Theological Mathematics
"The mathematics of the Trinity doesn’t make sense. How can three be one? But that’s the trouble with trying to understand the triune God by mathematics–He can’t be reduced to a formula." –unknown
Little Minds Trying to Understand a Big God
"The first thing the doctrine of the Trinity says to us is that there are some things in life too big for us to get into our little skulls." –unknown
My idea
The best illustrations I (Keith) use are
1×1x1=1 (Each 1 has equal value, is distinct from the other ones and still produces a total of 1) obviously there are problems with this illustration, but it gets some of the point across.
I ask the person to imagine a cup of hot boiling water with an ice cube in it. Only it is a bit special. The ice cube doesn’t melt and the water never cools.
In this cup: liquid, ice and steam but all are made of water. (Again the problem of metaphor is that it never quite matches the thing you are trying to explain. Thank you Tower of Babel of destroying any chance of adequately explaining the idea, even to ourselves)