The idea of symmetry resulted originally from the study of 

 geometrical forms and the observation of natural objects. Now, 

 after its mathematical formulation has been elaborated, and all 

 the conclusions drawn from it have been systematically gathered 

 into what is commonly named "the general doctrine of sym- 

 metry", the said principle also finds application in those fields 

 of natural science, such as e. g. physics and chemistry, where 

 geometrical properties are generally taken into account in cases 

 in which the dimensions considered will most probably always 

 remain beyond the scope of direct observation. 



2. By the use of the word "symmetry" in the study of forms 



and figures it is intended to 

 draw attention to some geome- 

 trical regularity, to a certain 

 process of repetition and perio- 

 dical arrangement J ) which mani- 

 fests itself in the external habit 

 of the figure considered. It is 

 well known, that there is im- 

 plied a powerful aesthetic fac- 

 tor 2 ) in the mere repetition of a 

 visual impression, and it is in 

 this, that symmetry became an 

 Fig j important aesthetic principle in 



decorative art and architecture. 



In Fig. i a perfectly arbitrary complex of large and small black 

 dots is represented. The figure formed by them does not make any 



1 ) The Greek word au/ji/xsTpta signifies: right proportion, evenness, measura- 

 bleness, dimension; avppsTpos is: uniform, suitable, proportional, measured-off ; and 

 likewise the adverb <7u/x/*Tf$ has the meaning: keeping the due medium be- 

 tween. Democritos e. g. speaks of: IU/X/JIST^I*? |3fou for: the equableness of life; etc. 



The French authors on problems of symmetry often use the expression: "ques- 

 tions d'ordre", which very well illustrates the true meaning of the theory, as one 

 of regular arrangement. 



2 ) The significance of symmetry as an aesthetic principle was already brought 

 into the fore by the ancients. Thus e. g. Plotinos in his famous book on Aes- 

 thetics, in the first Ennead, liber 6, cap. 1, says: "Now almost by all persons 



is maintained, that it is the symmetry of the different parts with respect 

 to each other and the beautiful colour, which produce beauty for visual 

 observation; and for those as well for the common intellect beauty is identical 

 with symmetry and being shaped after fixed proportions." 



