Geometry through drawing, crocheting, and other arts

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Bodily experiences can be helpful at learning aspects of mathematics and physics because we begin to make a physical connection through movement, sensory experiences, or gestures to understand mathematical theory. At an early age, we use our fingers to count numbers and perform simple arithmetic operations like add and subtract. In this reading, it was discussed that a circle can go to infinity if it has infinite radius; a circle with infinite radius has zero curvature and is a straight line. We can use bodily experiences to visualize this: tie both ends of a string so that it is a closed loop which gives us a shape that appears geometrically a circle. Then using our two hands, we can try to make the radius (or diameter which is two times the radius) as large as possible by pulling the sides of the “circle.” What we notice, is that the geometric shape now begins to “flatten.” The more we continue pulling the circle, the straighter (and flatter) it appears in the Euclidean plane. Henderson & Taimina note that circles with infinite radius are not straight in hyperbolic planes but are called horocycles (n.d.).

Figure 1: Animation of a circle with infinite radius. 

We can and should incorporate bodily experiences as resources to learn in mathematics and physics classrooms. For example, we have already seen the Right-hand Rule used as a helpful mnemonic for remembering things. The Right-hand Rule can be used to find the direction of a magnetic force on a positive moving charge or understand orientation of axes in a 3D space. The Right-hand rule has also been seen in vector calculus: for a positively-oriented curve C bounding a surface S, the normal to the surface n vector is defined such that the right thumb points in the direction of n vector, and the fingers curl along the orientation of the bounding curve C.

Figure 2: Right-hand Rule. 
Figure 3: Right-hand Rule showing cross product of vectors.


Bodily experiences can also be used in group activities to learn about a mathematical idea. Knot theory for example is the study of closed curves in 3D and their possible deformations without cutting through another knot. Students can form a “human knot” by linking their arms and work together to unknot themselves. Group activities like this is often very engaging and sparks communication and discussions in the classroom.


Reading:

Henderson, D.W., Taimina, D. n.d. Experiencing meanings in geometry. Mathematics and the Aesthetic. Pp. 58-83


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