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infinity-imagined:

Sunsets and sunrises seen from the International Space Station.

Amazing video of space shuttle launch, be sure to watch it till the end.

DID YOU KNOW 3.14 is PIE backwards.

DID YOU KNOW 3.14 is PIE backwards.

fouriestseries:

Gabriel’s Horn and the Painter’s Paradox 
Gabriel’s Horn is a three-dimensional horn shape with the counterintuitive property of having a finite volume but an infinite surface area.
This fact results in the Painter’s Paradox — A painter could fill the horn with a finite quantity of paint, “and yet that paint would not be sufficient to coat [the horn’s] inner surface” [1].
If the horn’s bell had, for example, a 6-inch radius, we’d only need about a half gallon of paint to fill the horn all the way up. Even though this half gallon is enough to entirely fill the horn, it’s not enough to even coat a fraction of the inner wall!
The mathematical explanation is a bit confusing if you haven’t taken a first course in calculus, but if you’re interested, you can check it out here.
Mathematica code:
x[u_, v_] := u
y[u_, v_] := Cos[v]/u
z[u_, v_] := Sin[v]/u
Manipulate[ParametricPlot3D[{{x[u, v], y[u, v], z[u, v]}}, 
    {u, 1, umax}, {v, 0, 2*Pi}, 
    PlotRange -> {{0, 20}, {-1, 1}, {-1, 1}}, 
    Mesh -> {Floor[umax], 20}, Axes -> False, Boxed -> False], 
    {{umax, 20}, 1.1, 20}]
Additional source not linked above.

fouriestseries:

Gabriel’s Horn and the Painter’s Paradox 

Gabriel’s Horn is a three-dimensional horn shape with the counterintuitive property of having a finite volume but an infinite surface area.

This fact results in the Painter’s Paradox — A painter could fill the horn with a finite quantity of paint, “and yet that paint would not be sufficient to coat [the horn’s] inner surface” [1].

If the horn’s bell had, for example, a 6-inch radius, we’d only need about a half gallon of paint to fill the horn all the way up. Even though this half gallon is enough to entirely fill the horn, it’s not enough to even coat a fraction of the inner wall!

The mathematical explanation is a bit confusing if you haven’t taken a first course in calculus, but if you’re interested, you can check it out here.

Mathematica code:

x[u_, v_] := u
y[u_, v_] := Cos[v]/u
z[u_, v_] := Sin[v]/u
Manipulate[ParametricPlot3D[{{x[u, v], y[u, v], z[u, v]}}, 
    {u, 1, umax}, {v, 0, 2*Pi}, 
    PlotRange -> {{0, 20}, {-1, 1}, {-1, 1}}, 
    Mesh -> {Floor[umax], 20}, Axes -> False, Boxed -> False], 
    {{umax, 20}, 1.1, 20}]

Additional source not linked above.

s-c-i-guy:

Bill Nye Fights Back
How a mild-mannered children’s celebrity plans to save science in America—or go down swinging.
Read the full article on Popular Science

s-c-i-guy:

Bill Nye Fights Back

How a mild-mannered children’s celebrity plans to save science in America—or go down swinging.

Read the full article on Popular Science

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….

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