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Prehistoric Europe

Fibonacci Numbers in Cucuteni Culture

by Christian Horgos, 25 October 2023

The Cucuteni culture existed in the Neolithic farmer world of 'Old Europe' some six or seven millennia ago. Did its people manage to estimate the complexity of those tasks which were connected to ploughing, sowing, or reaping in storypoints which were based on Fibonacci numbers?

Not likely!

However, Fibonacci numbers can apparently be found in connection with several Cucuteni archaeological sites across its home in today's Romania.

Fibonacci numbers were first described in Indian mathematics as early as 200 BC, some two thousand eight hundred years after the disappearance of the Cucuteni.

They reappeared in western culture only in AD 1200 when the Italian mathematician, Fibonacci, rediscovered them for himself.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89...

The Fibonacci sequence is one of the most remarkable mathematical sequences to be known today, but it is also present in the living world.

It can be recognised in the pattern of the branches of some species of tree, in the arrangement of pineapple fruit and pine seeds, or in the inflorescence of artichokes and sunflowers, as well as in many other ways.

Moreover, in work which was published by Luke Hutchinson in 2004 under the title Growing the Family Tree: The Power of DNA in Reconstructing Family Relationship (reproduced in the Proceedings of the First Symposium on Bioinformatics and Biotechnology BIOT-04), a method of chromosomal calculation is highlighted which is also based on the Fibonacci sequence.

The sequence which bears the name of the Italian mathematician, Fibonacci, who documented it in AD 1202 was also known by the Indian mathematician and poet, Acharya Pingala, who was active around the third or second centuries BC (precisely when is unclear).

Cucuteni culture finds from Isaiia
The 'Council of the Goddesses' from the Isaiia site in today's Romania includes thirteen thrones, twenty-one female statuettes, twenty-one stylised cult objects in the form of phalluses, and forty-two beads (caryopes)

Leonardo Pisano Fibonacci

Leonardo Pisano Fibonacci, noted Italian mathematician who introduced Arabic numerals to medieval Europe


Even more remarkable is the fact that non-trivial numbers from the Fibonacci sequence are found in representative Cucuteni settlements which are between six to seven millennia old.

This involves a hypothesis which states that, in Neolithic culture, the elements of worship were intertwined with the 'magic' of Fibonacci numbers.

The 'Council of the Goddesses' (or 'Soborul Zeitelor') from the commune of Poduri, Dealul Ghindaru, in today's Romanian Bacău county, includes thirteen thrones of burnt clay and twenty-one statuettes (fifteen of which are larger in size while six are smaller).

Moreover, the 'Council of the Goddesses' from the Isaiia site (in Iași county) includes thirteen thrones, twenty-one female statuettes, twenty-one stylised cult objects in the form of phalluses, and forty-two beads (caryopes). This all helps to distinguish the Fibonacci numbers of 13, 21, and 55, with the last of those as a sum between 13 and 42.

The 'Holy Family' grouping (or 'Sfanta Familie'), also from Isaiia, includes seven anthropomorphic statuettes, plus one throne, with a total Fibonacci figure of eight.

Cucuteni culture also extended over what today is the southern region of Ukraine, with the result being that it is attached to the sister culture there to form the cojoined Cucuteni-Tripolye culture.

An example of the Fibonacci number 21 is noted in the Nebelivka mega-site.

The Thinker Sculpture of the Hamangia Culture
The Cucuteni-Tripolye culture developed on plains around the Carpathian Mountains - continuing into eastern Romania and south-western Ukraine, with both areas having extremely fertile soil - and the culture was next door to the Hamangia, which produced artistic marvels such as 'The Thinker', dated to around 4000 BC (click or tap on image to view full sized)


In an article by Gaydarska, Nebbia, and Chapman we find the following paragraph: 'The most striking collective find was the group of twenty-one miniature vessels, with six vessels showing the first examples of graphite painted decorations'.

It is possible that archaeologists and cataloguers of museum collections who have specialised in Cucuteni culture still know of such examples, or vice versa.

It should also be noted that Fibonacci numbers do not dominate the entire landscape of Cucuteni culture, a counterexample being the 'Hora de la Frumușica' which was discovered in Bodeștii de Jos (Romania's Neamț county), which includes six female silhouettes.

As a matter of additional curiosity, the Fibonacci sequence is the solution to the old pastoral riddle regarding the number of millets which accumulate in ten years, starting from a single millet and knowing that each millet annually gives 'birth' to another millet, but also in regard to a young millet not giving 'birth' in the second year of its life but only starting in the third.

 

Main Sources

Luke Hutchinson - Growing the Family Tree: The Power of DNA in Reconstructing Family Relationship (2004, reproduced in the Proceedings of the First Symposium on Bioinformatics and Biotechnology BIOT-04)

Online Sources

Bisserka Gaydarska , Marco Nebbia, & John Chapman - Trypillia Megasites in Context (Cambridge University Press, 2019)

Maths is Fun website

 

 

     
Images and text copyright © Christian Horgos. An original feature for the History Files.