Of Pegs and Holes, of Circles, Squares and Other Shapes

Of Pegs and Holes, of Circles, Squares and Other Shapes     —by Jinny Batterson

Geometry has never been my strong suit.  Shapes don’t register with me as intensely as words or colors or numbers or images. Formulas for calculating areas and proofs of geometric theorems quickly fade from my memory as soon as I’m no longer required to regurgitate them on tests. Still, I do notice squares and circles, which tend to dominate our man-made and natural landscapes, respectively. 

Since childhood, I’ve been intrigued by expressions about “square pegs in round holes.”  A real-life square/round anomaly from the U.S. space program was recreated in the film “Apollo 13.”  (https://www.youtube.com/watch?v=C2YZnTL596Q)  A potentially lethal problem developed with the space module’s air filtration system, and ground-based engineers had to quickly come up with a way to retrofit it by linking a square peg and a round hole. Though I lack the technical skills of the NASA engineers who helped bring Apollo 13 safely back to earth, my spacial imagination sometimes plays through various scenarios of adapting pegs and/or holes so there are ways to get the two together.

Squares fit into a more general category of “polygon,”  “a plane figure with at least three straight sides and angles, and typically five or more.”  So my rarely-satisfied-with-either-or-solutions brain starts adding more and more sides to an initial square, trying to imagine whether a very large number of sides can approximate a circle. As long as there are discrete angles, a requirement for a polygon, the fit is not perfect, but it comes closer and closer. 

My most vivid real-life experience of varying shapes came during a glorious summer of working at Expo 67, a world’s fair held in Montreal, Quebec, Canada from late April through late October of 1967. (A 50th anniversary retrospective of the fair and impressions of people who visited it in our youth will be held in Montreal this summer.) Although some exhibition halls were based on four-sided structures, others had many different shapes, among them the nearly spherical geodesic dome that housed the U.S. pavilion. It was designed by architect and futurist Buckminster Fuller, with a surface of interlocking triangles, hundreds of them. Fuller discovered that if a nearly spherical structure was created from triangles, it would have unparalleled strength. It could also “do more with less.” Such a sphere encloses the largest volume of interior space with the least amount of surface area, thus saving on materials and cost. Nearly 300,000 geodesic structures have been built worldwide, in widely varying locations and climates.

Nature rarely builds in squares. The only example that comes readily to mind is salt crystals, which usually require a microscope to validate their squareness. Certain rare rushes also seem to be endowed with square stems, but most of what we observe in the natural world tends to roundness.  While noodling around for roundness examples, I did an online search for “Why are tree trunks round?” (originally posed by the parent of a 4-year-old) and found this naturalist’s response:

“Living things adapt to the environment around them, or at least they do if they wish to go on being living things.

Trees tend to spend a lot of time outside and so they adapt to their surroundings.

A round or tubular shape allows them to resist the force of the wind better than the flat surface of a square or rectangle would.

Not only does its round shape help resist the wind, but it also is a very strong shape that helps support a lot of branches.

And it’s a matter of protection. With the exception of beavers and maybe woodpeckers or some bugs, it’s hard for most animals to get a good bite on a round shape. There aren’t any corners to get a start on.”  (www.azcentral.com/story/opinion/op-ed/claythompson/…trees-round/82917948/)

So please, take an occasional break from your squarish computer or smart-phone screen and instead take a look at your surroundings, maybe even venture outside—it can help make you a better rounded human. 

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