People who say they’re bad artists but when they draw they’re like:

(Source: ziorno)

oh my god

the squirrel

is trying to bury

the nut

in the dog’s fur

and the dog is just like

um

excuse me

sorry

but i’m not designed for that

sorry

(Source: youtube.com)

ladies and gentlemen, the coolest president ever

People may or may not agree with his politics but Obama as a person is seriously amazing.

(Source: skyisawake)

Non-Orientable SurfacesAn orientable surface is a surface on which it’s possible to make a consistent definition of direction. Most surfaces we encounter – like spheres, planes, and tori (doughnut shapes) – are orientable. When visualized in three dimensions, orientable surfaces have two distinct sides.

Non-orientable surfaces, on the other hand, have only one side. From Wikipedia, “The essence of one-sidedness is that [an] ant can crawl from one side of the surface to the ‘other’ without going through the surface or flipping over an edge, but simply by crawling far enough.” At any point on a non-orientable surface it’s impossible to uniquely define, for example, the “clockwise” direction.

The GIFs above show two examples of non-orientable surfaces: a Klein bottle and a Möbius strip.

Mathematica code [Klein Bottle]:

xk[u_, v_] := (-2/15)*Cos[u]*(3*Cos[v] - 30*Sin[u] + 90*Cos[u]^4*Sin[u] - 60*Cos[u]^6*Sin[u] + 5*Cos[u]*Cos[v]*Sin[u]) yk[u_, v_] := (-15^(-1))*Sin[u]*(3*Cos[v] - 3*Cos[u]^2*Cos[v] - 48*Cos[u]^4*Cos[v] + 48*Cos[u]^6*Cos[v] - 60*Sin[u] + 5*Cos[u]*Cos[v]*Sin[u] - 5*Cos[u]^3*Cos[v]*Sin[u] - 80*Cos[u]^5*Cos[v]*Sin[u] + 80*Cos[u]^7*Cos[v]*Sin[u]) zk[u_, v_] := (2/15)*(3 + 5*Cos[u]*Sin[u])*Sin[v] kb[u_, v_] := {xk[u, v], yk[u, v], zk[u, v]} Manipulate[ParametricPlot3D[kb[u, v], {u, 0, umax}, {v, 0, 2*Pi}, PlotRange -> {{-1.8, 2}, {0, 4.5}, {-0.75, 0.75}}, Axes -> False, Boxed -> False, PlotStyle -> {Opacity[0.65]}, Mesh -> {20, 11}, MeshStyle -> Directive[Gray, Opacity[0.65], Thickness[0.003]]], {umax, 0.001, Pi}]Mathematica code [Möbius Strip]:

xm[u_, v_] := (1 + (v/2)*Cos[u/2])*Cos[u] ym[u_, v_] := (1 + (v/2)*Cos[u/2])*Sin[u] zm[u_, v_] := (v/2)*Sin[u/2] ms[u_, v_] := {xm[u, v], ym[u, v], zm[u, v]} Manipulate[ParametricPlot3D[ ms[u, v], {u, 0, umax}, {v, -1, 1}, PlotRange -> {{-1.1, 1.5}, {-1.5, 1.5}, {-0.5, 0.5}}, PlotStyle -> {Opacity[0.65]}, Axes -> False, Boxed -> False, Mesh -> {20, 5}, MeshStyle -> Directive[Gray, Opacity[0.65], Thickness[0.003]]],

{umax, 0.001, 2*Pi}]

1/4 + 1/16 + 1/64 + 1/256 + … = 1/3

1/3 + 1/9 + 1/27 + 1/81 + … = 1/21/2 + 1/4 + 1/8 + 1/16 + … = 1

1 + 2 + 3 + … + n = n * (n+1) / 2

1 + 3 + 5 + … + (2n − 1) = n^{2}

a^{2}+ b^{2}= c^{2}

CITATION ( source) :Nelsen, R. B.

Proofs Without Words: Exercises in Visual Thinking.Washington, DC: Math. Assoc. Amer., 1997.

One of my favorites of the visual math posts, specifically the top 3.

long distance relationships

This made me laugh louder than it should

he has the magic touch that make all dem bitches scream

(Source: daniels-gillies)

DIY Easy 2 Ingredient Sensory Rainbow Bubbles and Foam Tutorial from Fun at Home with Kids here.I know there are Littles following me. They might enjoy this.

best part is that it’s even scarier when they lift the cup and nothing is there and they think it got out

i think you need a nap satan

Slow down, grab the wall

Wiggle like you trying to make yo ass fall off

(Source: sheepfilms)