Lmst

Still works even when the quadrilateral is concave
#Tiling #Pattern #Geometry #MathArt #MathsArt #loop #animation #geogebra

A generalisation of Varignon’s Theorem https://en.wikipedia.org/wiki/Varignon's_theorem inspired by https://mathstodon.xyz/@ColinTheMathmo/114563307151366884
#Tiling #Pattern #Geometry #MathArt #MathsArt #loop #animation #geogebra

Street paving, Marrakesh, Morocco
#TilingTuesday #Tiling #IslamicPattern #Pattern #Geometry #MathArt #MathsArt #photography

A top-down photograph of grey rectangular street paving. Each paver has a 12-pointed star in the centre surrounded by kites and different kinds of pentagons.
The pavers are grimy and worn from use over time. Two of the pavers are broken: brown earth and metal pins are visible.

Wish you all a nice #KaleidoSaturday!

#Art #GenerativeArt #kaleidoscope #mandala #MastoArt #MathArt #MathsArt #PsychedelicArt #visuals

8-fold mandala with softly structured bright blue and pinkish red colors.

A crystally object for #TilingTuesday

All pentagons are glued to a friend, all triangles face outwards.

#3D #Geometry #MathArt #MathsArt

Further thoughts on the pretty picture. While I was stitching it, I was wondering if there were any other permutation matrices that would produce Fibonacci snowflakes. There are indeed — after I finished it, I turned it over and there was the order 3 snowflake in the centre. (The photo below is less clear than the front view because of the knots where I had to join thread, but hopefully it’s clear enough.) This corresponds to taking our original permutation matrix “backwards”, i.e. [17, 18, 20, 21, 14, 11, 24, 10, etc].

I like this because it’s a result that’s trivial to see once you’ve stitched it but is not at all obvious from any other way of rendering it (e.g. drawing it on paper or digitally).

#MathArt #MathsArt #Maths #Math #Embroidery #Sashiko

A piece of mottled dark pink/light pink fabric with a sashiko-style design embroidered on it with purple thread. It’s clearly the back of the piece, because several knots are visible where new threads have been joined in. In the middle is the order 3 Fibonacci snowflake, surrounded by small squares and Greek crosses (these, incidentally, are the order 1 and 2 snowflakes, respectively). Around the edges are zigzag lines. Like the front of the design (see previous post), the design has C4 symmetry.

This construction is known as the “square ice” model, because in statistical mechanics it can be used to model ice (as in normal physical ice, made from water). The vertices correspond to oxygen atoms, each of which is bonded to four hydrogen atoms that lie “within” the bonds of the lattice (and each hydrogen atom is thus bonded to two oxygen atoms). The hydrogen atoms are not positioned symmetrically along the bonds, but are closer to one of their oxygen atoms than the other one; the arrow on each bond of the lattice points to the closest oxygen atom for that bond’s hydrogen atom.

OK, here’s the pretty picture, i.e. the embroidered loop diagram corresponding to the permutation matrix [16, 15, 13, 12, 19, 22, 9, 23, 26, 8, 6, 29, 30, 5, 31, 32, 1, 2, 28, 3, 4, 27, 25, 7, 10, 24, 11, 14, 21, 20, 18, 17]. The small white stitches mark the non-zero matrix entries where the arrows on the lattice change direction and hence the corresponding stitch is twice as long as usual.

#Maths #Math #MathsArt #MathArt #Sashiko #Embroidery