1. Cube projections

    1. 2D projection folding into 3-cube

    2. 3D projection folding into 4-cube

     

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  3. geekymerch:

    These awesome science and math inspired cutting boards can be found at Elysium Woodworks!

    (via spectacularuniverse)

     

  4. How many squares in the image?

     

  5. Find the number of squares in the figure

     

  6. Is the sun going to sleep?

    Researchers observing the sun have noticed the sun is strangely quiet. This is unusual..
    The sun goes through periodic cycles of weak and strong activity that last approximately 11 years. Currently the sun should be in a solar maximum, with increased magnetic activity. The solar maximum manifests itself in an increase in sunspots, which are actually huge magnetic storms on the surface of the sun. 
    The strange inactivity of the sun has been seen before, In the 17th century, the sun showed the same inactivity. This was called a Maunder Minimum. The activity of the sun is dropping the fastest in the past 10 000 years and, should this trend continue, scientist estimate that within about 40 years or so there is a 10% to 20% - nearer 20% - probability that we’ll be back in Maunder Minimum conditions.
    Solar activity drives our climate, and should we enter a Maunder minimum, we could be in for a cold snap. During the 17th century, Europe endured bitterly cold winters and this period has been described as a the Mini Ice Age.
    Scientists are now considering the effect on the rest of the world’s climate, and what are the implications of global warming? 
    Predicting the outcome of climate events is extremely complicated and unpredictable. Small changes can have huge consequences.. we may just have to wait and see…

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  7. fathom-the-universe:

    Who is Schrödinger’s Cat?

    No doubt Schrödinger’s Cat is the most famous cat in quantum mechanics.
    It is the main character in a thought experiment by the physicist Erwin Schrödinger.

    According to Copenhagen Interpretation of quantum physics, quantum particles exists partly in all their possible states until measured. This is called superposition. 
    Schrödinger wanted to make a point by proving that absurd situations occur when you apply quantum mechanics to the macroscopic world. The experiment was never intended to be a serious possibility, so animal lovers can breathe easy..

    The experiment goes as follows:
    A cat is placed in a steel box together with a device containing a small amount of radioactive material. The radioactive material will decay (break down) at a certain rate and release alpha particles. These particles can then trigger a Geiger counter which in turn will release a hammer which will smash a bottle containing lethal gas.
    The cat can either survive the ordeal or die from inhaling the gas, depending on the chance of a random event. Assuming the chance of a particle triggering the Geiger counter in one hour is 50%, is the cat dead or alive after one hour?
    According to quantum mechanics, the cat’s fate is tied in with the decay of the radioactive particles and it is both dead and alive at the same time unless you open the box to find out what happened. There is no way of knowing whether the cat is dead or alive when the box is closed.

    If we apply the Copenhagen Interpretation to the macroscopic world, the cat is in superposition of both it’s possible states, dead and alive. If we open the box we will know what has happened and the other possibility will no longer exist. 
    Of course a cat cannot be both dead and alive at the same time, but in quantum mechanics superposition is a real phenomenon, and it can be observed with many experiments, including the famous double slit experiment, where light exists both as a wave and a particle until it is measured. 
    Schrödinger’s cat is now a popular icon of quantum weirdness. It gives us something to think about.

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  8. Here is the solution to the magic star problem I posted earlier. 
    A magic star is formed when the sum of the four numbers on each straight line in the star is the same. this is called the magic sum

    Unfortunately the 5 pointed star is not technically a magic star, because it cannot be made with consecutive numbers.. in this case 1-10. 
    The lowest possible magic sum (24) is formed with the numbers from 1 to 12, leaving out the 7 and the 11.

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  9. Christmas Math 

    Complete the magic star, so that the sum of all connected straight lines is the same in all directions.



    Solution after Xmas 
     

  10. Christmas tree math - happy days everyone

     

  11.  

    Soap film surfaces

    There are many beautiful and mysterious shapes found in nature. Some very fascinating shapes are formed by nothing more than soap films and they have captured the imagination of artists and mathematicians alike. Molecules in the soap film assume a state where the energy required is minimal. The surface tension in soap films create a surface of minimal energy inside the boundary in which they form. This surface is called a minimal surface. Minimal surfaces are formed inside boundary constraints, like a wire frame. The minimal surfaces are created by the soap films between the frame. A bubble or a sphere is not a minimal surface in this sense even though its shape has minimal surface to volume ratio.. The maths behind minimal surfaces is anything but simple and mathematicians have studied the problem of how such surfaces can be expressed extensively. The area of maths that deals with minimal surfaces is called “calculus of variations”. Minimal surfaces have far reaching implications in geometry and engineering. Stadiums and bridges often use the design . The shape is very efficient and naturally beautiful. These tensile structures can be used to span large areas and still remain strong. You can create minimal surfaces yourself by playing around with wire frame objects (spirals, cubes, tetrahedrons) and a soap solution. You can also make the frames with straws or K’nex. To make the soap solution, just add a generous amount of dishwashing liquid to a bucket of water and add a squirt of glycerin. Don’t allow froth to form in the solution. The glycerin keeps the bubbles strong. Dip a frame object into the solution and gently lift it out, the soap will form a minimal surface within the frame.


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    "Bubble Art " (by A. van der Net)

     

  12. (Source: davidaedwards)

     

  13. Wising you an inspirational Christmas !

     

  14. The physics of music

    These patterns are made with nothing but sound. They are called Chladni patterns, after the German physicist Ernst Chladni (1756–1827) who used his violin bow to vibrate a metal plate with sand on it. A pattern appears in the sand when a surface is made to vibrate at certain resonances. A plate or membrane vibrating at resonance is divided into regions vibrating in opposite directions, bounded by lines of zero vibration called nodal lines. The sand is moved around the plate and collects at the nodes on the plate. The patterns that form are highly symmetrical and beautiful.


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    Watch this video with coloured sand: 
    http://www.youtube.com/
    watch?feature=player_embedded&v=Oz53w_k_j_A
     

  15. Why does ice float on water?

    In ice, hydrogen bonds cause the formation of a solid crystal that is less dense than the liquid form. This causes ice to float on water. This property of water is unusual in the chemical world, and it is very important for the existence and survival of life on earth. If ice formed on the bottom of oceans or lakes, life as we know it would not be possible on earth because all bodies of water would eventually freeze solid.
    Because ice floats, the water below is insulated and does not freeze. It allows life to thrive in the liquid water just below the ice.

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