June 22, 2012
This is a hyperbolic pseudosphere — made with nothing more than yarn and a crochet hook.
Hyperbolic geometry describes surfaces that are negatively curved. Negative curvature appears in coral reefs, kale leaves and Pringles potato chips. A surface with negative curvature is at every point like a saddle—your legs rest on a surface that curves down whereas the front and back of the saddle curve up.
In the past decade or so many mathematicians have embraced crochet both as a way to visualize difficult concepts in hyperbolic geometry and as an outreach activity: With a little instruction and practice, even high school students can create their own hyperbolic models.
Pictured here, the pseudosphere is a hyperbolic surface that has constant negative curvature. It is named in analogy to the sphere, which has constant positive curvature (every point is just as curvy as every other point). Some would call this a half-pseudosphere; it is analogous to one hemisphere of a globe, with the point sticking up in the middle (held up by orange yarn in this picture) the “north pole.”
Daina Taimina is the mathematician who first used crochet to create models of the hyperbolic plane. She noticed that paper models were quite fragile and wanted something sturdier that allowed freer manipulation and exploration of hyperbolic space. She turned to yarn. Creating negative curvature using crochet is relatively simple: in each row, you add stitches at a constant rate. The more frequently stitches are added, the curlier (and more negatively curved) the surface gets.
Sean Lawton, an assistant professor of mathematics at the University of Texas–Pan American, is one of the many mathematicians who has followed in Taimina’s footsteps. He uses hyperbolic crochet as an outreach and teaching tool. He has worked with students from middle school to college as well as given public lectures, demonstrations and even crochet instructional sessions at libraries and museums.
The pseudosphere shown here was created by Claudia Carranza, an undergraduate student who worked with Lawton before she became a public school teacher. For this project, she added a stitch every three stitches. As you can see, the border gets very curly. She made this piece over the course of a year but says, “If I had sat down and worked nonstop, I figure it might have taken me about a week.”
– Evelyn Lamb
what would it be like if it were knitted – I have tried but need to be certain that I have knitted the Hyperbolic Pseudosphere before I try posting any photos as am not a mathematician but love playing.
I have been so tied up with establishing this new garden here in Miranda, where there was none before, and have not been knitting nearly enough.
We are also in the midst of a drought like no other on record in New Zealand and we use rain water for all of our watering needs. Best Beloved and I did install an additional water tank at the end of 2011, quite soon after we arrived back in New Zealand and that gives us 50,000 litres of water storage. Sounds great but sadly I left the hose on some weeks ago which depleted it somewhat. We save dish washing and hand washing water for the trees and to flush the toilet. Our rain water is used for everything else from drinking, showering, water for the chickens and for the steers when they are in our paddock and obviously to water our extensive vegetable gardens.
The steers belong to next door family but our paddock is used in turn to help feed them and to help maintain the health of our paddock.
Knitting – well not much is happening. I am playing with ideas, trying things – but making little progress – it has been too hot with temperatures about 28 to 30 degrees Celsius (82 to 86 Fahrenheit – doesn’t sound so hot but it is for me) on most days since late December and right now at 11 am on an April autumnal day it is already 23.6. When it is too hot over the mid 5 or 6 hours of the day it is also too hot to be shrouded in knitting.
So my stack of books by my seat grows, my swatch pile grows as do my very bad sketches.
Surely it will soon rain and cool down and I can get on with the knitting.
I know I have been a bit quiet over the past 18 months or so. I am still knitting at odd times and have now set up a Craftsy Pattern Store. There are 3 patterns there so far – my Kiwi Cape, The Capelet of many Colours and the Connie Cowl. Hope you will take a look. It is free to join Craftsy and it does offer many opportunities for learning new skills, finding patterns and selling your patterns.
headland “Sculpture on the Gulf” Waiheke Island 25 January – 17 February 2013
You still have time to go and walk the “Sheep Track”
Sheeps wool, fibre, metal, wood. 25 metres x 560mm x 900 mm
A Knitted path which all walked upon!! I felt strangely guilty at walking on a knitted piece but as there was nowhere else to walk I had to continue along the path and I did of course. Thank you Gina for creating a piece which surprised and challenged and delighted us.
Sheep Track recalls the crafted ‘colonial’ blanket, made to protect, cover and keep the wearer warm, transformed into a carpet-like woollen path nestled into the landscape – a draped farmer’s scarf.
“In traversing the cliff-side track like a flock of sheep in single file, each step changes the nature and surface of the work as it collects detritus, getting dirtier and becoming increasingly threadbare…… (verbatim from catalogue of the sculpture exhibition)
Curiously “Peplum” has two distinct and almost separate definitions. Its early origins are Greek, and peplum was simply the word for tunic. The peplum, a term dating back to the 19th century, is also a short overskirt that is usually attached to a fitted jacket. My jacket is certainly a fitted jacket with a short skirt.
Is this the jacket you would like the pattern for? It has pointed sections over the hand and at the back of the peplum skirt. There is no collar and is very fitting in 12ply mohair. The mohair was black with sections of rich blues and is no longer available.
Jacket Pattern Brewing for rather a long time.
or one of these designs below?
Sleeveless again with pin fastening, no collar, but includes lapel flap. (not sure if that describes it or not – the lapel does not continue around the back of the neck). The skirt or peplum is much fuller and longer and without the pointed section.
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- A Gallery of Artists
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- The Big Idea Te Aria Nui
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- World arts & artists – An arts portal
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