The Author of this paper has developed a Tangram based upon the Golden Ratio. This introduction to the tiling properties of the Golden Tangram focuses upon the property called Preciousness and a Matrix called the Precious Matrix. It includes a discussion of some of the convex polygons that can be created and their non periodic tessellating patterns. It continues with examples of the unique way in which they can produce an infinite number of tiling patterns. It explains the iterative nature of the process as applied to designs for Mosaics and Quilts.