CLOSE
Original image

6 Math Concepts Explained by Knitting and Crochet

Original image
This crocheted Lorenz manifold gives insight "into how chaos arises." Image credit: © Hinke Osinga and Bernd Krauskopf, 2004

 
Using yarn and two pointy needles (knitting) or one narrow hook (crochet), pretty much anyone can stitch up a piece of fabric. Or, you can take the whole yarncraft thing light-years further to illustrate a slew of mathematical principles.

In the last several years, there’s been a lot of interesting discussion around the calming effects of needlecraft. But back in 1966, Richard Feynman, in a talk he gave to the National Science Teachers’ Association, remarked on the suitability of knitting for explaining math:

I listened to a conversation between two girls, and one was explaining that if you want to make a straight line…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!

Both mathematicians and yarn enthusiasts have been following Feynman’s (accidental) lead ever since, using needlecraft to demonstrate everything from torus inversions to Brunnian links to binary systems. There’s even an annual conference devoted to math and art, with an accompanying needlecraft-inclusive exhibit. Below are six mathematical ideas that show knitting and crochet in their best light—and vice versa.

1. HYPERBOLIC PLANE

Courtesy of Daina Taimina

 
A hyperbolic plane is a surface that has a constant negative curvature—think lettuce leaf, or one of those gelatinous wood ear mushrooms you find floating in your cup of hot and sour soup. 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. There’s no analytic formula for a hyperbolic plane, but Taimina and her husband, David Henderson, also a math professor at Cornell, worked out an algorithm for it: if 1^x = 1 (a plane with zero curvature, made by crocheting with no increase in stitches), then (3/2)^x means increasing every other stitch to get a tightly crenellated plane.

2. LORENZ MANIFOLD

© Hinke Osinga and Bernd Krauskopf, 2004

 
In 2004, inspired by Taimina and Henderson’s work with hyperbolic planes, 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. This is a complicated surface that arises from the equations in a paper about chaotic weather systems, published in 1963, by meteorologist Edward Lorenz and widely considered to be the start of chaos theory. 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. CYCLIC GROUPS

You can knit a tube with knitting needles. Or you can knit a tube with a little handheld device called a Knitting Nancy. This doohickey looks something like a wooden spool with a hole drilled through its center, with some pegs stuck in the top of it. When Ken Levasseur, chair of the math department at the University of Massachusetts Lowell, wanted to demonstrate the patterns that could emerge in a cyclic group—that is, a system of movement that’s generated by one element, then follows a prescribed path back to the starting point and repeats—he hit on the idea of using a computer-generated Knitting Nancy, with varying numbers of pegs. “Most people seem to agree that the patterns look nice,” says Levasseur. But the patterns also illustrate applications of cyclic groups that are used, for example, in the RSA encryption system that forms the basis of much online security.

4. MULTIPLICATION

Courtesy of Pat Ashforth and Steve Plummer

 
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.

5. 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 1x1. “What if a pixel could be 1x2, or 5x3?” he asks. “A 9x9 pixel grid could become a 40x40 metapixel grid, if the pixels had varying widths and heights.” The catch: metapixels have both X and Y dimensions, and when you place one of them on a grid, it forces all the metapixels in the X direction (width) to match its Y direction (height), and the other way around. To take advantage of this, Post-Quinn charts a numerical progression that’s identical on both axes—like 1,1,2,2,3,3,4,5,4,3,3,2,2,1,1—to achieve results like the ones you see here. He’s also in the process of writing a computer program that will help him plot these boggling patterns out.

6. 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. If you wanted to make one of these bands out of a strip of paper, you’d give an end a half-twist before attaching the two ends to each other. Or, you could knit one, like Cat Bordhi has been doing for over a decade. 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. She keeps coming back to it because, she says, it can be “distorted into endlessly compelling shapes,” like the basket pictured here, and two Möbii intersecting at their equators—an event that turns Möbius on its ear by giving it a continuous “right side.”

Original image
Kehinde Wiley Studio, Inc., Wikimedia Commons // CC BY-SA 3.0
arrow
presidents
Barack Obama Taps Kehinde Wiley to Paint His Official Presidential Portrait
Original image
Kehinde Wiley
Kehinde Wiley Studio, Inc., Wikimedia Commons // CC BY-SA 3.0

Kehinde Wiley, an American artist known for his grand portraits of African-American subjects, has painted Michael Jackson, Ice-T, and The Notorious B.I.G. in his work. Now the artist will have the honor of adding Barack Obama to that list. According to the Smithsonian, the former president has selected Wiley to paint his official presidential portrait, which will hang in the National Portrait Gallery.

Wiley’s portraits typically depict black people in powerful poses. Sometimes he models his work after classic paintings, as was the case with "Napoleon Leading the Army Over the Alps.” The subjects are often dressed in hip-hop-style clothing and placed against decorative backdrops.

Portrait by Kehinde Wiley
"Le Roi a la Chasse"
Kehinde Wiley, Wikimedia Commons // CC BY 3.0

Smithsonian also announced that Baltimore-based artist Amy Sherald has been chosen by former first lady Michelle Obama to paint her portrait for the gallery. Like Wiley, Sherald uses her work to challenge stereotypes of African-Americans in art.

“The Portrait Gallery is absolutely delighted that Kehinde Wiley and Amy Sherald have agreed to create the official portraits of our former president and first lady,” Kim Sajet, director of the National Portrait Gallery, said in a press release. “Both have achieved enormous success as artists, but even more, they make art that reflects the power and potential of portraiture in the 21st century.”

The tradition of the president and first lady posing for portraits for the National Portrait Gallery dates back to George H.W. Bush. Both Wiley’s and Sherald’s pieces will be revealed in early 2018 as permanent additions to the gallery in Washington, D.C.

Original image
Made.com
arrow
Art
What the Homes of the Future Will Look Like, According to Kids
Original image
Made.com

Ask a futurist what the house of tomorrow will feature and she might mention automatic appliances and robot assistants. Ask a kid the same question and you’ll get answers that are slightly more creative, but not altogether impractical. That’s what Made.com discovered when they launched Homes of the Future, a project that had kids draw illustrations of futuristic homes that served as the basis for professional 3D renderings.

According to Co.Design, the UK-based furniture retailer recruited children ages 4 to 12 to submit their architectural ideas. The doodles, sketched in pen, marker, and colored pencil, showcase the grade-schoolers' imaginations. Paired with each picture is concept art made with a 3D illustrator that shows what the homes might look like in the real world.

The designs range from colorful and whimsical to coldly realistic. In one blueprint, drawn by Ameen, age 10, a neighborhood of rainbow buildings and flowers float among the clouds. Another sketch by Ellis, age 7, shows a “home built to last” with titanium, bricks, a steel roof, and bulletproof windows. Some kids seemed less concerned with durability than they were with the tastiness of the infrastructure. Cherry-flavored bricks, candy windows, and a giant jelly slide were just some of the features built into the future homes. Sustainability was also a major theme, with solar panels appearing on two of the houses.

Check out the original artwork and the 3D versions of their ideas below.

House of the future drawn by kid.

House of the future drawn by kid.

House of the future drawn by kid.

House of the future.

House of the future.

House of the future.

House of the future.

House of the future.

House of the future.

House of the future.

[h/t Co.Design]

All images courtesy of Made.com.

SECTIONS

arrow
LIVE SMARTER