"Do you wish to be great? Then begin by being. Do you desire to construct a vast and lofty fabric? Think first about the foundations of humility. The higher your structure is to be, the deeper must be its foundation."

- Saint Augustine

admiralpotato:

Circular Associations - B - InfinityUsing source PNGs

Source: admiralpotato

Vajrapāṇi(from Sanskritvajra, “thunderbolt” or “diamond” andpāṇi, lit. “in the hand”) is one of the earliest bodhisattvas of Mahayana Buddhism. He is the protector and guide of the Buddha, and rose to symbolize the Buddha’s power. Vajrapani was used extensively in Buddhist iconography as one of the three protective deities surrounding the Buddha. Each of them symbolizes one of the Buddha’s virtues: Manjusri (the manifestation of all the Buddhas’ wisdom), Avalokitesvara (the manifestation of all the Buddhas’ compassion) and Vajrapani (the manifestation of all the Buddhas’ power as well as the power of all 5 Tathagathas). Furthermore, Vajrapani is one of the earliest Dharmapalas and the only Buddhist deity to be mentioned in the Pali Canon as well as be worshiped in the Shaolin Temple, Tibetan Buddhism, and even Pure Land Buddhism (where he is known as Mahasthamaprapta and is one of a Triad comprising Amitabha and Avalokiteshwara). Manifestations of Vajrapani can also be found in many Buddhist temples in Japan as Dharma protectors called Nio. Vajrapani is also associated with Acala who is venerated as Fudo-Myo in Japan where he is serenaded as the holder of the Vajra.^{[1]}Vajrapani here is different from that mentioned in the Vedas as Indra, the king of the Gods and the most widely mentioned deity in all of the Indian scriptures.

(via jessicorvus)

Source: nishad

neat trick i figured out for nesting pentagons…

An even number of (at least 8) regular tetrahedra can be connected along their edges to form a ring in a way that allows them to be continuously rotated “inside-out” without disconnecting. Such configurations are commonly referred to as kaleidocycles. Shown above are kaleidocycles with 8, 10, and 12 tetrahedra exhibiting 4, 5, and 6-fold rotational symmetry, respectively. There has to be at least 8 regular tetrahedra, because any less would result in the tetrahedra colliding into each other at certain instances of the rotation. You can even make your own paper model using this guide.

Mathematica code:

v1[t_] :=

{Cos[t], 0, Sin[t]}

v2[t_, a_] :=

1/Sqrt[1 + Sin[t]^2 Tan[a]^2] {-Sin[t], -Sin[t] Tan[a], Cos[t]}

v3[t_, a_] :=

1/Sqrt[1 + Sin[t]^2 Tan[a]^2] {-Sin[t]^2 Tan[a], 1, Cos[t] Sin[t] Tan[a]}

P[t_, a_] :=

{v3[t, a][[2]]/Tan[a] - v3[t, a][[1]], 0, -v3[t, a][[3]]/2}

Q[t_, a_] :=

{v3[t, a][[2]]/Tan[a], v3[t, a][[2]], v3[t, a][[3]]/2}

vertices[t_, a_] :=

{P[t, a] - Sqrt[2]/2 v1[t], P[t, a] + Sqrt[2]/2 v1[t],

Q[t, a] - Sqrt[2]/2 v2[t, a], Q[t, a] + Sqrt[2]/2 v2[t, a]}

Tetrahedron[T_, t_, a_, o_] :=

Table[

{FaceForm[White], Opacity[o], EdgeForm[Thick],

Polygon[

Table[

T[vertices[t, a][[1 + Mod[i + j, 4]]]], {i, 1, 3, 1}]]},

{j, 0, 3, 1}]

Kaleidocycle[pr_, t_, n_, o_, A_] := Graphics3D[

Rotate[

Table[

Rotate[

Table[

Tetrahedron[T, t, 2 Pi/n, o],

{T, {TransformationFunction[IdentityMatrix[4]],

ReflectionTransform[{-Sin[2 Pi/n], Cos[2 Pi/n], 0}]}}],

r*4 Pi/n, {0, 0, 1}],

{r, 0, n - 1, 1}],

A*Sin[t], {0, 1, 0}],

PlotRange -> pr, ImageSize -> 500, Axes -> False, Boxed -> False,

Lighting -> "Neutral", ViewPoint -> {0, 0, 2}, Background -> White ]

Manipulate[

Kaleidocycle[pr, t, n, o, A],

{pr, 1.5, 50}, {t, 0, 2 Pi}, {n, 8, 16, 1},{o, 1, 0}, {{A, 0}, 0, 2 Pi}]

pythagorus fractal tree necklace by naked geometry

some rainbow clouds from naked geometry :)

*of*4