Stone Silver Gold and Wood Riddle

Looking for the answer to the riddle called stone silver gold and wood riddle. Here is the answer and my thoughts on the riddle below.

This is like the the Chocolate bar trick where you cut it up and remove one piece and when reassembled makes it look like it didn’t reduce in size.

To get the limit solution:

(1) Start with a rectangle with an aspect ratio of phi^2 to 1 (2.618:1).

(2) Cut the rectangle along the diagonal, so you end up with 2 congruent triangles with the same aspect ratio.

(3) Lay the triangles one on top of the another and align them so they appear as one triangle.

(4) On the longer side of the triangles, mark a perpendicular line at phi^-1 (0.618) of the way in.

(5) Cut the triangles along the marked line.

(6) Rearrange the resulting triangles and trapezoids into a square. In the limit case, you should not have any excess or missing material.

Another way to think about it that only requires elemental geometry is that in the point where the 3 unit length side of the trapezoid intersects with the triangle, the triangle is less than 3 units tall because the side of the triangle is 3 units.