Kind of an interesting problem, and it's been a long time since I've done much statics, so I'm not 100% sure on this one. However, I think this is what's going on.
In the stock setup, there is one pulley for the jib halyard up at the hounds. Therefore the tension on the halyard is constant everywhere (negating friction). So the tension along the luff equals the tension running vertically down the mast to the cleat. Assume this is 600lb. The mast compression resulting from halyard tension is then the sum of these two component forces acting along the axis of the mast. So it would be 600lb (vertical component of halyard running down to the cleat) + 600lb x cos a (tension along luff wire) where a = the angle between the jib luff and the mast. If we assume a=30 degrees then the mast compression due to the stock jib halyard equals 600lb + 519lb = 1119lb.
With the Aussie setup, the tension along the luff remains the same, however the tension running down the mast is reduced to 1/3 the luff tension due to the 3:1 purchase up at the hounds. Therefore given the same 600lb luff tension the resulting mast compression due to the jib halyard is 200lb + 519lb = 719lb or a 35% reduction in mast compression.
Keep in mind however that we are only looking at mast compression induced by jib halyard tension. In reality, there are several other factors that influece mast compression, namely downhaul tension, shroud loading, and trapeze loading. These are all going to add hundreds of additional pounds of compression on the mast. So while there is a reduction in mast compression from using the aussie system, it's pretty minimal - certainly much less than the 66% claimed by the advertising.
PS: It's more about physics than geometry.
PPS: Physics, geometry, and trigonometry are all interrelated. You can't solve a physics problem without having a solid understanding of geometry and trig.