Correction to: Scientific Reports https://doi.org/10.1038/s41598-021-84310-w, published online 12 March 2021


This original version of this Article contained repeated errors, where the Greek character ϒ (Upsilon) was incorrectly given as Ψ (Psi) and fractions were incorrectly shown as superscripts.


As a result, in the “Period relations and ancient Greek theories” section,


“Then came a notable discovery in 2016 in the FCI12: unexpected numbers ΨΞΒ (462) in the Venus section of the FCI and ΨMΒ (442) in the Saturn section, translating into highly accurate period relations: for Venus (289462) and Saturn (427442) (Fig. 1b, Supplementary Fig. S4)”


now reads:


“Then came a notable discovery in 2016 in the FCI12: unexpected numbers ϒΞΒ (462) in the Venus section of the FCI and ϒΜΒ (442) in the Saturn section, translating into highly accurate period relations: for Venus (289462) and Saturn (427442) (Fig. 1b, Supplementary Fig. S4)”


In the legend of Fig. 1,


“The numbers ΨΞΒ (462) in the Venus section and ΨMΒ (442) in the Saturn section are highlighted12 (Supplementary Fig. S4).”


now reads:


“The numbers ϒΞΒ (462) in the Venus section and ϒΜΒ (442) in the Saturn section are highlighted12 (Supplementary Fig. S4).”


In the “Theoretical mechanisms for our model” section,


“A rotation of -12/223 for the Line of Nodes, derived from the Metonic and Saros cycles9, could not be mechanized because of the large prime 223. We show that a simpler ratio -5/93, with a more accurate period of 18.6 years14, can be calculated by a 4-gear epicyclic train (Fig. 3a, Supplementary Figs. S21, S22).”


now reads:


“A rotation of  \(- \frac{12}{223}\) for the Line of Nodes, derived from the Metonic and Saros cycles9, could not be mechanized because of the large prime 223. We show that a simpler ratio \(- \frac{5}{93}\) , with a more accurate period of 18.6 years14, can be calculated by a 4-gear epicyclic train (Fig. 3a, Supplementary Figs. S21, S22).”


Lastly, in the Supplementary Information 4 file, the legend for Supplementary Fig. S4,


“The numbers ΨΞΒ (462) in Line 6 and ΨMΒ (442) in Line 33 are highlighted in red.”


now reads:


“The numbers ϒΞΒ (462) in Line 6 and ϒΜΒ (442) in Line 33 are highlighted in red.”


The original Supplementary Information 4 file is provided below.


The original Article and accompanying Supplementary Information 4 file have been corrected.