Scanline VFX has created some amazing computer generated water effects with their proprietary Flowline fluid simulation software. Their website has some great videos demonstrating what they have done.
You can create similar effects with the free open-source software Blender. Of all the physical phenomena you can simulate with Blender, fluid dynamics is the easiest.
Here are the greatly simplified steps:
1. Create a starting shape for initial state the liquid will be in. In my short video I started with a sphere.
2. Create a shape to contain the water. I used a cube that was slightly larger than the sphere.
3. Tell Blender how many frames of animation to create.
4. Tell Blender to “bake” and Blender goes to work cranking out your animation.
By default the only force acting on your fluid is gravity. You can increase the complexity by adding inflows, outflows, obstacles, etc.
A Möbius strip is a mathematical surface with only one side and one boundary component, or what you might call an edge. If you put a half-twist in a rectangular piece of paper and join the ends the the result is like a Möbius strip.
As far as I can tell, not being an astronomer, the only way to measure the distance of a star using geometry is by measuring stellar parallax and angular diameter. The problem with angular diameter is that not all stars are the same diameter. A more distant, larger star could have the same angular diameter as a closer, smaller star and so it becomes more difficult to determine which star is closer. That’s when astronomers begin measuring things with a spectrophotometer and other instruments. Astronomers say that even the closest stars are light-years away.
If you believe that the earth is round and that it orbits the sun along with the other planets in our solar system, then you must conclude that the stars are at least as far away as the farthest planet. Thanks to Johannes Kepler and others we have a pretty good idea how far away the planets are.
Alexander Overwijk draws a perfect freehand circle 1 meter in diameter in less than a second. Basically he goes swoosh with a piece of chalk and he’s done. It’s quite impressive.
The video is here.
Pi is the ratio of a circle’s circumference to it’s diameter. This ratio has been calculated to be approximately 3.141592653. An engineer designing a large circular building would not need a measurement any more accurate than that, but mathematicians have calculated Pi to billions of digits.
∏ (The symbol for Pi, may not display correctly in some browsers)
Website with many digits of pi in a beautiful layout. http://3.14.maxg.org/