Abstract. Geometer Mark Reynolds demonstrates the use of an ancient system for new ways of thinking and seeing: on the triple square and the diagonal of the Golden Section.

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The Geometer's Angle No. 7:
On the Triple Square and the Diagonal of the Golden Section

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CONCLUSION
Here we have a demonstration of using ancient systems for new ways of thinking and seeing. Part of my own pleasure was in finding that through all the irrational numbers and creative energy being put into the system, it generated the triple square, an elegant and beautiful rational system. It is also a good demonstration of how geometry builds things. Through the interplay of the static and dynamic elements of the grid, and the creative actions taken to rearrange and recombine them, the possibilities seem limitless. The eternal question for me remains: What is the force that initiates and enables geometry to build in such elegant and endless ways in nature?

In the Summer issue, I would like to look at a couple of irrational polygons, the 11-gon, the 13-gon, and the rational 15-gon and the golden section of a circle, all from the Square Root 2 rectangle system!

Happy Spring! Go look at the Geometry of Spring things, from the fields to the vegetable stands, from Mount Tamalpais to the Apennines.

Beginning of article | back to Step 11 | Conclusion

 The correct citation for this article is:
Mark A. Reynolds, "On the Triple Square and the Diagonal of the Golden Section", Nexus Network Journal, vol. 4, no. 2 (Spring 2002), http://www.nexusjournal.com/GA-v4n2.html

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