Nefer sat in the shade of a yellow-green willow, tracing shapes in the sand at her feet with a piece of dry reed. She had been interested in shapes for days now, ever since the full moon festival, and was busily engaged in the process of constructing straight lines.

It had started when she had noticed that tall grass trailing in the desert sand would trace little circles, like outlines of the moon she thought, as the wind blew them around and around. Now, she could make circles for herself with a tightly twisted line of hemp cord and a stick stuck in the ground. She was concerned over how to fit circles inside squares, and how long her string would need to be to make a circle fit exactly inside a square she had already constructed: something about the idea seemed innately pleasing to her. Consequently, her mind had run off over a series of interesting ideas, all of which she had endeavoured to construct on the floor before her in scratches in the sand. Now, she wanted to know how long the diagonal line drawn between two corners of a square would need to be. It shouldn’t be hard to figure out, but it was, and she stuck her tongue out of her mouth slightly in irritation at the concepts which wouldn’t quite evenly stack up.

She looked at what she had drawn; a square of four nicely neat lines (she had invented the idea of the straight line when she stretched that hempen cord taut to construct her first circle, and the right-angle had shortly followed) with a straight line like a stiff snake stretching from the bottom left corner to the top right. She wondered if she could make it more regular if she added another, so, with a deft swoop of her hand (she imagined she was drawing along a reed as perfectly straight as the stretched cord, although she actually accomplished this stroke by muscle alone), she drew another straight line from the bottom right to the top left. The two snakes met in the middle of their bellies, each seeking to hide its face in the right angle.

Now there was a point in the middle of the square, and Nefer imagined constructing another, smaller square around it, and wondered how to make it exactly half the size of the original square. But, as she was looking, the shape seemed to hurt her eyes, and she squinted, instinctively shading her eyes with her hand, as though the picture she had drawn was reflecting the bright glare of the sun, who was actually floating safely far away in the ripples of the Nile.

“That’s interesting,” she thought, looking as straight at the miracle as she could. “I expect you could actually make that if you had enough square, flat things. You would only have to use fewer every time, piling them up evenly, taking one layer away from every side as you went. Maybe you could put a nice layer of smooth mud over the top to make it even.”

She shook her head to herself at the impenetrability of these curious shapes she had invented. Over at the camp, the boys were fighting. She wondered if she should tell them about it.