A Coffee Moment
Type of Spirals: A spiral is a curve in the plane or in the space, which runs around a centre in a special way.
Different spirals follow. Most of them are produced by formulas:The radius r(t) and the angle t are proportional for the simplest spiral, the spiral of Archimedes. Therefore the equation is:
(3) Polar equation: r(t) = at [a is constant].
From this follows
(2) Parameter form: x(t) = at cos(t), y(t) = at sin(t),
(1) Central equation: x²+y² = a²[arc tan (y/x)]².
You can make a spiral by two motions of a point: There is a uniform motion in a fixed direction and a motion in a circle with constant speed. Both motions start at the same point.
(1) The uniform motion on the left moves a point to the right. - There are nine snapshots.
(2) The motion with a constant angular velocity moves the point on a spiral at the same time. - There is a point every 8th turn.
(3) A spiral as a curve comes, if you draw the point at every turn(Image).
Figure 1: (1) Archimedean spiral - (2) Equiangular Spiral (Logarithmic Spiral, Bernoulli’s Spiral).
Figure 2 : (1) Clothoide (Cornu Spiral) - (2) Golden spiral (Fibonacci number).
More Spirals: If you replace the term r(t)=at of the Archimedean spiral by other terms, you get a number of new spirals. There are six spirals, which you can describe with the functions f(x)=x^a [a=2,1/2,-1/2,-1] and f(x)=exp(x), f(x)=ln(x). You distinguish two groups depending on how the parameter t grows from 0.
Figure 4: If the absolute modulus of a function r(t) is increasing, the spirals run from inside to outside and go above all limits. The spiral 1 is called parabolic spiral or Fermat’s spiral.
Figure 5: If the absolute modulus of a function r(t) is decreasing, the spirals run from outside to inside. They generally run to the centre, but they don’t reach it. There is a pole. Spiral 2 is called the Lituus (crooked staff).
Figure 7: Spirals Made of Line Segments.
Source: Spirals by Jürgen Köller.
See more on Wikipedia: Spiral, Archimedean spiral, Cornu spiral, Fermat’s spiral, Hyperbolic spiral, Lituus, Logarithmic spiral,
Fibonacci spiral, Golden spiral, Rhumb line, Ulam spiral,
Hermann Heights Monument, Hermannsdenkmal.
Raul Ramirez - Amsterdam
album: Ecomusica Vol. 2Played 123 times.
Fresh Clam Chowder
4 pounds small, raw Manila clams in the shell
1 pound red potatoes (about 3 medium), chopped into 1/2-inch bite-size cubes
2 tablespoons olive oil
4 sprigs fresh thyme
1/2 pound pancetta, cubed or bacon, sliced
1 large red onion, thinly sliced
1 stalk celery, thinly sliced
3 cloves garlic, minced
2 large carrots, peeled and thinly sliced into rounds
1 to 3 tablespoons chili paste, to taste
1 1/2 cups whole milk
1 cups heavy cream
Freshly ground black pepper
Italian flat leaf parsley, for garnish
Place the clams in a colander and rinse thoroughly under cold running water. Discard any clams with broken or open shells. Allow the clams to drain in the sink while you prepare your stock base.
In a large stock pot, bring about 5 cups of water to a boil and cook the potatoes until al dente, 4 to 5 minutes. Remove the potatoes with a slotted spoon, but do not drain off the water.
While the potatoes are boiling, in a second large, heavy-bottomed pot, heat the oil and thyme over low heat. Add the pancetta to the oil and thyme and cook, stirring often, about 5 minutes, making sure not to burn the bacon. Add the red onion, celery and garlic, and cook, stirring often, until the vegetables are translucent, 4 to 5 minutes. Add the carrots and chilli paste, and cook until the carrots soften slightly, 2 to 3 minutes. Add the potatoes and 3 cups of potato water and stir to combine.
Keep this chowder base warm over low heat, or refrigerate for up to 1 day. When ready to finish the soup, warm the chowder base over low heat.
When ready to serve, cook the clams. Working in batches, place enough clams to fill but not crowd the bottom of a heavy-bottomed sauté pan over medium heat. Ladle 1 cup of the chowder base on top and cover the pan. Simmer for about 4 minutes, or until the majority of clams open. Pick out any clams that have not opened. Transfer cooked clams to the pot with the chowder base, and continue cooking in batches until clams are all cooked.
Serve with cracked black pepper and chopped parsley.
Alone (by Marser)
Housen-in Temple, Kyoto, Japan
Isaac Hayes - Never Can Say Goodbye
album: Black Moses
(via the-theme-is:)Played 301 times.
Participation in Swink project - Poster Exhibition. Inspired by Django Reinhardt.
Illustration by Nearchos Ntaskas
You fall in love with people’s minds.
— Anaïs Nin, Henry & June: From the Unexpurgated Diary of Anais Nin. Harcourt, 1986