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Task 6.2 : The octagonal formula


2016.1 - c 

(EN) A mathematics teacher of Chinon, Mrs Françoise Jacot did describe in her words the construction process for our octagonal formula. it's a great job already.

(FR) Un professeur de mathématiques de Chinon, Madame Françoise Jacot a fait de décrire avec ses mots le procédé de construction du bras octogonal pour notre formule de l'octogonal. c'est un déja grand travail.

PDF file :


 Procédé de construction du bras octogonal.png

 2016.1 - d

(FR) Un professeur de mathématiques de Chinon, Françoise Jadot a fait un démo de la formule de l'octogonal. C'est très intéressant. Jetez un oeil ci-dessous SVP!   Merci bien!

(EN) A mathematics teacher of Chinon, Françoise Jadot made a demo of the octagonaral formula with GeoGebra. It's very interesting! Please take a look following!  Thank you!


2016.1 - e

Our octagonal formula now is alive and very happy with the math teacher. She explains that this is similar with the Cardoid curve. Henceforth she is a director of the formula!


The formula of the voluntary movement that we have seen was part of the octagonal linkage. This octagonal linkage can be stacked spirally infinitely.

If each voluntary movement is likened to fruit, the formula (a linkage, from (α1) up to (γ5): « fig.VII ») is a seed, and this octagonal infinite linkage is a tree of voluntary movement.

The octagonal formula  is an infinitive element

Small extension affects gradually. When the links number is small, the difference is not noticeable. However, when the number has increased more, we can clearly see the difference.

« The left side  » The perfect result : no stretching margin.
« The right side » The butterfly effect : with a stretching margin.


The laws of nature have a very large margin. That is why it took a long time to find the formula of voluntary movement from the days of Leonardo da Vinci.




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