Crocheting the hyperbolic plane

@article{Henderson2001CrochetingTH,
  title={Crocheting the hyperbolic plane},
  author={D. Henderson and Daina Taimina},
  journal={The Mathematical Intelligencer},
  year={2001},
  volume={23},
  pages={17-28}
}
A brief look at the evolution of modeling hyperbolic space
(ProQuest: ... denotes formulae omitted.)IntroductionThe original introduction of hyperbolic geometry, also known as non-Euclidean or Lobachevskian geometry, was not widely celebrated. At the time,Expand
Crocheting adventures with hyperbolic planes
been able to consider without such tools. Finally, in Chapter 7, one works with data sets as inputs for the parameters defined in programs constructing models. Data sets might be images orExpand
Distributed Branch Points and the Shape of Elastic Surfaces with Constant Negative Curvature
TLDR
It is argued that, to optimize norms of the curvature, i.e., the bending energy, distributed branch points are energetically preferred in sufficiently large pseudospherical surfaces. Expand
Do the Angles of a Triangle Add up to 180{\deg}? -- Introducing Non-Euclidean Geometry
How canwe convince students, who havemainly learned to follow givenmathematical rules, that mathematics can also be fascinating, creative, and beautiful? In this paper I discuss different ways ofExpand
Geometric approach to mechanical design principles in continuous elastic sheets
Using a geometric formalism of elasticity theory we develop a systematic theoretical method for controlling and manipulating the mechanical response of slender solids to external loads. We formallyExpand
Using isometries for computational design and fabrication
We solve the task of representing free forms by an arrangement of panels that are manufacturable by precise isometric bending of surfaces made from a small number of molds. In fact we manage to solveExpand
Distributed branch points and the shape of hyperbolic surfaces
We develop a theory for distributed branch points and their role in determining the shape and influencing the mechanics of thin hyperbolic objects. We show that branch points are the naturalExpand
Happy Hookers: findings from an international study exploring the effects of crochet on wellbeing
TLDR
Crochet is a relatively low-cost, portable activity that can be easily learnt and seems to convey all of the positive benefits provided by knitting, adding to the social prescribing evidence base. Expand
Representation of Crochet Stitches using a Tile-Based Method
Crochet is a type of fabrication that allows for flexible manipulation of the yarn in order to create different objects. There exists an international crochet notation that can be used to pictoriallyExpand
Representing Crochet with Stitch Meshes
TLDR
This work introduces a special edge type which captures the idea of the current loop – the loop of yarn held on the crochet hook during fabrication, and creates a library of mesh face types which model commonly-used crochet stitches. Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 10 REFERENCES
Experiencing Geometry: In Euclidean, Spherical and Hyperbolic Spaces
1. What Is Straight? Problem 1.1: When Do You Call a Line Straight? How Do You Construct a Straight Line? The Symmetries of a Line. Local (and Infinitesimal) Straightness. 2. Straightness on Spheres.Expand
Differential Geometry: A Geometric Introduction
Preface. How to Use This Book. 1. Surfaces and Straightness. When Do You Call a Straight Line? How Do You Construct a Straight Line? Local (and Infinitesimal) Straightness. Intrinsic Straight LinesExpand
Three-dimensional geometry and topology
Preface Reader's Advisory Ch. 1. What Is a Manifold? 3 Ch. 2. Hyperbolic Geometry and Its Friends 43 Ch. 3. Geometric Manifolds 109 Ch. 4. The Structure of Discrete Groups 209 Glossary 289Expand
A comprehensive introduction to differential geometry
Spivak's Comprehensive introduction takes as its theme the classical roots of contemporary differential geometry. Spivak explains his Main Premise (my term) as follows: "in order for an introductionExpand
Efimov's theorem about complete immersed surfaces of negative curvature
Preface ............................ Introduction and Statement of Efimov’s Theorem .......... 1. Proof of Efimov’s Theorem Modulo His Main Lemma ...... 1.1. An Outline of the Proof .................Expand
Geometry and the Imagination
The simplest curves and surfaces Regular systems of points Projective configurations Differential geometry Kinematics Topology Index.