Once upon a time, in a land far, far away, a little girl sat one dark and stormy night paging through her father’s math teaching manual and discovered the most exquisite picture.
“Father,” she cried, “I have found the most lovely thing! What is it?”
Her kindly father peered over the child’s shoulder and, smiling, replied, “My dear girl, it is the representation of a most intriguing number, a useful ratio of ancient origin – dating back even before the days of wise Pythagoras and the great Archimedes. The number is called pi and the picture you so ardently admire, its symbol.
The child returned her gaze to the page, running a tiny finger along the outline of the figure. After a pause of some moment – an eternity in child-time – the girl raised her eyes once more and declared, “I love pi.”
During the following months, the little girl painstakingly traced the numbers “3.14” upon paper, and crowned her modest achievements in crayon with the curvaceous legs and head of a most wondrous figure. Her indulgent parents looked upon these scrawls and smiled. “It is small, like me,” she laughed, “and yet brings me such joy.”
After some time, the girl’s appetite for greater knowledge arose again. “Mother,” she said, “what does pi represent?”
Her young mother, though careworn from a day of work and caring for her family, sat down with the girl and pondered. A thoughtful look wrinkled her forehead momentarily, and then she said, “Child, pi is the constant for a circle. God gave us the gift of our minds, that we might derive pi, and gain some understanding of the universe, and so find comfort and reason out of the darkness.”
The child was pensive, puzzled by these words, and by the image of her precious symbol glowing as a beacon in the night. “It is small, like me,” she said, “and yet it is a mystery.” And she treasured this mystery in her heart.
Many months passed, and soon the girl entered school. Her mind was diverted by new playmates, and knowledge of great things. She learned of lands beyond the ocean, of lovely words that express a thought ever so well, and of numbers to the left of zero. She learned the games played in a schoolyard, and how to tie knots, and why it is important to brush one’s teeth. She learned of trees which are green and full in the spring, and become gray and bare in the winter. All manner of things lay before her, and she wished to consume it all. Yet, at night as she lay in bed near sleep, the image of pi crept into her dreams.
As will happen with little girls, the child grew into a big girl. Though still small in stature, her mind absorbed new and wonderful things, and she discovered an ability for athletics. Afternoons and evenings were dedicated to homework, or tennis, or basketball. She gained great strength and a passion for reading. Her wonder in numbers, however, did not cease but increased, and she developed an affinity for algebra. She found herself endlessly entertained by the challenge of solving equations, and often she became oblivious to the day’s end while examining increasingly complex expressions.
One day, after having scored particularly well on an exam, the girl stayed behind after her classmates left for lunch and, timidly approaching the old algebra teacher, asked, “Can you tell me about pi?”
The old man’s eyes twinkled, and his moustache twitched into a grin. “Why yes, I can,” he replied. “It is a key component in equations of a circle, a precise constant relationship between the diameter of a circle and its circumference. It is fascinating because while it is constant, it’s a ratio very difficult to express. We roughly say, pi is 3.14159, yet truly the number extends wells past 5 decimal places!”
The girl listened intently and, after politely thanking the old teacher, walked out of the room, musing. “It is small, like me,” she thought, “and yet it has great depth.”
Years passed, and the girl grew into a young woman. Her education included trigometry, and world literature, and biology, and chemistry. Along the way she encountered all manner of symbols: integrals, logarithms, imaginary numbers. Some were intriguing, and some quite tame, others were useful and still more were forgetable. And none became quite so dear to her as the representation for pi.
With childhood now behind, and her formal education completed, the young woman entered into the cares associated with adulthood. Bits of the outside world began to assert themselves into her life, and gradually she became busy with work, friends, marriage and home. At the end of a wearying day, a cup of tea in hand, sat at the kitchen table with paper and pencil in hand, and the cares of the day danced out of her mind as she created number games. Ever so frequently, when deep in thought, her hands absently drew the poetic figure pi.
One such evening her husband sat down at the table, and as she worked her problems, read a book. A companionable silence ensued, until she impulsively laid her pencil aside and asked him, “Tell me, dearest, what does pi signify to you?”
He paused for several moments, staring down at the tabletop in deep thought then, raising his eyes to hers, replied, “I had never much thought of pi, except as a particular symbol in math. But now that I consider it, I recall it is also the 16th letter of the Greek alphabet.”
And with a smile she said, “It is small, like me, but significant.”
And we might think that in the passage of time and the growing complexities of adulthood the thought of this figure might have melted from her mind, replaced by thoughts of children and bills and what to cook for dinner. Yet, the thought persisted. In time she bought herself a box of paints and, as she had done in crayon as a small child, she painted the figure over and over at the kitchen table. The use of a brush was unfamiliar and awkward, but after much practice she finally crafted a version of the symbol which filled her with contentment.
“Yes, yes, this will do!” she said. And she laughed to herself in secret pleasure at a thought she had formed in her mind.
For then came a dark and stormy afternoon, when she rested her chest against a pillow propped upon a chair, and an artist of great skill etched the precious symbol in ink upon her shoulder. After washing the area with salve, he beckoned her to a mirror where she might see her reflected back.
She smiled broadly. “It is small, like me, and it is beautiful.”