He had two families: the Appelbaums and the Bergquists. Privately, he referred to them as Family A and Family B. Family A had members {Mom, Stepdad, Tryg, Natalie, Isabel}. Family B had members {Dad, Stepmom, Tryg, Elliott, Parker}. They were separate families, but together they were his family, A ∪ B, {Mom, Stepdad, Dad, Stepmom, Tryg, Natalie, Isabel, Elliott, Parker}. He was the only member of both sets, the only intersection, A ∩ B, {Tryg}. That was what defined him. He had the largest family out of anyone, and was the most alone.

His sisters (half-sisters technically), shy red-haired girls whose faces and limbs were spotted with freckles, were perched on the window seat. The breeze coming through the bay window rustled their clothing, checkered blouses and khaki shorts. Natalie’s body < Isabel’s body, yet, oddly, Natalie’s head > Isabel’s head. They had been passing the time until dinner looking at puzzle books with hidden objects in the illustrations. They set the puzzle books aside, drawing their knees up to their chins, wearing concerned expressions.

If the city was graphed, using miles for coordinates, with the axes expanding from an origin downtown, his mother lived at (−1.2, +3.1), his father lived at (+1.3, −3.4). That is, north-northwest, south-southeast. Per the visitation arrangement, he spent [Monday, Friday] with his mother and [Friday, Monday] with his father.

Lately, in his leisure reading, he had been studying ratios. Ratios were about relationships. Relationships between numbers. There was a certain ratio, known as the golden mean, that especially captivated him. The golden mean often appeared in nature: the branches of trees, the curves of shells, the scales of pineapples, the seeds of sunflowers, the spirals of genomes, the dimensions of bones, the bodies of galaxies, the trajectory of falcons, the ancestry of bees. It had been used in the design of drawings and photographs and paintings and sculptures. It was considered the most beautiful proportion in the universe. Expressed numerically, its first nine digits were 1.61803398.

Reaching for the handle of the door, he suddenly thought to calculate something. When he did, the result was staggering. Between weekdays with his mother, weekends with his father, alternating holidays, and periodic vacations, the time he spent with his families roughly approximated the golden mean. On average, 4.3 days per week with Family A, 2.7 days per week with Family B.

If that were true, shouldn’t the situation have seemed beautiful, instead of so ugly?

Tryg was in-between age-wise—not quite child, not yet teenager—a pudgy, clumsy, nervous creature who routinely slaughtered standardized tests. He was taking calculus at a high school. He counted everything, instinctively, avoided doing anything in uneven numbers, obsessively, and, from memory, could recite the first hundred decimals of π. His only serious crush was on ∞. His sense of fashion was logical to a fault, favoring comfort over style, loose sweatshirts and baggy slacks, shoe inserts for arch support. He read mathematics journals for recreation.