One advantage that the ancients did have over us is that they were not mentally trapped within a decimal-style mindset. When it came to number patterns, it was natural for them to think in terms of special geometric properties that a particular number may or may not enjoy. For example, numbers such as 10 and 15 are triangular, something that is visible to us through the triangle of pins in ten-pin bowling and the triangular rack of fiteen red balls in snooker. But this is not something that comes to mind from the base ten displays of these numbers alone. The freedom the ancients enjoyed by default we can recapture by casting aside our base ten prejudices and telling ourselves that we are free to think of numbers in quite different ways.