Black fine-line tattoo of a unit circle diagram with labelled axes above the equation e^(iπ)+1=0, across the upper back.

Enlarged with AI from a smaller original

Euler's formula and unit circle on upper back

Fine line · Back · Black and grey · Photo

A black ink tattoo across the upper back shows a unit circle diagram with labelled Re and Im axes, angle markers and small handwritten style labels for cos φ and sin φ, with the equation e^(iπ)+1=0 beneath it. The linework is thin and even, with the circle, axes and lettering drawn in a clean, precise style. The tattoo sits centrally on bare skin against a grey draped garment, with foliage softly blurred in the background.

Fine line Back Circle Axe

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A story inspired by this tattoo · fiction

By eleven the rain had got into every book on my trestle, so the cardboard boxes sagged and the spines of the maths texts bloomed like mushrooms. Dad always said never sell a book you haven't read the first page of. I hadn't read the first page of the fat green Complex Analysis at the back, which is how I found the notebook tucked inside its cover, damp at one corner and smelling of pipe tobacco.

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Inside, in careful pencil, someone had drawn a circle with two crossing lines, labelled the flat one Re and the upright one Im, and marked a small angle with a curl of arc. Beside it, in a schoolmaster's hand, ran a line I could half follow: cos φ plus i sin φ. The last page held the equation I had once seen on a mug in a shop in Colchester, e to the iπ plus one equals zero, underlined twice. Under it he had written, Ask Ruth. She will say it is only going round.

Ruth Parr came on the Saturday after, in a grey coat with the hood up, and stood at my trestle the way people stand at a bus stop they have given up on. She didn't want a book. She turned the notebook over in her hands for a long time before she spoke. 'Edwin used to say that if you walk the circle all the way round, you come back exactly where you began. But halfway, at the bottom of the turn, you are pointing the opposite way from where you started. He thought that was the cleverest thing anyone had ever got to with a pencil.'

She opened to the page with the circle and ran her thumb along the arc, slowly, the way you might trace a scar that has healed well. The rain had stopped for once. 'He never finished the last bit,' she said. 'He always stopped at minus one and laughed.' She tucked the notebook under her coat and walked out past the fishmonger, and I watched the hood grow smaller until it was just one more grey shape turning at the end of the lane.