Nudibranchs, Coral, Crochet and Math

Nudibranchs may not be able to do math, but perhaps they are performing math: For your somewhat advanced students with a healthy curiosity about and interest in topics like marine biology, especially nudibranchs and coral), geometry, holograms.. and crochet!
“Living in tropical coral reefs are species of sea slugs known as nudibranchs, adorned with flanges embodying hyperbolic geometry, an alternative to the Euclidean geometry that we learn about in school, and a form that, over hundreds of years, many great mathematical minds tried to prove impossible…..”

“Corals and sea slugs construct hyperbolic surfaces and it turns out that humans can also make these forms using iterative handicrafts such as knitting and crochet – you can do non-Euclidean geometry with your hands. To crochet a hyperbolic structure, one just increases stitches at a regular rate by following a simple algorithm: ‘Crochet n stitches, increase one, repeat ad infinitum.’ By increasing stitches, you increase the amount of surface area in a regular way, visually moving from a flat or Euclidean plane into a ruffled formation that models the ‘hyperbolic plane’. Mathematically speaking, the hyperbolic plane is the geometric opposite of the sphere: where the surface of a sphere curves towards itself at every point, a hyperbolic surface curves away from itself. We can define these different surfaces in terms of their curvature: a Euclidean plane has zero curvature (it’s flat everywhere), a sphere has positive curvature, and a hyperbolic plane has negative curvature. In this sense, it is a geometric analogue of a negative number.”
Well, let’s just make it easier on ourselves and say healthy curiosity and sense of wonder.

Want more? Hundreds of strangely compelling an hypnotic hyperbolic images on pinterest, including crocheted versions, which also include crocheting, pinch me this cannot be real, a coral reef! They are not all crocheted, so if handicrafts give you an itchy feeling, scroll on down and look at the others.

Background stuff:

The Math Forum’s brief definition of hyperbolic geometry:
“The geometry with which most people first learned to visual basic shapes such as lines, triangles, and squares is the traditional geometry that most of us are used to, formally called Euclidean geometry. In two-dimensions, Euclidean geometry is viewed in a flat, infinite plane. However, there also exists non-Euclidean geometry, examples of which include the elliptic and hyperbolic geometries. ”

Meriam Webster: Definition of hyperbolic paraboloid
:a saddle-shaped quadric surface whose sections by planes parallel to one coordinate plane are hyperbolas while those sections by planes parallel to the other two are parabolas if proper orientation of the coordinate axes is assumed.


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  1. ms
    Posted March 21, 2017 at 4:26 pm | Permalink

    Oh! I love this 😀 I’ve been crocheting a gigantic hyperbolic paraboloid for years, (I told people it was going to be a scarf, and then later a blanket) and had no idea that’s what I was doing, thanks so much for the pics and articles

    • Headmistress
      Posted March 24, 2017 at 2:38 am | Permalink

      That is delightful.

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