equilaterals

Swastika is a small community founded around a mining site in Northern Ontario, Canada in 1908. The town was named after the Sanskrit good-luck symbol Swastika.

The swastika is a symbol that generally takes the form of an equilateral cross, with its four legs bent at 90 degrees. It is considered to be a very sacred and auspicious symbol in Hinduism, Buddhism and Jainism.

The word swastika derives from the Sanskrit svastika “lucky or auspicious object”.  [x]

During the second world war, various attempts were made by government officials to change the name to Winston, in honor of Winston Churchill. But the locals resisted, tearing down new signs and replacing them with another: “To hell with Hitler. We had the swastika first”. The town is still called Swastika. [x]

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A hyperbolic tessellation in Poincaré’s disk model, using only regular heptagons (light blue). Connecting the midpoints of adjacent heptagons gives a tessellation with hyperbolic equilateral triangles (dark blue), in groups of seven around common vertices.

This kind of hyperbolic patterns, published by mathematician Harold Coxeter, inspired Maurits Escher to his famous Circle Limit woodcuts.

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More support for the “Rose Quartz is actually Pink Diamond” theory! As we can see, the equilateral triangle is a symbol of the diamonds—you see them on the mural and the seal on Jasper and Peridot’s ship. You also see it in a place no one would expect—on the door to Rose’s room, inside what appears to be a stylized rose.

We also see a yellow diamond on both Peridot’s and Jasper’s clothing, which makes sense given that they report to Yellow Diamond. But what do we see on Pearl’s space suit? A pink diamond. She intended to go back to homeworld, and wanted to make it clear where her loyalties lay. Now, why she would want to advertise her allegiance to a traitor isn’t actually clear…but we already knew Pearl was absolutely, unflinchingly loyal to Rose.

Maureen Corrigan on the plot of the new Ken Kalfus novel, Equilateral:

The real-life premise is this: In the late 19th century, astronomers spotted what they thought were canals on Mars. Many of those astronomers theorized that, therefore, there must be life on the red planet. Kalfus’s fictional astronomer, Sanford Thayer, is an Englishman who’s obsessed with the dream of contacting the Martians. Thayer has launched an internationally funded project to carve out an enormous equilateral triangle—300 miles to each side—in the Western deserts of Egypt. Once it’s dug out, the triangle will be filled with petroleum.

Image of Mars through a telescope via Flickr

Reuleaux polygons

Reuleaux triangle is a constant width curve based on an equilateral triangle. All points on a side are equidistant from the opposite vertex. Because, it always has the same width so, it will rotate happily within a square. However, the Reuleaux pentagon rotating more happily within a hexagon - See more: Gifs at Hall of Hexagon.

Reuleaux triangle is made by forming an arc centred on each corner of an equilateral triangle.

If we rotate a reuleaux triangle within a square or reuleaux pentagon within a hexagon, then reuleaux polygons really useless:

That’s why it’s not a circle or an other shape.

(Image: Film stick-slip movement mechanism of soviet movie camera )

Maureen Corrigan on the new Ken Kalfus novel Equilateral:

[T]hose workers are under strict command not to deviate one inch in their digging lest the Martians mistakenly think that a geometrically imprecise triangle is a natural, rather than a man-made, phenomenon.  That’s why, when the workers stumble upon the tip of a buried pyramid as they’re digging a 40-foot trench on one side of the Equilateral, Thayer orders them to bury the pyramid again and pour the pitch over it. At this point, we readers begin to catch on that Thayer, in the fine literary tradition of Englishmen abroad, has stayed out in the mid-day sun too long.

Image of the Egyptian desert via panaramio

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