(Source: twocubes)

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(Source: a-na5)

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underthesymmetree:

Fibonacci you crazy bastard….

As seen in the solar system (by no ridiculous coincidence), Earth orbits the Sun 8 times in the same period that Venus orbits the Sun 13 times! Drawing a line between Earth & Venus every week results in a spectacular FIVE side symmetry!!

Lets bring up those Fibonacci numbers again: 1, 1, 2, 3, 5, 8, 13, 21, 34..

So if we imagine planets with Fibonacci orbits, do they create Fibonacci symmetries?!

You bet!! Depicted here is a:

  • 2 sided symmetry (5 orbits x 3 orbits)
  • 3 sided symmetry (8 orbits x 5 orbits)
  • sided symmetry (13 orbits x 8 orbits) - like Earth & Venus
  • sided symmetry (21 orbits x 13 orbits)

I wonder if relationships like this exist somewhere in the universe….

Read the Book    |    Follow    |    Hi-Res    -2-    -3-    -5-    -8-

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un:

L&R always reminded me of a grity OMD

(Source: citiesoftheinterior144)

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ashestoashes-funktofunky:

Enola Gay
Is mother proud of little boy today
This kiss you give
It’s never ever going to fade away

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ondabed:

Valloria, Italy

ondabed:

Valloria, Italy

(Source: boredpanda.com)

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normaltd:

just-close-your-eyes-and-leap:

Shirley Bassey - This Is My Life

─═ڿڰۣڿ☻ڿڰۣڿ═─

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dywiann-xyara:

The mathemagician’s room - by, now it comes, meeeee :P
It’s a place full of wonder, strangeness and bizarre beauty: the room - or should I say space - of a “mathemagician”…It’s a common optical illusion, a kind of tricky paradox. “If our brains are simple enough for us to understand them, then we’d be so simple that we couldn’t.” ~ Quote by Ian Steward (a mathematician)In my mind, mathematics equals (somehow) magic, mathematics is magic, therefor “mathemagic” :PThe floor self is an impossible figure - a typical symbol for paradoxes… The spirals on the chessboard-floor are Fibonacci spirals. (If you want to know more, then check out my Phi/Fibonacci tag.This drawing is mostly about the beauty of Phi Φ, Psi ψ and the Fibonacci-sequence.The fibonacci sequenceThe fibonacci sequence works this way:1+1 = 21+2 = 32+3 = 53+5 = 85+8 = 138+13 = 2113+21 = 3421+34 = 5534+55 = 8955+89…… and so on…The sequence then is: 1;1;2;3;5;8;13;21;34;55;89;…….Let’s play with these numbers!1/1=12/1=23/2=1.55/3=1.66666…8/5=1.613/8=1.62521/13=1.615384 …34/21=1.6190476………If we continue this more and more, it will come closer and closer to a mathematial constant: Phi ΦBtw: Φ=1.618033988749894848…It can be calculated as followed:Φ= 1+√5’ /2__________________Phi, the golden ratio as ratio:If you have two lines:The proportions are 1to1.618:Or here demonstrated: 10 to 16.18Like:  _ _ _ _ _ _ _ _ _ _ (10) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ (16 (aka~16.18)lines) This is the proportion/ratio stupidly demonstrated in a text. xD
Psi ψPsi is the golden angle. Its value is about 137.5°.So.. Let’s connect Φ with π (Pi)ψ = 2π -2π/Φ = ~2.40 And now we show this as an angle:2.40/2π = x/360°(2π is the circumference of a circle (consider without r or r=1 :P ); 2π is equal to a 360° circle: So 2.40 of 2π (It’s about 6.2831) is equal to x of 137.5°)And here the x equals ~137.5° :P2.40/2π = x/360° : And now we solve the equation for x → *360x = 2.40/2π *360 = 137.5Yepp, that’s math :PThe golden angle can be found in nature almost everywhere!Did you ever wondered about the awesome arrangement of the blossoms’ leaves? Check out this picture:
 I would also recommend you to read the golden angle article of wikipediaMath can be really beautiful - Psi, Phi and Fibonacci show you the most awesome aspects of math! :)_________________________________After all I would really recommend you to visit my phi/fibonacci tag again^^There you can find REALLY awesome things, such as finding Phi, the golden ratio ind the proportions of your body, your hand, bee population, plants etc…it’s just WOW! :)



________________________________
This picture is dedicated to the beauty of mathematics, as well as the majesty of the Fibonacci-sequence, the golden ratio and the golden angle, which appear to be a sort of important algorithm in life… :)________________________________Because I am a real math advocate, here are some quotes too:• “Mathematical beauty is a highly abstract, inner beauty, a beauty of abstract form and logical structure, a beauty that can be observed, and appreciated, only by those sufficiently well trained in the discipline.” ~ Keith Devlin• “The difference between the poet and the mathematician is that the poet tries to get his head into the heavens while the mathematician tries to get the heavens into his head.” ~ G.K. Chesterson• “Nevertheless, the fact is that there is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics. It is every bit as mind blowing as cosmology or physics… and allows more freedom of expression than poetry, art, or music…Mathematics is the purest of the arts, as well as the most misunderstood." ~ Paul LockhartHave a good day :)

dywiann-xyara:

The mathemagician’s room - by, now it comes, meeeee :P

It’s a place full of wonder, strangeness and bizarre beauty: the room - or should I say space - of a “mathemagician”…

It’s a common optical illusion, a kind of tricky paradox. “If our brains are simple enough for us to understand them, then we’d be so simple that we couldn’t.” ~ Quote by Ian Steward (a mathematician)

In my mind, mathematics equals (somehow) magic, mathematics is magic, therefor “mathemagic” :P

The floor self is an impossible figure - a typical symbol for paradoxes… 
The spirals on the chessboard-floor are Fibonacci spirals. (If you want to know more, then check out my Phi/Fibonacci tag.

