R Corona Borealis is the 8th star in the Northern Crown. The brighter seven stars lie like gems on a curved line east of Arcturus and west of Vega. At the times of the Hipparcos mission (1991), the magnitude was VT = 5.959 (Tycho2 catalog). This means, that the star was visible to the naked eye under fine conditions (no moon, well-adapted eyes etc.).

The astronomer Søren Toft observed this star with the refractor of the Goetheanum observatory and a Canon EOS 550D camera.


Introductory Workshop followed by Seminar at The Field Centre, Nailsworth Gloucestershire UK, 

February 21st - 25th, 2018

We will introduce the path curves through practical drawing exercises led by several experienced teachers and researchers.  Those without any experience can see how the path curves arise and how they manifest in the forms of nature, and those with some understanding already can explore them further.

After a short break we will go into the Seminar to see where Path curve research is leading us.This seminar will be followed by a longer one in the summer of 2018 in Romania, to more fully explore the potential of this work and where we hope new collaborative research can be initiated.

To be kept informed please contact simon.charternoSpam@live.co.uk.

Paper on bud research

In the framework of the research project Rhythmical Change of Shape in Mistletoe Berries According to Moon and Zodiac Constellations by Renatus Derbidge at the Natural Science Section of the Goetheanum a first paper was published in the open access journal PLOS ONE. It presents methods and software to capture and measure the shape changes of mistletoe berries and leaf buds over time. The paper describes the software used to automatize a number of tasks including contour recognition, optimization of fitting the contour via hill-climbing, derivation of the path curves, computation of Lambda and blinding the pictures for the operator. The validity of the program is demonstrated by results from three independent measurements showing circadian rhythm in mistletoe berries. The program is available as open source and will be applied in a project to analyze the chronobiology of shape in mistletoe berries and the buds of their host trees.

Coauthors of the paper are Linus Feiten (Faculty of Engineering, Chair of Computer Architecture, University of Freiburg, Freiburg, Germany), Oliver Conradt (Section for Mathematics and Astronomy, Goetheanum, Dornach, Switzerland), Peter Heusser (Centre for Integrative Medicine, University of Witten/Herdecke, Witten, Germany) und Stephan Baumgartner (Hiscia Institute, Society for Cancer Research, Arlesheim, Switzerland). The paper and further material can be found HERE.

Compilation of publications

A compilation of publications on themes of the Section for Mathematics and Astronomy is available as pdf document. The overview comprises publications in German as well as in English language. The books, journals and calendars listed were released by various publishing houses and editors, as at April 2013. Further information can be found HERE.



Section for Mathematics and Astronomy

of the School of Spiritual Science at the Goetheanum, Dornach (CH).

The School of Spiritual Science, Goetheanum, is organized in different Sections, in the sense of faculties. The Mathematical-Astronomical Section is one of currently eleven Sections.

The task of the Mathematical-Astronomical Section includes research and teaching in the field of Mathematics und Astronomy in the sense of the Anthroposophical Spiritual Science as well as the coordination of the collaboration on a local, European and worldwide level.