## Archive for 2006

### chain and parabel

Friday, December 15th, 2006

I attached a little silvery chain to a mathematical curve template in order to illustrate the difference between a catenary and a parabola.

Then I put the curve template (also called french curve, also on google images) into the dishwasher in order to get it upright for an orderly scientific photo. The forks and knives in the image are disturbing, but well one has to live with them for now.

The experiment displays a line which is described by a hanging chain.

If one compares it with the line of a parabola given by the function f(x)=x^2 (on the curve template) then one sees that the two lines are only almost fitting and in fact a better mathematical model for a hanging chain is the catenary, given by the cosh function f(x)=cosh(x), i.e. the hyperbolic cosine (not to be confused with a hyperbola). The model is constructed via the physical picture of many chain links taking each other by the hand which are subject to a constant gravitational force, or in other words: if you cut the chain at various points then the repective chunks would fall down separately.
There are very beautiful partially interactive links on the Wikipedia catenary site, which illustrate this.

The above observation is already described in this old mathematical physics paper from the early 17th century, which is beautifully accessible thanks to the work of people who had fun with mathematics. There is also a tender drawing of down parabolas.

### at

Thursday, December 14th, 2006

The at sign (or commertial at) is nowadays mostly known for its use in e-mail addresses. (more…)

### abbrev.

Wednesday, December 13th, 2006

### Make peace not war

Tuesday, December 12th, 2006

(some images are from wikipedia ->here and here)

Monday, December 11th, 2006

Confocal quadrics are known to form a triply orthogonal coordinate system on most of the three dimesional space. (more…)

### different media

Monday, December 11th, 2006

While tidying up I found the above vinyl records. Some people swear on the sound of vinyl. Some dont hear a difference to the digital. I think one should be less dogmatic about vinyl vs. digital. Its the sound that is different and not the music. Both are ok.

In any case: “Sonne statt Reagan” (sun instead of rain/Reagan) should also be on YOU-TUBE.

### game developpers

Sunday, December 10th, 2006

### killer

Sunday, December 10th, 2006

submarine produced an animated and set to music version of the graphic novel the killer by Jacamon and Matz. While the sujet is not my favorite I found the style pretty impressive.

### batrachian

Friday, December 8th, 2006

The images display two batrachians: a real toad (a gulf coast toad) and one from the nvidia demo (of their current graphics card flag ship). One can interact with both of them now (gulf coast toad and nvidia frog). While the graphics are amazing (but obviously still not photo realistic in case of the nvidia frog), the simulated frog seems to miss quite some ai. So maybe they should give it some boost with an ai accelerator card.