This drawing is mostly about the beauty of Phi Φ, Psi ψ and the Fibonacci-sequence.

The fibonacci sequence
The fibonacci sequence works this way:
1+1 = 2
1+2 = 3
2+3 = 5
3+5 = 8
5+8 = 13
8+13 = 21
13+21 = 34
21+34 = 55
34+55 = 89
55+89…
… and so on…
The sequence then is: 1;1;2;3;5;8;13;21;34;55;89;…….

Let’s play with these numbers!
1/1=1
2/1=2
3/2=1.5
5/3=1.66666…
8/5=1.6
13/8=1.625
21/13=1.615384 …
34/21=1.6190476…


…If we continue this more and more, it will come closer and closer to a mathematial constant: 

Phi Φ
Btw: 
Φ=1.618033988749894848…
It can be calculated as followed:
Φ= 1+√5’ /2
__________________
Phi, the golden ratio as ratio:
If you have two lines:
The proportions are 1to1.618:
Or here demonstrated: 10 to 16.18
Like:  _ _ _ _ _ _ _ _ _ _ (10) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ (16 (aka~16.18)lines) This is the proportion/ratio stupidly demonstrated in a text. xD


Psi ψ
Psi is the golden angle. Its value is about 137.5°.
So.. Let’s connect Φ with π (Pi)

ψ = 2π -2π/Φ = ~2.40 And now we show this as an angle:
2.40/2π = x/360°
(2π is the circumference of a circle (consider without r or r=1 :P ); 2π is equal to a 360° circle: So 2.40 of 2π (It’s about 6.2831) is equal to x of 137.5°)
And here the x equals ~137.5° :P

2.40/2π = x/360° : And now we solve the equation for x → *360
x = 2.40/2π *360 = 137.5

Yepp, that’s math :P

The golden angle can be found in nature almost everywhere!
Did you ever wondered about the awesome arrangement of the blossoms’ leaves? 
Check out this picture:

 

I would also recommend you to read the golden angle article of wikipedia

Math can be really beautiful - Psi, Phi and Fibonacci show you the most awesome aspects of math! :)
_________________________________

After all I would really recommend you to visit my phi/fibonacci tag again^^
There you can find REALLY awesome things, such as finding Phi, the golden ratio ind the proportions of your body, your hand, bee population, plants etc…
it’s just WOW! :)

________________________________


This picture is dedicated to the beauty of mathematics, as well as the majesty of the Fibonacci-sequence, the golden ratio and the golden angle, which appear to be a sort of important algorithm in life… :)

________________________________

Because I am a real math advocate, here are some quotes too:
• “Mathematical beauty is a highly abstract, inner beauty, a beauty of abstract form and logical structure, a beauty that can be observed, and appreciated, only by those sufficiently well trained in the discipline.” ~ Keith Devlin
• “The difference between the poet and the mathematician is that the poet tries to get his head into the heavens while the mathematician tries to get the heavens into his head.” ~ G.K. Chesterson
• “Nevertheless, the fact is that there is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics. It is every bit as mind blowing as cosmology or physics… and allows more freedom of expression than poetry, art, or music…
Mathematics is the purest of the arts, as well as the most misunderstood." ~ Paul Lockhart

Have a good day :)

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(Source: likeaphysicist)

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suburbx:

Straight Lines…

It’s funny how our sense of sight can so easily be fooled

Mathematically, all you need to do is subtract or add +1 to the position of each ball and you get a perfect circle roll. Cool

suburbx:

Straight Lines…

It’s funny how our sense of sight can so easily be fooled

Mathematically, all you need to do is subtract or add +1 to the position of each ball and you get a perfect circle roll. Cool

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appil:

Miha Pavlin

appil:

Miha Pavlin

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xysciences:

Each dot is only moving in a straight line, but is created by balls moving in circles through 3 dimensional space. 
[Click for more interesting science facts and gifs]

xysciences:

Each dot is only moving in a straight line, but is created by balls moving in circles through 3 dimensional space. 

[Click for more interesting science facts and gifs]

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(Source: mariamagnolia6)

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mizoguchi:

The Israel-Gaza violence is visible from space

The fighting between Israel and Gaza-based Palestinian militant groups, now in its 15th day, is so severe that it is visible from space. A German astronaut on the International Space Station named Alexander Gerst, who has been posting photos on his Twitter account, posted this on Wednesday, in which he says the explosions of Israeli air strikes and Palestinian rockets are visible:

The photo is oriented such that north is to the right and south to the left; that dark area at the top is the Mediterranean Sea and the brightest spot, on the coast, is Tel Aviv. To the left of Tel Aviv, just 44 miles to the south, is Gaza City, the largest city in Gaza and the location of a lot of the worst fighting.

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