Posted 6 hours ago

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}]```

Posted 7 hours ago
Posted 1 day ago

handletheheat.com

THIS IS GLORIOUS.

YES

ok but who thought of vodka pie crust

effleague, you should learn from dis.

Tag

your

effin porn

Posted 1 day ago

I need feminism because I’m still charged 5% tax on sanitary products because they’re classed as ‘non-essential’ by the government.

What the motherfuck.

Solve this by bleeding on everything they love.

*AGGRESSIVELY PROJECTILE BLEEDING AT POLITICIANS* ARE YOU FEELING IT NOW, MR. POLITICIAN?

Posted 2 days ago

girls being kept out of the sciences and pushed into the humanities; the humanities being valued less in our society than the sciences; and the humanities and sciences being looked at as stark opposites that couldn’t possibly be enjoyed for the same reasons are all problems that need to in some degree be tackled together

Posted 2 days ago

Scooby Doo has great life lessons to teach:

If something evil is happening, it’s probably an old white man trying to make money.

Posted 3 days ago

There was a bunny at Lowes today eating all the flowers

haha u go lil bun
fight the power

live the dream, small friend

a criminal

Posted 3 days ago

You shouldn’t feel ashamed of your identity. But remember, there is nothing wrong with staying in the closet until you feel safe enough to come out.

Do whatever makes you feel better.

You’re not an attention-seeker if you come out.

You’re not a coward if you stay in the closet.

Take care of yourself, friend.

Posted 5 days ago

what is this. magical bird.

Quetzal. That bird is a Quetzal and it can be found on Western Mexico.  It’s on a near threatened status.

It’s so pretty.

They turn up in all kinds of Precolumbian art and iconography.  IIRC, they were named for the god Quetzalcoatl.  Their feathers were used in… Aztec? ceremonial headpieces.  Can’t remember for the life of me what their taxonomy is.

(Source: proyectopbs)

Posted 5 days ago