Somniloquy II Photo by Mike Taylor


Somniloquy II Photo by Mike Taylor

(Source: pinkmanjesse)



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:  SpiralArchimedean spiralCornu spiralFermat’s spiralHyperbolic spiralLituus, Logarithmic spiral
Fibonacci spiral, Golden spiral, Rhumb line, Ulam spiral
Hermann Heights Monument, Hermannsdenkmal.

Image: I shared at Spirals by Jürgen Köller - Ferns by Margaret Oomen & Ferns by Rocky.

Spiral compulsion. But this is a handy reference.

"My response to the “I am not a feminist” internet phenomenon….

First of all, it’s clear you don’t know what feminism is. But I’m not going to explain it to you. You can google it. To quote an old friend, “I’m not the feminist babysitter.”

But here is what I think you should know.

You’re insulting every woman who was forcibly restrained in a jail cell with a feeding tube down her throat for your right to vote, less than 100 years ago.

You’re degrading every woman who has accessed a rape crisis center, which wouldn’t exist without the feminist movement.

You’re undermining every woman who fought to make marital rape a crime (it was legal until 1993).

You’re spitting on the legacy of every woman who fought for women to be allowed to own property (1848). For the abolition of slavery and the rise of the labor union. For the right to divorce. For women to be allowed to have access to birth control (Comstock laws). For middle and upper class women to be allowed to work outside the home (poor women have always worked outside the home). To make domestic violence a crime in the US (It is very much legal in many parts of the world). To make workplace sexual harassment a crime.

In short, you know not what you speak of. You reap the rewards of these women’s sacrifices every day of your life. When you grin with your cutsey sign about how you’re not a feminist, you ignorantly spit on the sacred struggle of the past 200 years. You bite the hand that has fed you freedom, safety, and a voice.

In short, kiss my ass, you ignorant little jerks.”

- Libby Anne (via newwavenova)

(Source: dumbledoresarmy-againstbigotry)


Bob Stone
Website | Flickr


Bob Stone

Website | Flickr


Karijini NP, Western AustraliaPaul Pichugin


Karijini NP, Western Australia
Paul Pichugin



(Source: ellismiranda)


Individual Cinnamon-Apple Tarts Recipe


Individual Cinnamon-Apple Tarts Recipe





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