math art

introduction

hey there everyone, i’ve been meaning to make a study blog for a while now. i honestly love school and love take notes and looking at other peoples notes, so i figured why not finally just make one! i’m 16 and i live somewhere in canada. you can call me vee of vani or some version of vanesssa  ( it doesn’t really matter to me lol )

things i like

  • science + maths
  • harry potter
  • disney
  • art! drawing, sketching, painting, i have an artstagram it’s @nessiliee
  • reading reading reading
  • learning new languages, i think it would be really cool to be bilingual, but learn on my own
  • writing novels; tbh i wanna publish a current work 
  • sports; any really but mostly basketball, volleyball, and soccer, i’m also kind of getting into weight lifting lol, gotta grow a booty ya know?

about me

i’m currently going into grade 11, that is this fall, and i figured that this year i needed to get my shit together and try to end my procrastination as well as prepare for uni (or college in the states) which is coming faster than i think. i’m a 95% average student, but i really wanted to up that as well as make my notes better, which i figured a studyblr could help me with.

as far as my future, i want to go to med school, right now i’m looking at either oncology or pathology, but that is very likely to change before i actually get to my career

languages i wanna learn

  • french (started in school when i was 9, took my last french course this past semester, not fluent tho)
  • estonian
  • german
  • other languages?

favourite studyblrs

@nerdstudies @hufflepuffsstudies @elienstudies

@candiestudyblr @studyblr @stvdybuddies

@alimastudies @studyoblivion @jiyeonstudies

@studyhardlikegranger @studiousminds @studylilium

@ambstudy @prettylittlestudies @isabella-study @studyhardlikegranger

…and more!! but i’m super happy to be joining part of this community xx

Thank you for reading, and hello! Welcome!

The Complex Geometry of Islamic Design

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.

okay but real talk, lets just replace the course material used to teach mathematics in k-12 in the usa with the art of problem solving. everyone would be so much better for it. and its already written, theres no work involved. 

JUST REPLACE THE FUCKING MCGRAW HILL BOOKS WITH THE ART OF PROBLEM SOLVING. burn the mcgraw hill books to the ground. set them all on fire. leave none of them unburnt. delete mcgraw hill from this earth.

3

akaashi in this chapter was the best because he literally… did not have to do any of that like he tried so so hard (look at his face in those panels. he is so stressed) to get bokuto back in the game – but they didnt need him to win at all (e.g. washio says this SUPER OUTRIGHT)! and then when konoha at the end tells akaashi “you ignore him if u want” he basically ignores him completely O|-<

i bet after the match akaashi’s regretting everything