Today is know as National Math Storytelling Day. While this isn’t exactly a story, I do feel it is an appropriate blog topic, given what today is.
There is an intriguing and beautiful correlation between math and crochet, with crochet often serving as a tangible way to explore and express mathematical concepts. Here are a few examples where the two intersect:
1. Geometry:
Crochet naturally lends itself to the exploration of geometrical shapes. By controlling increases, decreases, and stitch counts, crocheters can create flat circles, hyperbolic planes, spheres, and other geometric forms.
– Hyperbolic crochet is a famous example. Hyperbolic geometry is a non-Euclidean geometry with constant negative curvature, and mathematician Daina Taimina famously used crochet to model hyperbolic planes. The structure of hyperbolic surfaces cannot be easily visualized with paper, but crochet allows for a flexible and tactile representation.
– Spherical crochet: Spheres and other complex 3D forms can be created using specific increases or decreases in stitches, demonstrating concepts from topology and differential geometry.
2. Algebra:Patterns in crochet follow a mathematical logic, often involving counting, sequences, and symmetry. Reading a crochet pattern requires following specific instructions about the number of stitches to create, where to place increases, decreases, and repeat patterns. The regularity and structure are akin to following a set of mathematical rules or algorithms.
– Modular arithmetic can appear in crochet as well. For example, when crocheting in the round, the number of stitches can follow cyclical patterns, much like working with numbers in modular systems.
3. Fractals:
Crochet patterns can be used to generate fractal structures. A fractal is a complex pattern that looks similar at various scales. This self-similarity is found in certain types of crochet patterns, where increasing the size of a motif can resemble the whole.
– The Sierpiński triangle or the Menger sponge can be crocheted by starting with simple shapes and iterating a sequence of stitches, mimicking how fractals are generated mathematically.
4. Patterns and Sequences:
Crochet often involves repeating sequences of stitches, which can model different mathematical sequences, such as the Fibonacci sequence. In fact, some crochet designs explicitly use Fibonacci numbers or golden ratios in their arrangements, particularly in creating spirals, shells, or floral motifs.
5. Topology and Knots:
Crochet can also serve as a tool for visualizing concepts from topology, the branch of mathematics concerned with the properties of space that are preserved under continuous deformations. For example, crocheters can create torus shapes (a donut-like surface) or even models of knots, which relate to knot theory, a subfield of topology.
6. Tessellations and Symmetry:
Many crochet patterns, especially granny squares or other motifs, involve tessellations, where the repeated use of shapes covers a surface without gaps or overlaps. This is directly linked to the mathematical study of tilings and symmetry. Crocheters can explore different types of symmetry (e.g., rotational, reflective) through the arrangement of their stitches.
7. Algorithmic Thinking:
Writing and interpreting crochet patterns is similar to coding. Both involve following instructions and loops, akin to an algorithm. Mathematicians and computer scientists may find the way crochet uses patterns of repetition, recursion, and optimization familiar.
In summary, crochet can be used as a creative way to explore mathematical ideas, especially in geometry, sequences, and topology. Many mathematicians and artists alike have embraced crochet as a medium for visualizing and understanding complex mathematical concepts.
