The Sequence of Carboncettus Octagons

  • Fabio CaldarolaEmail author
  • Gianfranco d’Atri
  • Mario Maiolo
  • Giuseppe Pirillo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11973)


Considering the classic Fibonacci sequence, we present in this paper a geometric sequence attached to it, where the word “geometric” must be understood in a literal sense: for every Fibonacci number \(F_n\) we will in fact construct an octagon \(C_n\) that we will call the n-th Carboncettus octagon, and in this way we obtain a new sequence \(\big \{C_n \big \}_{n}\) consisting not of numbers but of geometric objects. The idea of this sequence draws inspiration from far away, and in particular from a portal visible today in the Cathedral of Prato, supposed work of Carboncettus marmorarius, and even dating back to the century before that of the writing of the Liber Abaci by Leonardo Pisano called Fibonacci (AD 1202). It is also very important to note that, if other future evidences will be found in support to the historical effectiveness of a Carboncettus-like construction, this would mean that Fibonacci numbers were known and used well before 1202. After the presentation of the sequence \(\big \{C_n\big \}_{n}\), we will give some numerical examples about the metric characteristics of the first few Carboncettus octagons, and we will also begin to discuss some general and peculiar properties of the new sequence.


Fibonacci numbers Golden ratio Irrational numbers Isogonal polygons Plane geometric constructions 



This work is partially supported by the research projects “IoT&B, Internet of Things and Blockchain”, CUP J48C17000230006, POR Calabria FESR-FSE 2014–2020.


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Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversità della CalabriaArcavacata di RendeItaly
  2. 2.Department of Environmental and Chemical Engineering (DIATIC)Università della CalabriaArcavacata di RendeItaly
  3. 3.Department of Mathematics and Computer Science U. DiniUniversity of FlorenceFirenzeItaly

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