Crocheting the hyperbolic plane

  title={Crocheting the hyperbolic plane},
  author={David W. Henderson and Daina Taimina},
  journal={The Mathematical Intelligencer},
A brief look at the evolution of modeling hyperbolic space
  • S. Frazier
  • Mathematics
    The Mathematics Enthusiast
  • 2017
(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,
Crocheting adventures with hyperbolic planes
In Chapter 7, one works with data sets as inputs for the parameters defined in programs constructing models, which might be images or environmental data such as temperature, wind or the sun’s azimuth and elevation.
Visualizing Crocheting Overlay
Crafts are human-material interaction. Documentation of handicrafts is challenging and needs creativity because individual craftwork heavily depends on the understanding of the materials at hand and
Shearman, Toby L.; Venkataramani, Shankar C. Distributed branch points and the shape of elastic surfaces with constant negative curvature
The authors argue that these surfaces are good candidates for minimizing bending energy. By using the discrete model, they made numerical experiments that corroborates this expectation. They also
Oceans of Inspiration: A Marine Based STEAM Project
  • Julie Boyle
  • Education
    European Journal of STEM Education
  • 2021
This paper describes a set of project-based learning activities focused on a theme of the oceans and marine life. Whilst still providing a clear link to existing physics curricula, the STEAM
Navigating Higher Dimensional Spaces using Hyperbolic Geometry
This work introduces a novel method of interactive visualization of higher-dimensional grids, based on hyperbolic geometry, making it applicable in data visualization, user interfaces, and game design.
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 solve
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 of
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 formally
Distributed Branch Points and the Shape of Elastic Surfaces with Constant Negative Curvature
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.


Three-Dimensional Geometry and Topology, Volume 1
is a recursive definition!) The first term of the 'Goodstein sequence' of a number is the number itself. The nth term of the Goodstein sequence is obtained by expressing the previous term in 'pure
Efimov's theorem about complete immersed surfaces of negative curvature
Geometry and the Imagination
The simplest curves and surfaces Regular systems of points Projective configurations Differential geometry Kinematics Topology Index.
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 Lines
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.
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 introduction
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 289