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08.09.2013
An important aspect of entertainment is the audience, which turns a private reaction or leisure activity into entertainment.
Answer: Not to worry Anne and Ed, you can go ahead and prepare this coffee just as you would regular coffee. Michiel and Arno are both mathematicians in the Netherlands at the Radboud Universiteit Nijmegen Institute for Mathematics, Astrophysics and Particle Physics. Did you notice when looking at the tiled sphere that both the Icosidodecahedron and the Hexastersphaira graphics are actually identical.
At the same time, when looking at the Polarsphaira, one may notice 8 triangular shapes made with 3 rhombus patterns each. I made up the words Astersphaira, Polarsphaira, and Hexastersphaira using mostly the Greek language to give homage to Greek geometry.
While playing around with knight moves on the chessboard from the home page, I ended up with an interesting symmetrical pattern that could be turned into a very nice four color chain-linked tessellation.
After making the above animation, I connected the four symmetrical patterns from the 8x8 square to make a 7x7 square tessellation piece. Four copies of the 7x7 square shown above on the right, can be connected together in such a way as to make a single larger tessellation piece. While creating these square chain-linked tessellations, I decided to go ahead and make a simple interlocking ring tessellation. Depending on one's perception of the tiling, different objects may appear with various 2-D or 3-D orientations.
The further your eyes are from the screen, the more the lines in the "Still Motion" tessellation appear to oscillate when looking at the web-page background.
As for the unique geometry created by knight moves that can make beautiful 2-dimensional, 3-dimensional, and multi-dimensional tessellations, I call this geometry: Springer Geometry (patented as Geometric Craft and Educational Kit - Patent #7029364, April 18, 2006).
Polygonal shapes made by chess pieces on the chessboard, especially those made by the knight, are the subjects of this text. Many thanks goes to Paul Bourke for his excellent and professional renderings of my Springer Geometry concepts.
Much of my work on Knight Tours is referenced on hundreds of other Web sites, and used by schools, universities, and technical institutes to help their students learn programming logic, create artwork such as tessellations from Knight Tours, and to learn basic concepts about geometry (platonic solids) and other areas of mathematics. Philipps-Universitat Marburg, Fachbereich Mathematik und Informatik: Ubungen zu, Parallelitat in funktionalen Sprachen Nr.

It will have a unique taste that is more bold or pungent, but even at this time, the coffee I have in house is Starbucks Espresso Roast that I prepare in my Cuisinart drip brewer. By replacing the perimeter edges in the Icosidodecahedron with star limbs, the Hexastersphaira takes its form. I used 67 lb white cover paper, a drink sterring straw, coated copper wire, thick piano wire, and Elmer's glue. I then divided each individual pattern within the square into three smaller shapes representing the 2x1 "L" shaped move of the Knight. The curves are a bit rough, so I'll need to redo the rings when I get a better graphics program. Check out the following letter from Paul Bourke to see how he is using my geometry in Astrophysics. Our page is related to the Entertainment which consists of everything u want like Funny pictures, videos, gifs, memes, comics, and many more which can't make you bore..
Each compass contains four rhombus patterns (representing North, South, East, and West) made from the knight's move on the chess board.
Both the Hexahedron and the Octahedron are harmoniously intertwined, as is the Dodecahedron and Icosahedron mentioned earlier. Inside of the Polarsphaira resides the final shape of the knight's tour, a square which makes a cube containing the hidden Tetrahedron. The cube in the center of the ornament can still be the various jeweled tiles but with a small lightbulb in the center to radiate the various colors of red, green, blue, purple, yellow, and clear.
I got the quarter inch wood cube and quarter inch jeweled tiles from Michaels, a local craft store. I changed the colors of the red squares within the four symmetrical patterns of the Knight's Tour to include blue, green, yellow, and white. In fact, espresso coffee is making reference to how dark the bean has been roasted so in that respect, any coffee can be roasted to be espresso coffee. If a boarder-line was drawn around the outer perimeter of each compass, 6 square patterns would appear, thus making a Cube or Hexahedron (6 sided figure). The Hexahedron has 6 faces and 8 vertices while the Octahedron has 8 faces and 6 vertices, an exact reciprocal of each other. It is a quarter inch block of wood that will have six different jeweled tiles covering each of the faces.

Rotating the individual spheres in opposite directions while lighting the cube would make an interesting effect. When you make the spheres out of paper, you can actually collapse the spheres inward to make other star or spur shapes. Notice that those shapes can be easily created from spheres when using the 3-d tiling of the knight move patterns.
The tiles represent the cyrstals or precious gemstones of the earth that have a cubic or hexagonal crystaline structure (diamond, ruby, emerald, sapphire, topaz, amethyst). Pretty cool patterns appear similar to the beautiful candle lantern shown on either side of the paper model. The cube at the center of the Polarsphaira contains the Tetrahedron but it is not visible to the eye. But to befriend the one who regards himself as your enemy is the quintessence of true religion. But today well lived makes every yesterday a dream of happiness, and every tomorrow a vision of hope.
Take the opportunity to learn from your mistakes: find the cause of your problem and eliminate it. Appreciate your mistakes for what they are: precious life lessons that can only be learned the hard way. Make a decision to relinquish the need to control, the need to be approved, and the need to judge. The world is all gates, all opportunities.”– Ralph Waldo Emerson“We are still masters of our fate.
We are still captains of our souls.”— Winston Churchill“What is life but a series of inspired follies?

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