2013/08/27 by Carlos Roberto da Silveira, Carlos Silveira, Silveira, Carlos
Materials Science · Mathematics · Physics and Astronomy · #11Z99 #51M99 #Advanced Mathematical Theories and Applications #FOS: Mathematics #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Number Theory (math.NT) #Quasicrystal Structures and Properties #math.MG #math.NT #msc:11Z99 #msc:51M99
paper · pdf · doi:10.48550/arxiv.1308.5941
12 pages, 5 figures
arxiv created 2013/08/27 · openalex publication_date 2013/08/27 · arxiv updated 2013/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We have extended some known results of the approximate golden spirals to generalized m-spirals built with whirling squares for any m ratio (m>1). In particular, we have proved that circumscribed circles around squares intercept the pole. This implies that poles of any m-spirals lie on a circumscribed circle about the first square. We show here that these and other fascinating properties are not exclusive of golden rectangles. The classical golden constructors may not be alone.