It’s all a game….maths is a game played in the mind. All of maths is perfectly pure, it has only an isomorphic relationship with the real world. Isomorphic means of similar form. The real world applications are reduced and imperfect versions of the pure ideas. Sometimes the ideas that can be thought of have no corollary in the ‘real’ world. An example of this is the square root of minus one. It is actually very useful in certain calculations and the results however certainly can be of practical significance.
What you see when you make a pattern of rods or put any rod down is up to you. If you are relatively unconditioned you are free to see more possibilities. This is an important attribute of the perceiver. Part of the teacher’s role is to allow this to be. To allow the perceiver to be free to perceive and then to conceive.