gracewashko:

“The symbolic forms which Mr. Betts has evolved through his system of Representation resemble, when developed in two dimensions, conventionalised but very scientifically and beautifully conventionalised leaf-outlines. When in more than two dimensions they approximate to the forms of flowers and crystals. …. The fact that he has accidentally portrayed plant-forms when he was studying human evolution is an assurance to Mr. Betts of the fitness of the symbols he has developed, as it affords presumptive evidence that the laws he is studying intuitively admit of universal application.”

(via freshphotons)

Source: publicdomainreview.org

aamukherjee:

Documentary: Fermat’s Last Theorem

This is none other than Simon Singh’s famous documentary of Andrew Wiles’ extraordinary search for the most elusive proof in number theory: Fermat’s Last Theorem. If you doubt the fact that mathematics can be a moving subject (and I assure you, it has the power to move people as much as any natural science or literary study), I hope that this will change your mind.

(via kinasekinasekinase)

Source:

jtotheizzoe:

Doodling in Math Class: Connecting Dots

Turn that inverted parabola upside-down!

Next time you’re sitting there in math class pondering the greater existential significance of translating various quadratic functions into parabolas, I hope you think of this Vi Hart experience … take the time to doodle those dots, stitch together those segments, and fill your cup with the reflected sunshine of a beautiful cardioid.

I want to hug my computer when I watch this. Such beauty lies in connecting dots, and not knowing exactly what will come out the other side.

Well done. This one’s for Vi Hart (via benice equation):

(If you liked that one, check out more from benice equation here)

jtotheizzoe:

Visualizing Prime Numbers

Jason Davies has created a way to visualize prime numbers as periodic curves (curves that repeat every n points). Wherever only two curves intersect (for 1 and the number), that’s a prime.

Play with the interactive, zoomable version here. Awesome stuff!

(via proofmathisbeautiful)

Source: jtotheizzoe

skeptv:

Numberphile- Infinity is bigger than you think

Sometimes infinity is even bigger than you think… Dr James Grime explains with a little help from Georg Cantor.

Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
James Grime: http://singingbanana.com/

Videos by Brady Haran

Minute Physics video on this topic http://www.youtube.com/watch?v=A-QoutHCu4o (somewhat more fast-paced… but we did film ours BEFORE his was uploaded, so similarities are coincidental… well actually, no they are not… we are all building upon Cantor’s work!!)

skeptv:

Another Lock Puzzle

Imagine a combination lock with three wheels. The wheels are labelled with the numbers 1, 2, 3. Turn the wheels and numbers increase, until 3 turns back to 1. You may only turn the first two wheels together or the last two wheels together. Starting from the combination 333 what series of moves do I need to make to get 221?

shychemist: prologi: scienceisbeauty: The Lagrangian who describe all physical processes (except gravity). Pretty easy, isn’t it? Clue: “H” represents the Higgs Boson. My Intro to Modern Physics prof included this in his slides, probably so we would feel less terrified when he highlighted the two rows we’d be dealing with. Equations like these are why I don’t have a future in physics or mathematics. XD
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shychemist:

prologi:

scienceisbeauty:

The Lagrangian who describe all physical processes (except gravity). Pretty easy, isn’t it? Clue: “H” represents the Higgs Boson.

My Intro to Modern Physics prof included this in his slides, probably so we would feel less terrified when he highlighted the two rows we’d be dealing with.

Equations like these are why I don’t have a future in physics or mathematics. XD

Source: scienceisbeauty

discoverynews:

Three Girls Discover their Love of Science

Let me just say this is not amazing~ or anything. All kids love science because it’s fucking cool. When girls grow into women and are told that ‘women are like this’ and ‘men are like this’, of course most of them opt out of dealing with that sexist BS. When you’re indoctrinated in a culture where science is ‘traditionally’ a dude-bro situation, what did you expect? It’s not amazing when girls like science. It’s horrible when they grow up to feel like there’s no room for them in that world. All kids like science when you show them how spectacular it is.

pretendy: Like many viruses, adenoviruses (pictured) have a distinctive icosahedral structure, a la: This is because an icosahedron is the optimum way of assembling a closed shell out of identical sub-units. A virus is constructed in just this way - identical triangular units called capsomers arrange themselves to form a protective closed shell around the virus’ genetic material. And they do this in the most mathematically optimum way, as if they’ve studied calculus. Yay for maths!
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pretendy:

Like many viruses, adenoviruses (pictured) have a distinctive icosahedral structure, a la:

This is because an icosahedron is the optimum way of assembling a closed shell out of identical sub-units. A virus is constructed in just this way - identical triangular units called capsomers arrange themselves to form a protective closed shell around the virus’ genetic material. And they do this in the most mathematically optimum way, as if they’ve studied calculus.

Yay for maths!

matthen: How would you arrange 100 dots so that no two were too close, but no dot was too far from the centre.  The answer would be useful in nature, where the dots might correspond to growing structures which can’t be overcrowded.  One solution that evolution has found is the Fibonacci spiral, in e.g. a sunflower head.  This animation shows the output of a program which tries to find a good solution. At the start the dots are placed randomly, then each dot is moved in turn to a better position in the image.   [code]
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matthen:

How would you arrange 100 dots so that no two were too close, but no dot was too far from the centre.  The answer would be useful in nature, where the dots might correspond to growing structures which can’t be overcrowded.  One solution that evolution has found is the Fibonacci spiral, in e.g. a sunflower head.  This animation shows the output of a program which tries to find a good solution. At the start the dots are placed randomly, then each dot is moved in turn to a better position in the image.   [code]

quantumaniac: Simple and Circular Motion Although it may seem counterintuitive, simple harmonic motion (left) and simple circular motion (right) have a great deal in common. If one looks at an object undergoing simple circular motion, it is clear that there are two scales to which an extreme can be reached - a polarized left/right, and an equally polarized up/down. However, looking from the side - only the top and bottom can be seen, and by looking at circular motion from the side it looks exactly like simple harmonic motion.  The physical equations governing these bodies are also quite similar:  Angular Velocity: Of a spring undergoing simple harmonic motion:  A pendulum:  Time Period Spring:  Pendulum:  k is a spring constant, m is the object’s mass, g is gravity, l is the length of the pendulum ‘arm.’ 
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quantumaniac:

Simple and Circular Motion

Although it may seem counterintuitive, simple harmonic motion (left) and simple circular motion (right) have a great deal in common. If one looks at an object undergoing simple circular motion, it is clear that there are two scales to which an extreme can be reached - a polarized left/right, and an equally polarized up/down. However, looking from the side - only the top and bottom can be seen, and by looking at circular motion from the side it looks exactly like simple harmonic motion. 

The physical equations governing these bodies are also quite similar: 

Angular Velocity:

  • Of a spring undergoing simple harmonic motion: \sqrt{\frac{k}{m}}
  • A pendulum: \sqrt{\frac{g}{l}}

Time Period

  • Spring: 2\pi \sqrt{\frac{m}{k}}
  • Pendulum: 2\pi \sqrt{\frac{l}{g}}

k is a spring constant, m is the object’s mass, g is gravity, l is the length of the pendulum ‘arm.’