A family in a village outside Samarkand had a square vegetable garden and, one spring, the room to make it bigger. The land to the east allowed three more metres; the land to the north allowed five.
The father, who had built walls all his life, drew the new garden in the dust with a stick, and what he drew was not one rectangle but four pieces, not two.
There is the old square, unchanged. There is a long strip three metres wide running down the eastern side. There is a second strip five metres deep along the northern edge. And there, in the top corner where the two extensions meet, is a small rectangle three metres by five — fifteen square metres that belongs to neither strip.
That corner is the whole point of the drawing. It is the piece people leave out when they multiply in their heads, and it is easy to forget precisely because nobody walked through it before.
The numbers came later. The old garden had been ten metres on a side, so it held one hundred square metres. The eastern strip added thirty, the northern one fifty, and the corner fifteen: one hundred and ninety-five square metres in all.
His daughter, who was doing algebra at school, measured the finished garden instead — thirteen metres by fifteen — and multiplied. She got one hundred and ninety-five as well, and spent the walk home working out why the two methods could not disagree.