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Cool recursive tiling by Lee Sallows.

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5 Greatest a Discoveries in Mathematics #3

Godel’s Incompleteness Theorem

At the beginning of the 20th century, mathematician David Hilbert presented a list of 23 of the most important unsolved problems in mathematics. Second on his list was to prove that the axioms of arithmetic are consistent i.e. free from internal contradictions.

It may appear obviously true, yet in a groundbreaking 1931 paper that unified logic, mathematics and philosophy, Gödel is widely believed to have proven Hilbert’s problem in the negative. In fact, his incompleteness theorems went so far as to show that in any axiomatic system, such as arithmetic, there exist statements that are undecidable. An imperfect but useful analogy is found within the liar paradox. In this paradox we begin with a machine that can be fed any statement and outputs whether that statement is true or false with unfailing accuracy. Now consider inputting the statement:”this statement is false”. The machine could output neither “true” nor “false” without producing a contradiction - the equivalent of an undecidable proposition.

The results from Gödel’s theorems still resonate within many areas of mathematics and philosophy and have been extended, perhaps speciously at times, to speculate on the philosophical limitations of computational systems and even the human mind itself.

From: polymic.com

Comic: nucleardelight.com

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It’s funny how SJWs throw this word around to describe their “oppressors” (aka anyone who’s different than them) when these definitions describe them to a fucking T.

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wheel forever

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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! :) _________________________________ I deleted the content here because a lot of it is just speculated and not fact. I wish I had caught it sooner, I didn’t notice the presence of these pictures initially! 

-Visualizingmath

________________________________

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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Levitating Superconductor on a Möbius strip [video]

h/t hilker

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Watch the video of this 3D rendering young girl

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Is it too soon to share another awesomely creative piece of furniture? No way! This one-of-a-kind insectoid armoire is called the BUG and it was designed Latvian designer Janis Straupe of True Latvia. Full of customizable shelves, drawers, cubbies and even a few secret compartments, it’s a beautifully functional piece of furniture as well as an amazing work of art.

Click here to learn more about the BUG and its myriad features.

[via Yanko Design]

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What are the ingredients of an “all natural” banana?

Thanks to I F-ing Hate Pseudoscience 

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thanks to tumblr, i now hate extreme liberals as much as i do hardcore conservatives

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Holy yes

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tumblr spreads messages like

"i don’t care if my bad mood and attitude offends you i’m not put on this earth to make you comfortable and happy deal with it"

and with the same breath they say shit like

"please don’t use these words and names with me they make me uncomfortable and i want you to stop using them also please be nice to me I’m sensitive and don’t touch me"