(Mathhombre) Miscellanea
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

engineeringhistory:

John Von Neumann’s designs for a nCr calculator, 1944

engineeringhistory:

John Von Neumann’s designs for a nCr calculator, 1944

More Jo Niemeyer.

I am so loving this artist’s work. The top gif is a generalization of the 2nd image, another of his constructions of the Golden Ratio. It turns out there are plenty of interesting values besides the Golden Ratio formed from these three squares, and many patterns. I also included the locus of a few vertices because they were interesting, too. EDIT: it’s here on GeoGebraTube

The last three images are more of Niemeyer’s art. The first two are from his Golden Construktions page (go look because there is a lot of amazing stuff there), and the last is his piece from the 2011 Bridges Math/Art Exhibition. (Guess the ratio of white to black. He envisioned this as a fair darts game! Explanation at the Bridges site.)

If I have time I’ll do one more piece, because he has a great Pythagorean/Golden Section connection.

Don Steward featured a video of this great construction by the artist & designer Jo Niemeyer. (Video on YouTube) Niemeyer is someone that I’d somehow missed before, despite his amazing geometric aesthetic. Jo’s website: http://www.partanen.de/jncom/jo_niemeyer/home.html This sketch compares Niemeyer’s Golden construction from the video to the classical construction. I find it interesting that the section is NOT of the initial length AB - that’s new to me.  Here it is on GGBTube.

Don Steward featured a video of this great construction by the artist & designer Jo Niemeyer. (Video on YouTube)

Niemeyer is someone that I’d somehow missed before, despite his amazing geometric aesthetic. Jo’s website: http://www.partanen.de/jncom/jo_niemeyer/home.html

This sketch compares Niemeyer’s Golden construction from the video to the classical construction. I find it interesting that the section is NOT of the initial length AB - that’s new to me.  Here it is on GGBTube.

"The teachers are everywhere. What is wanted is a learner." - Wendell Berry
I love teachers and being a teacher. But I want to empower students to know that it’s not me, it’s them.
Via 12 Berry Quotes at Relevant. (I made the image.)

"The teachers are everywhere. What is wanted is a learner." - Wendell Berry

I love teachers and being a teacher. But I want to empower students to know that it’s not me, it’s them.

Via 12 Berry Quotes at Relevant. (I made the image.)

scienceisbeauty:

Some brain fitness (clic). When you’re done with them. try the “Famous Math Problems" from WolframAlpha.com, and then, if you feel strong, go to this wikipedia entry: List of unsolved problems in mathematics. Good luck!

Isaac Reed’s Famous Problems project.

scienceisbeauty:

Some brain fitness (clic). When you’re done with them. try the “Famous Math Problems" from WolframAlpha.com, and then, if you feel strong, go to this wikipedia entry: List of unsolved problems in mathematics. Good luck!

Isaac Reed’s Famous Problems project.

cinderellahope:


Wassily Kandinsky ~ Bunt im Dreieck (Bigarrure dans le triangle), 1927

cinderellahope:

Wassily Kandinsky ~ Bunt im Dreieck (Bigarrure dans le triangle), 1927

Sierpinski Play.
Cool pattern, but not what I’m shooting for! Need to screen out the extra values.

Sierpinski Play.

Cool pattern, but not what I’m shooting for! Need to screen out the extra values.

"Accurate Reckoning: the entrance into knowledge of all existing things and all obscure secrets." - Ahmes the Scribe
Quote seen at On This Day in Math.

"Accurate Reckoning: the entrance into knowledge of all existing things and all obscure secrets." - Ahmes the Scribe

Quote seen at On This Day in Math.

Sierpinski Doilies.

Inspired by a literal doily posted by mrvelocipede on tumblr.

I’m still thinking about how to dynamicize the number of levels of Sierpinski’s triangle… I thought it went nicely with Archimedean (semiregular) tilings.

The sketch is at GeoGebraTube if you want to play.