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.

Image:I shared at Spirals by Jürgen Köller - Ferns by Margaret Oomen & Ferns by Rocky.Spiral compulsion. But this is a handy reference.

Chemistry meets astronomy in today’s post, with a graphical guide to the atmospheres of our Solar System.

Read more about them here (there’s also a link to download the graphic, or to purchase it as a large poster): http://wp.me/p4aPLT-nV

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I’ve received a lot of letters from artists asking to check out their artwork and their blog, and I’ve noticed that a lot of them openly write unhealthy amounts of negative comments about their artwork, it was super depressing, honestly. :(

Confidence plays a very very important role as an artist, it’s what helps us learn and grow without the constant feeling of doubt and jealousy! You are a unique individual who must go down your own unique path, and as scary as it sounds, you can’t rely on others to hold your hand all the way through. You are the only one who can get yourself to where you need to go, and beating up your artwork is not the way! Trust yourself and your abilities to make a change, and you can do anything!!

Love your art, love yourself!

Fridge LogicTanuki often turn into things, have stuff put in them, and then transform back. It’s what they do. It’s tanuki stuff.

Did I ever tell you I also got kicked out of cartoon network for flirting with Mordecai? I love that bird.

Toner whined and reached back to tug up the skimpy bathing suit he’d been forced to buy at the Resort’s shop. He’d outgrown the shorts he’d brought and now was overflowing and ripping apart this pair.

"I gotta stop going to the buffet" he whimpered, as he waddled toward that exact destination. He knew he shouldn’t be visiting for the third time since breakfast but his belly demanded it, gurgling with embarrassing intensity just half an hour after his last greedy snack. All that eating combined with the lazy atmosphere and enabling behaviors of the staff meant the dog was getting softer and softer in a hurry.