(Mathhombre) Miscellanea

s31415:

The 2014 Bridges conference on Arts and Mathematics is starting tomorrow (August 14th) in Seoul. These three works of mine will be on display in the art exhibition. More information and links here:
http://algorithmic-worlds.net/blog/blog.php?Post=20140813

explore-blog:

Such a prescient and important read: How We Think — John Dewey on cultivating the art of reflection and fruitful curiosity in an age of instant opinions and information overload. 

explore-blog:

Such a prescient and important read: How We ThinkJohn Dewey on cultivating the art of reflection and fruitful curiosity in an age of instant opinions and information overload. 

rhombitrihexagonal dual.

This sketch has a section of an Archimedean tiling (rhombitrihexagonal) and its dual.

The dual is found by taking the center of each polygon, then connecting those as vertices if the polygons they’re in are adjacent (share an edge).

When you move the slider or hit the play button, the sketch will shift between the original and the dual.

It’s called the dual, because if you do that again, you get back to the original (or a variation of the original.) You can use this technique to find the structure of tessellations.

If you download it, this sketch has tools to make your own. One tool finds the center of a polygon (barycenter), and the other family of tools is for making the animated dilations.

Inspired by bmk sketches like at [url]http://geogebrart.weebly.com/blog/duality-2[/url]

Sketch at GeoGebraTube.

"Art is fire plus algebra." - Jorge Francisco Isidoro Luis Borges
Seen at cab1729.

"Art is fire plus algebra." - Jorge Francisco Isidoro Luis Borges

Seen at cab1729.

Quadrilateral Duals.

Playing around with duals, like at the groovy GeoGebrart blog. (See Duals1 and Duals2) bmk’s are way cooler and more intricate than these so please go look.

I made tools to dilate by a factor (which can be a slider), and a tool to find the barycenter of a polygon up to 6 sides. These sketches show a dual centered on these barycenters. (Basically an average of the vertices.)

Eye Spiral.

Surprisingly, this spiral of eyes by playful_geometer that I dug up for the Carnival of Mathematics has become tumblr/popular. That got me wondering how to make it dynamic. Finally settled on translations, rotations and dilations of circles and ellipses.

And along the way I made an improved version of the kite spiral, too, which also now has a tool for making multiple.

On GeoGebraTube: Kite Spiral Kit and Eye Spiral. I know I’m missing an “I spy…” pun here…

Star Wars Common Core and SBAR posters by Paul Podraza, @teacherpaulp. These are posted at his blog teacherpaulp.wordpress.com

I’ll be printing these up for the classroom.

ryanandmath:

Mathematician Maryam Mirzakhani is the first woman and first Iranian to be awarded the Fields Medal!

The Fields Medal is one of the highest honors granted in math. Every four years the medal is awarded at the International Congress of the International Mathematical Union to two, three, or four mathematicians under the age of 40. Along with the Abel Prize, it is considered “the mathematician’s Nobel Prize.”

Mirzakhani’s work focuses on Riemann surfaces and their moduli spaces and connecting aspects of differential geometry, complex analysis, and dynamical systems. Currently she is working on developing the understanding of billiards and translation surfaces with fellow mathematician Alex Wright. A fantastic overview of her life can be found in this article.

The Fields Medal was also awarded to Artur Avila (dynamical systems), Manjul Bhargava (number theory), and Martin Hairer (stochastic differential equations).

(1, 2, 3, 4, 5)

"I belong to those theoreticians who know by direct observation what it means to make a measurement. Methinks it were better if there were more of them. ~Erwin Schrodinger"
Quote found at 8/12 On This Day in Math post. Happy birthday, ES! You restored my faith in physics.

"I belong to those theoreticians who know by direct observation what it means to make a measurement. Methinks it were better if there were more of them. ~Erwin Schrodinger"

Quote found at 8/12 On This Day in Math post. Happy birthday, ES! You restored my faith in physics.

Niemeyer-inspired Pythagorean Slide.
Wasn’t ever able to get the effect I was looking for, or find a visual that was a significant variation of the Golden Section construction or the Pythagorean tiling. Still the Pythagorean tiling with the golden ratio squares is pleasant.
Cf. previous post

Niemeyer-inspired Pythagorean Slide.

Wasn’t ever able to get the effect I was looking for, or find a visual that was a significant variation of the Golden Section construction or the Pythagorean tiling. Still the Pythagorean tiling with the golden ratio squares is pleasant.

Cf. previous post