#Tiling

[szimmetria-airtemmizs]

Mathematical fun fact of the day 3:

You can tile a regular 30-gon using a pentagon and rhombus.

[cant-think-of-a-good-one]

the Spectres aren't just a few shapes. they're an infinite family of shapes. a family that includes this:

i'm naming this particular shape

The Fuckre

[arc-hus]

Homerton College Dining Hall, Cambridge - Fielden Fowles

[allanodyne]

we show no fear, go

by AllanOdyne

[polyphonetic]

NEW SHAPE DROPPED

Spectre

As a refresher on tiling:

The above image is an example of penrose tiling. It lacks translational symmetry, but it does have reflection and fivefold rotational symmetry. It's very cool but note that it has two different "shapes", two rhombi.

Below us is Hat!

Hat is a tile that is especially cool because you only need itself and a reflection of itself to make a provably aperiodic tiling!

It is kind of a whole wiggly range of similar shapes (like if you tweak the edges a little it can still repeat) BUT it requires a reflection of itself, which is kind of using *two* shapes. Spectre, however, only needs itself:

You can read about Spectre here!

Like Hat, it also can exist as a range of slightly similar shapes! For example, here's doggy : )

[madsciencepottery]

On the subject of "little things that don't remind me of a rapidly-encroaching wall of doom" here's a quick&easy tutorial I threw together for making scale stamps that can be used for a wide variety of projects: cobblestone, jewelry etc. Take and use as you please

[sovenasark]

18 - Lizards and lizards and lizards and lizards and

[mathhombre]

Randominoes

Riffing off of @anitanh's sweet dominoes. I like these, but I think she's right in that we want a single tile you can place in different ways. Maybe two? Regardless, made a tool that made random polygons in a polyline, so that's new.

Anita's pattern and extended.

A bit of a random 8x8.

I'll post the GeoGebra on request if anyone's interested.

[bfoxgamescreens]

TilingSpartanTexture.png

[raaaaaauhrawr]

⭐️⭐️star backgrounds✨⭐️✨✨⋆˙⟡♡✧˖°

dont reccomend using the flashy ones for website backgrounds.....

[stone-cold-groove]

The modern electrified kitchen.

[szimmetria-airtemmizs]

Did you know that there is a way of cutting an equilateral triangle into seven similar triangles that have pairwise different sizes, and they are not right triangles? (With right triangles it is easy to cut into any number of similar pieces.)

One of the angles in each triangle is 120 degrees and the other two are roughly 40.67915375798 and 19.32084624 degrees. You can read the details in the paper:

A note on perfect dissections of an equilateral triangle by Andrzej Zak

[webdec]

colourlovers

[once-upon-a-bathtime]

Electric blue bathroom by To&From

[kararadaygum]

..