I’ll start this post with a quote from the Statutory Guidance: National Curriculum for England: Mathematics Programmes of Study: Purpose of study for maths.
“A high-quality maths education therefore provides … an appreciation of the beauty and power of mathematics…”
My granddaughter Elin showed me this as she thought I’d find it interesting. She has a degree in Maths and Music and later this year is going to study for a PGCE; she plans to become a Maths teacher in a secondary school. We agreed that the power and beauty of music is evident, it works its magic on everyone from infancy, but that helping children to appreciate the power and beauty of maths is more of a challenge. I don’t remember that my maths lessons at school gave me this appreciation.
Years later though, I read The Curves of Life, which is an account of spiral formations and their application to growth in nature, science, and art, written by Theodore Andrea Cook in 1914 and illustrated with many photographs. Cook writes that “I shall not be more mathematical than I can possibly help” and geometrical drawings are more prominent than equations. The Curves of Life made it easier for me to appreciate the mathematical power and beauty of spirals, from the shells of the common snail to the arms of a galaxy, the horns of the greater kudu or the twists of the umbilical cord. I didn’t understand the maths any better than when I was young, but I felt the power of maths in exploring the beautiful forms of the natural world.
So now I see the distance between maths and moths as a short stretch, the distance a tiny caterpillar of a Geometer moth might travel in one move. The caterpillars, known as inchworms, travel by stretching forward, anchoring their front legs and then moving the back legs forward, giving the impression that the caterpillar is measuring the distance as it moves along. You can see inchworms at https://animalsake.com/facts-about-inchworms-you-probably-didnt-know
The Geometer family includes many species, see some British species at https://ukmoths.org.uk/thumbnails/geometridae
THE HEAVENLY GEOMETER
And the caterpillar said
I am the inchworm, the measurer,
Look at the way I move -
I hold fast with my back legs
while I advance my supple body
to grasp the future with my front legs.
I let go and heave myself forward into a curve
that mirrors a graph of the height of Manchester men
or the wing spread of Mandarin ducks.
See how I flatten myself,
to rule on the span of each leaf.
Watch me when I hang
on a thread of silk that measures the height
from the last leaf I chose to the ground below.
But this isn’t the end of my surprises
I’ll lie buried in dirt then fly up transformed
into a perfect geometer
with angelic wings.
I fly in the formidable storm of moths
that scrawl though the evenings of the world,
look at our pigments and iridescent shadings;
to give you an inkling
flag our names, large emerald, mottled umber,
argent and sable, coppery dysphania.
Don’t ever think we’re just aerial flotsam
floundering in the dusk -
our wings, scalloped, indented,
curved, angled or swallow tailed,
are inscribed with geometry
that Euclid would have gazed at in wonder:
graphical zig zags,
curves that duplicate maps of islands and bays,
trace segments of spheres,
delineate waves, copy windblown clouds.
Marvel at my patterns
for my wings are signed with cryptic configurations
that you’ll never decipher,
for I am the Geometer that measures out the world
I span the universe and mark each curve and angle
throughout the cosmos.