"Stars must die so that I can live. I stepped out of a supernova” -Phil Hellenes

The rotation of Earth really makes my day!

Gabriel’s Horn and the Painter’s ParadoxGabriel’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.

Doctor Who - Season 8 - Intro

Numbers are simple.

While

sunspotsare relatively cool and quiescent regions on the Sun, thephotospherearound them sometimes erupts with outflows of high energy particles in active regions. Most often these eruptions are in the form of loops and sheets calledprominenceswhich remain under the control of the intense magnetic fields associated with solar storms. There are other events which in a matter of minutes can release enormous amounts of energy and eject material out into space. Such violent events are calledsolar flares.

Images credit:TRACE/NASA

Orion constellation