An Introduction to the Golden Tangram and its Tiling Properties

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Stanley Spencer: An Introduction to the Golden Tangram and its Tiling Properties. In: Bridges 2005. Pages 31–36



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.

Extended Abstract


Used References

[1] Spencer, Stanley J, The Tangram Route to Infinity ISBN 141202917-1

[2] Mathematical Connections in Art, Music and Science. Bridges Conference 2004 ISBN 0-9665201-5-7.

[3] Tangrams, (Accessed 6.12.2003)<>

[4] Spencer, Stanley J (Accessed 6.12.2003)<>

[5] Meeting Alhambra. ISAMA-Bridges 2003 Conference Proceedings ISBN 84-930669-1-5

[6] Fu Traing Wang and Chuan-Chih Hsiung A Theorem on the Tangram. American Mathematical Monthly, vol. 49, 1942

[7] Steven Dutch Rep-Tiles (Accessed 1.4.2004)

[8] Solomon W Golomb, Polynomials Puzzles, Patterns, Problems, and Packings, pg. 8, Appendix C, Pg 148, Princeton University Press, 2nd edition, 1994.

[9] Jay Bonner, Three Traditions of Self Similarity in 14th and 15th Century Islamic Geometric Ornament, Meeting Alhambra, ISAMA Bridges Conference Proceedings 2003, ISBN 84-930669-1-5.


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