Daniel Piker

@[email protected]

[Daniel Piker @KangarooPhysics]

1
https://t.co/q8PcaJfcTY
2
https://t.co/efGFk6H03E
3
https://t.co/9y8TpmPssz
4
https://t.co/JupjtA6SeL

[Daniel Piker @KangarooPhysics]

@emlplsn @JuhaniHalkomaki https://t.co/oQpfODCGUo

https://t.co/f2UoHYS53I

https://t.co/KyeisU51Ks

https://t.co/dxyWYbk3xp

[Daniel Piker @KangarooPhysics]

@sl2c @bengineer8u Ah yes, quite right you are. 6R with 1dof is the one that doesn't fit the mobility criterion.

[Daniel Piker @KangarooPhysics]

Here's a fun little kinematic toy that's easy to make - an equilateral orthogonal hexagon linkage with 1 degree of freedom:

[Daniel Piker @KangarooPhysics]

@dodecahedra Interesting to see which of those you chose match the best known solutions for the
https://t.co/9vVwwTVsi3
(the 'equivalent polyhedra' in the table there are for N vertices, so you'd need to take the duals for N faces)

[Daniel Piker @KangarooPhysics]

@RonAvitzur @alytile You can have strips of finite width which are periodic in one direction
https://t.co/egYRayl61v

[Daniel Piker @KangarooPhysics]

@hamish_todd This all started many years ago (https://t.co/mATdsSgLak) with thinking about the equivalent of a loxodrome in one dimension up. A Hopf link does make the most direct analogue for the 2 poles, with the surface twisting from one to the opposite one through the 3 sphere.

[Daniel Piker @KangarooPhysics]

@hamish_todd That's one of many possibilities!
https://t.co/QazHR85DaB

[Daniel Piker @KangarooPhysics]

@bennywahwah Whereas purely Imaginary would look like this

[Daniel Piker @KangarooPhysics]

@bennywahwah Not exclusively. 3 parts Real + 1 part Imaginary.
Just the real part would look like this

[Daniel Piker @KangarooPhysics]

@garciadelcast I think
@BathshebaSculpt
uses https://t.co/25GgLG0TGS
https://t.co/zT0YPHgpsX
https://t.co/cGYm3ZgHoZ

[Daniel Piker @KangarooPhysics]

@alytile Number 2 there doesn't connect up across adjacent tiles.
If connecting midpoints, and we want closed curves, I believe we need to include either all the red pts below, all the green points, or all of both.

[Daniel Piker @KangarooPhysics]

@alytile

[Daniel Piker @KangarooPhysics]

@alytile Oh that's nice. I hadn't looked at patterns on the turtle yet. It seems there are several possibilities for connecting tangent arcs across the long edges

[Daniel Piker @KangarooPhysics]

@apgox Interesting. Here's a larger patch with this double-kite orientation colouring

[Daniel Piker @KangarooPhysics]

@m_u_s_h_r_o_o_m @TylerGlaiel There's a whole class of equivalent arrangements extremely close to the optimal one. You'd need some precision manufacturing and stiff material to make it impossible to fit them into the same frame
https://t.co/2jbg17jiqz

[Daniel Piker @KangarooPhysics]

Also - it's not that there aren't any symmetric arrangements possible for 17. It's just that they're not as compact as the one on the right.

[Daniel Piker @KangarooPhysics]

@alytile

[Daniel Piker @KangarooPhysics]

Similar to what @alytile showed for the H/T/P/F metatiles (https://t.co/586Vgxl7VN) these are the 2 fractal tiles for the substitution system in figure 2.11 of the new aperiodic monotile paper (https://t.co/h14Tanws4k).

[Yoshiaki Araki 荒木義明 @alytile]

今朝ビックニュースが飛び込んできました。ついに数学のアインシュタイン問題が解かたというのです。第一発見者のDave Smithさんはアーティストティックにテセレーションを探究する同志です。非周期にしか敷きつめられない不思議なタイルを自分でも理解しようと描いたが下のフラクタルタイルの図です