often think of the old times when I could play around with parameters and immediately see what is happening. For this reason, I have written a small extension to the Schnek simulation library that will create a window and plot a colour plot of any two-dimensional data field.

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Beware of square roots and exponentials!

In the last post I asked you the question, what is wrong with the following proof. As some of you noticed, the answer lies in the fact that the identity is only true for positive real numbers x and y. In general one has to be careful with the identity (xy)a = xaya for non-integer […]

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Another proof that -1=1

Here is a little maths teaser for you. Since I was a student, I always loved those “proofs” that zero equals one. Of course, most of the time, this was achieved by sneakily dividing by zero somewhere along the way. But yesterday I came across a proof that used a different, slightly more subtle trick […]

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