(Mathhombre) Miscellanea

Surprising data about the Growth Mindset tasks they experienced in elementary school from the same elementary PSTs. I will be investigating further!

The five traits are from a Jo Boaler slide.

See and Say.
Talking about instructional decisions with elementary preservice teachers. (PSTs) We did a description activity where students made quadrilaterals on geoboards and described them to a partner who tried to make it. I demonstrated with a triangle, then they tried.We capped the discussion afterward using the Talking Point structure. I loved that the discussion was student centered.

See and Say.

Talking about instructional decisions with elementary preservice teachers. (PSTs) We did a description activity where students made quadrilaterals on geoboards and described them to a partner who tried to make it. I demonstrated with a triangle, then they tried.We capped the discussion afterward using the Talking Point structure. I loved that the discussion was student centered.

Atiyah on math and art.
This is why I was looking for the Atiyah image! Excellent quote from himself found at John Cook’s Endeavour. Which also has a link to an interesting paper by Atiyah and others on aesthetic and math.

Atiyah on math and art.

This is why I was looking for the Atiyah image! Excellent quote from himself found at John Cook’s Endeavour. Which also has a link to an interesting paper by Atiyah and others on aesthetic and math.

halmos:

Photo Caption: M Atiyah 29 Mar 69  
“The Atiyah-Singer index theorem was the toughest hurdle for me, but, somehow, we conquered it too. (To be sure, after it appeared in print, Singer told me that it didn’t come out quite right—the relation with the Riemann-Roch theorem was unclear or perhaps even misstated—but there it was, and I feel sure that my fellow ignoramuses and I learned something worth knowing that we hadn’t known before.)”–Paul R. Halmos, I Want to Be a Mathematician 
Michael Francis Atiyah contributed to a wide range of topics in mathematics centering on the interaction between geometry and analysis. His work showed how the study of vector bundles on spaces could be regarded as the study of cohomology theory, called K-theory. He was awarded the Fields Medal in 1966. The ideas which led to Atiyah being awarded a Fields Medal were later seen to be relevant to gauge theories of elementary particles.  The theories of superspace and supergravity and the string theory of fundamental particles, which involves the theory of Riemann surfaces in novel and unexpected ways, were all areas of theoretical physics which developed using the ideas which Atiyah was introducing. 
In addition to the Fields Medal, Atiyah received many honors during his career including the Feltrinelli Prize from the Accademia Nazionale dei Lincei in 1981, the King Faisal International Prize for Science in 1987, the Benjamin Franklin Medal, and the Nehru Medal. In 2004, he and Isadore Singer were awarded the Neils Abel prize of £480 000 for their work on the Atiyah-Singer Index Theorem.
Michael Francis Atiyah Biography

One of my math heroes, photographed by another! 
Plus, had no idea there was this tumblr of Halmos’ personal photos. It is spectacular.

halmos:

Photo Caption: M Atiyah 29 Mar 69 

“The Atiyah-Singer index theorem was the toughest hurdle for me, but, somehow, we conquered it too. (To be sure, after it appeared in print, Singer told me that it didn’t come out quite right—the relation with the Riemann-Roch theorem was unclear or perhaps even misstated—but there it was, and I feel sure that my fellow ignoramuses and I learned something worth knowing that we hadn’t known before.)”–Paul R. Halmos, I Want to Be a Mathematician


Michael Francis Atiyah contributed to a wide range of topics in mathematics centering on the interaction between geometry and analysis. His work showed how the study of vector bundles on spaces could be regarded as the study of cohomology theory, called K-theory. He was awarded the Fields Medal in 1966.

The ideas which led to Atiyah being awarded a Fields Medal were later seen to be relevant to gauge theories of elementary particles.

The theories of superspace and supergravity and the string theory of fundamental particles, which involves the theory of Riemann surfaces in novel and unexpected ways, were all areas of theoretical physics which developed using the ideas which Atiyah was introducing. 

In addition to the Fields Medal, Atiyah received many honors during his career including the Feltrinelli Prize from the Accademia Nazionale dei Lincei in 1981, the King Faisal International Prize for Science in 1987, the Benjamin Franklin Medal, and the Nehru Medal. In 2004, he and Isadore Singer were awarded the Neils Abel prize of £480 000 for their work on the Atiyah-Singer Index Theorem.

Michael Francis Atiyah Biography

One of my math heroes, photographed by another!

Plus, had no idea there was this tumblr of Halmos’ personal photos. It is spectacular.

Des-man.

The gif is of mine - trying to make one dynamic.

The screenshot is of my students’ work. If you want to make one, go to student.desmos.com and enter code m4pd

If you’re a teacher, go to teacher.desmos.com and set one up for your class.

To restrict a graph, use curly brackets. Eg., y=2x {0<=x<3}

L Spiral.

This is a generalization of a diagram I saw from d3lt4 on Tumblr:

It is constructed by rotating and dilating the L shape to fit in with itself, rotated 90 degrees. There are some interesting properties that develop based on the height/width ratio and the thickness of the L-shape. At first I thought D3lt4’s diagram was based on an L from a square with thickness half of the width, but instead it is Golden.

The last image is close to real Golden ratio proportions.

On GeoGebraTube for play.

explore-blog:

John Dewey on the true purpose of education and how to harness the power of our natural curiosity – a must-read for parents, teachers, and lifelong learners alike.

explore-blog:

John Dewey on the true purpose of education and how to harness the power of our natural curiosity – a must-read for parents, teachers, and lifelong learners alike.

d3lt4:

"Fiboncci Sequence (Square)" Art print
Leonardo Fibonacci is an Italian mathematician from the 12th century.

d3lt4:

"Fiboncci Sequence (Square)" Art print

Leonardo Fibonacci is an Italian mathematician from the 12th century.

GeoBoard Triangles.

Found a nice online geoboard, and asked my students: Create a cool or interesting or pretty geoboard image with only triangles, screenshot it, and upload it to Facebook.

Today we’ll talk about what they found cool, interesting or pretty about it.

Seven Triangle Puzzle.

Seven different types of triangles. Name them - and make them assemble into a square!

(Cutting up a square into the seven types was a good problem that took me a while! Blogpost.)

EDIT: added pictures as they tried to solve it. Some focused on the longest edges, thinking that those might be the outside edges. Some tried finding matching lengths, others tried to make right angle corners. Even a solution if you want to peek.