Lmst

More artistic drawings based on the previous patterns. The second is very simple but I like it, it was done by just stacking circles.
#mathart #geometry #octogonal

Geometric drawing of purple circles making double spirals in a square grid pattern.

Circles growing from the center looking like a flower, purple with yellow stamen, octagonal symmetry.

I think I have found a novel tiling using hexagons, with octagonal symmetry, infinite inwards and outwards (at least I couldn't find it on-line). The hexagons are scaled with the ratio r = √(1+1/√2). See the measures of the hexagon in the second image (𝛕 = 2π). The hexagon can be cut in 6 similar triangles, which are 1/8 of a regular octagon. If the hexagons of the first tiling are decomposed into those triangles we get the the third image. And if some of those triangles are recombined into bigger ones, we get the fourth.
#geometry #Mathematics #tiling #hexagon #octogonal #infinity #mathart

A tiling using similar non-regular hexagons, scaled inwards and outwards, with octagonal symmetry. Colours blue, violet and pink.

Measures of the hexagon, given r = √(1+1/√2). Considering the smallest side as length 1, it has three noncontiguous sides of length r squared, and two sides of length r cubed. The two angles near the smallest side are 6/16 𝛕 and the rest are 5/16 𝛕 (𝛕 = 2π). The three bigger diagonals intersect at the same point, and cut the hexagon in 6 similar triangles (which are 1/8 of an octagon).

Same tiling but decomposing the hexagons into six similar triangles.

Same as before but some triangles are joint into bigger triangles, giving a spine figure.

#18Mayo para el #DíaInternacionaldelosMuseos un museo especial, el museo romano de Premià de Mar de planta #octogonal, con distribuidor central también octogonal y con cuatro fachadas orientadas según los cuatro puntos cardinales @MuseuRomaPM Un museo con mucha #MiradaMatemática

#octogonal

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