DOI: 10.68381/jca20057 ISSN: 0944-6532
An Evolutionary Structure of Convex Pentagons on a C
2
Complete Surface and a Creation Principle of some Weighted Dendrites of Order Three
Anastasios N. Zachos
We reveal some new evolutionary structures of convex pentagons on a
C^2
C
2
surface in the three dimensional Euclidean Space which is hidden on the notion of plasticity of weighted convex pentagons and quadrilaterals. We prove a creation principle for a weighted dendrite of order 3 on a
C^2
C
2
surface which is derived by decreasing the degree of plasticity of weighted convex pentagons from 2 to 1. The creation principle of weighted dendrites of order 3 characterize the process of creation of various leaf tree types on surfaces.