The focus on perception, with vision assisted by touch and other senses to play with the
objects to discover their properties, leads to a growing sense of space and shape,
developing through the use of physical tools—ruler, compass, drawing pins, thread—
to enable the child to explore geometric ideas in two and three dimensions, and on to the
mental construction of a perfect platonic world of Euclidean geometry. The focus on
the essential qualities of points having location but no size, straight lines having no
width but arbitrary extensions and on to figures made up using these qualities leads
the human mind to construct mental entities with these essential properties. Platonism is
a natural long-term construction of the enquiring human mind.