The Bowl of Integers and the Hexlet

INTO a hollow sphere of unit radius, with a curva-ture or bend, therefore, 1, put two solid spheres of radius, or bend + 2. The two solid spheres then kiss each other at the exact centre of the bowl, and kiss the latter at the extremities of its diameter through all three centres, no other disposition being theoretically possible. This three-sphere assembly may be termed the ‘bowl of integers', since it has the unique property that the bend of every sphere of the infinitely infinit © number of spheres that theoretically can be packed into it, so that each is located by its neighbours, is an exact integer which can be written down at once from those of its neighbours. It enables the nature of the ‘hexlet’ to be elucidated without either trigonometry or the algebra of irrationals.