Art and mathematics always had a connection. In the old world, the great artists were mathematicians and vice versa. Only in our modern world, we are told that some people have the skill for math and some for art. (and usually they are not the same person).

Richard Feynman, the great 20th century physicist, Nobel Laureate, and overall “curious character” said:”

I listened to a conversation between two girls, and one was explaining that if you want to make a straight line, you see, you go over a certain number to the right for each row you go up, that is, if you go over each time the same amount when you go up a row, you make a straight line. A deep principle of analytic geometry! …It turned out that one girl was explaining to the other how to knit argyle socks.”

Both mathematicians and yarn lovers have been following Feynman. Using crocheting and knitting to show mathematical ideas. Here are five of them from mental_floss

### 1. HYPERBOLIC PLANE

Courtesy of Daina Taimina

A hyperbolic plane is a surface that has a constant negative curvature. For years, math professors attempting to help students visualize its ruffled properties taped together paper models … which promptly fell apart. In the late ‘90s, Cornell math professor Daina Taimina came up with a better way: crochet, which provided a model that was durable enough to be handled.

### 2. LORENZ MANIFOLD

In 2004, Hinke Osinga and Bernd Krauskopf, both of whom were math professors at the University of Bristol in the UK at the time, used crochet to illustrate the twisted-ribbon structure of the Lorenz manifold. Osinga and Krauskopf’s original 25,510-stitch model of a Lorenz manifold gives insight. they write: “into how chaos arises and is organised in systems as diverse as chemical reactions, biological networks and even your kitchen blender.”

### 3. MULTIPLICATION

There’s a lot of discussion about elementary students who struggle with basic math concepts. There are very few truly imaginative solutions for how to engage these kids. The afghans knit by now-retired British math teachers Pat Ashforth and Steve Plummer, and the curricula [PDF] they developed around them over several decades, are a significant exception. Even for the “simple” function of multiplication, they found that making a large, knitted chart using colors rather than numerals could help certain students instantaneously visualize ideas that had previously eluded them. “It also provokes discussion about how particular patterns arise, why some columns are more colorful than others, and how this can lead to the study of prime numbers,” they wrote. Students who considered themselves to be hopeless at math discovered that they were anything but.

### 4. NUMERICAL PROGRESSION

Courtesy of Alasdair Post-Quinn

Computer technician Alasdair Post-Quinn has been using a pattern he calls Parallax to explore what can happen to a grid of metapixels that expands beyond a pixel’s usual dimensional constraint of a 1×1. “What if a pixel could be 1×2, or 5×3?” he asks. “A 9×9 pixel grid could become a 40×40 metapixel grid, if the pixels had varying widths and heights.

### 5. MÖBIUS BAND

Courtesy of Cat Bordhi

A Möbius band or strip, also known as a twisted cylinder, is a one-sided surface invented by German mathematician August Ferdinand Möbius in 1858. It ain’t so simple to work out the trick of it, though, and accomplishing it requires understanding some underlying functions of knitting and knitting tools—starting with how, and with what kind of needles, you cast on your stitches, a trick that Bordhi invented.