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photonskyto:
“ [10/Jan/2016] Geometria
Reference : THE ARTEFACT by Silverwing
http://www.silverwing-vfx.de/work_3D.html
”

Source: photonskyto

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The Complex Geometry of Islamic Design

teded

In Islamic culture, geometry is everywhere. You can find it in mosques, madrasas, palaces and private homes. This tradition began in the 8th century CE during the early history of Islam, when craftsman took preexisting motifs from Roman and Persian cultures and developed them into new forms of visual expression.

This period of history was a golden age of Islamic culture, during which many achievements of previous civilizations were preserved and further developed, resulting in fundamental advancements in scientific study and mathematics. Accompanying this was an increasingly sophisticated use of abstraction and complex geometry in Islamic art, from intricate floral motifs adorning carpets and textiles, to patterns of tile work that seemed to repeat infinitely, inspiring wonder and contemplation of eternal order.

Despite the remarkable complexity of these designs, they can be created with just a compass to draw circles and a ruler to make lines within them, and from these simple tools emerges a kaleidoscope multiplicity of patterns. So how does that work? Well, everything starts with a circle. The first major decision is how will you divide it up? Most patterns split the circle into four, five or six equal sections. And each division gives rise to distinctive patterns.

There’s an easy way to determine whether any pattern is based on fourfold, fivefold, or sixfold symmetry. Most contain stars surrounded by petal shapes. Counting the number of rays on a starburst, or the number of petals around it, tells us what category the pattern falls into. A star with six rays, or surrounded by six petals, belongs in the sixfold category. One with eight petals is part of the fourfold category, and so on.

There’s another secret ingredient in these designs: an underlying grid. Invisible, but essential to every pattern, the grid helps determine the scale of the composition before work begins, keeps the pattern accurate, and facilitates the invention of incredible new patterns. Let’s look at an example of how these elements come together.

We’ll start with a circle within a square, and divide it into eight equal parts. We can then draw a pair of criss-crossing lines and overlay them with another two. These lines are called construction lines, and by choosing a set of their segments, we’ll form the basis of our repeating pattern.

Many different designs are possible from the same construction lines just by picking different segments. And the full pattern finally emerges when we create a grid with many repetitions of this one tile in a process called tessellation.

By choosing a different set of construction lines, we might have created this any of the above patterns. The possibilities are virtually endless.

We can follow the same steps to create sixfold patterns by drawing construction lines over a circle divided into six parts, and then tessellating it, we can make something like the above.

Here’s another sixfold pattern that has appeared across the centuries and all over the Islamic world, including Marrakesh, Agra, Konya and the Alhambra.

Fourfold patterns fit in a square grid, and sixfold patterns in a hexagonal grid.

Fivefold patterns, however, are more challenging to tessellate because pentagons don’t neatly fill a surface, so instead of just creating a pattern in a pentagon, other shapes have to be added to make something that is repeatable, resulting in patterns that may seem confoundingly complex, but are still relatively simple to create.

This more than 1,000-year-old tradition has wielded basic geometry to produce works that are intricate, decorative and pleasing to the eye. And these craftsman prove just how much is possible with some artistic intuition, creativity, dedication along with a great compass and ruler.

Source: teded

basedheisenberg

campusreform.org

Prof: Algebra, geometry perpetuate white privilege

A University of Illinois math professor argues in a new book that algebra and geometry skills perpetuate “unearned privilege” among whites.

association-of-free-people

Gutierrez worries that algebra and geometry perpetuate privilege because “emphasizing terms like Pythagorean theorem and pi” give the impression that math “was largely developed by Greeks and other Europeans.”

She also worries that evaluations of math skills can perpetuate discrimination against minorities, especially if they do worse than their white counterparts.

A math education professor at the University of Illinois argued in a newly published book that algebraic and geometry skills perpetuate “unearned privilege” among whites.

Rochelle Gutierrez, a professor at the University of Illinois, made the claim in a new anthology for math teachers, arguing that teachers must be aware of the “politics that mathematics brings” in society.

“Are we really that smart just because we do mathematics?” Tweet This

“On many levels, mathematics itself operates as Whiteness. Who gets credit for doing and developing mathematics, who is capable in mathematics, and who is seen as part of the mathematical community is generally viewed as White,” Gutierrez argued.

Gutierrez also worries that algebra and geometry perpetuate privilege, fretting that “curricula emphasizing terms like Pythagorean theorem and pi perpetuate a perception that mathematics was largely developed by Greeks and other Europeans.“

Math also helps actively perpetuate white privilege too, since the way our economy places a premium on math skills gives math a form of “unearned privilege” for math professors, who are disproportionately white.

“Are we really that smart just because we do mathematics?” she asks, further wondering why math professors get more research grants than “social studies or English” professors.

Further, she also worries that evaluations of math skills can perpetuate discrimination against minorities, especially if they do worse than their white counterparts.

“If one is not viewed as mathematical, there will always be a sense of inferiority that can be summoned,” she says, adding that there are so many minorities who “have experienced microaggressions from participating in math classrooms… [where people are] judged by whether they can reason abstractly.”

To fight this, Gutierrez encourages aspiring math teachers to develop a sense of “political conocimiento,” a Spanish phrase for “political knowledge for teaching.”

Gutierrez stresses that all knowledge is “relational,” asserting that “Things cannot be known objectively; they must be known subjectively.”

___________________________________________

I knew we’d get here eventually.

Published academic declares math racist.

gouachevalier

I thought algebra was a product of Islamic civilization? Or are they walking that back now?

association-of-free-people

That doesn’t help drive the narrative.

Consider that children from married households fare far better as students than those from single parent families.

Also be aware of the propaganda in the link provided.

The Washington Post, even when reporting these facts, tries desperately to downplay the importance of family cohesiveness by separating the benefits that constitute the heart of the institution of marriage from marriage itself.

Then examine what the state has done to the black family in particular, the population overall, and the impact that might have on student performance.

In my county they spend 10,000.00 taxpayer dollars per year per student for horrible results. It costs between 4-6k to send a kid to a blue ribbon private school in the same town.

This isn’t to say you can’t come out of a difficult situation and make something of yourself; it is to say the odds are stacked against you.

Math isn’t racist. The people who propagate this type of postmodernist social justice bullshit are the vanguard of a system that is systematically enslaving society.