@article{10.18756/jfg.2012.129,
	title = {{Der Typus zwischen Irrationalit{\"a}t und Rationalit{\"a}t - oder: Das geheime Gesetz des Siebensterns (Trientalis europaea)}},
	shorttitle = {{Der Typus zwischen Irrationalit{\"a}t und Rationalit{\"a}t - oder: Das geheime Gesetz des Siebensterns (Trientalis europaea)}},
	author = {G{\"a}deke, Manfrid},
	journal = {Jahrbuch für Goetheanismus},
	year = {2012},
	volume = {2012},
	pages = {129--188},
	url = {https://dx.doi.org/10.18756/jfg.2012.129},
	doi = {10.18756/jfg.2012.129},
	issn = {Print :1866-4830 Online : 2750-2341 },
	language = {de},
	abstract = {},
	annote = {The typus between irrationality and rationality  or the secret law of chickweed wintergreen starflower Trientalis europaeaThe theory of phyllotaxis the positions of leaves on plants describes the reciprocal annidation of plant organs and thus the adaptation of the plant organism to itself so to speak In this respect it is related to the Darwinian theory of evolution But with this theory in the more readily comprehensible field of a microcosm it is evident that the principle of competition and delimitation always goes hand in hand with the polar principle of association and that from it diversity and harmony follow in equal measure The sequence of leaf primordia which initially aims at increasing temporal and spatial distance from the starting point of development cyclically returns in the vicinity of this starting point This results in labile neighbourhood constellations and sooner or later in various possible ways arrives at a shortcircuit Irrational geometrical distributive relationships  particularly clear in whorl formation  can modify themselves into rational successive appearance can become simultaneous New units and series arise and constantly form new starting points for further though cyclic  or more precisely spiral  development Goethes theory of metamorphosis with its concept of the archetypal plant and Rudolf Steiners indications on the relationship of astronomy to the other natural scientific disciplines takes into account the interplay between irrationality and rationality distance and convergence In the work here presented this interplay is illustrated with common and uncommon phyllotactic relationships and the history of their discovery By common leaf arrangements we mean the strictly alternating whorls as well as the leaf spirals which keep to the divergence angle of the golden section or its approximations corresponding to the SchimperBraun main series Among others the independent significance of a hitherto highly disregarded series of leaf positions the alternating series is emphasised In addition in the simple case of the change in leaf size the interplay of organ quality and the geometry of position is clarified and it is shown that the strict logical consistency of typological connections does not stop where considerations have to switch from mathematical to qualitative}
}