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On the self-organizing of Reality-Totality as living Knowledge
Published in Alfredo Pereira, William Alfred Pickering, Ricardo Ribeiro Gudwin, Systems, Self-Organization and Information, 2018
For example, we can consider here a simple model of distances in space: the Pythagorean Theorem. According to the theorem, in a right triangle we have the relation a2 = b2 + c2, in which a is the measure of the hypotenuse and b and c are the measures of the catheti. If the theorem is considered a property of physical space, then it is a relation between the results of the lengths of the hypotenuse and the catheti. Note that the arithmetical operations expressed in it also indicate possible operations on signs attached to the actions of measurements; we can, therefore, admit that models and theories express Reality.
The Dome of the Temple of Diana in Baiae: Opus Caementicium, Geometry and Mechanics
Published in International Journal of Architectural Heritage, 2021
Apollonius’s Proposition I.33 is fundamental for defining the features of a dome design, the profile of which corresponds to an upper parabola and a lower circle arc, matched in tangency continuity condition, once the dome span and rise have been defined. In fact, with reference to Figure 28, and having fixed only the height SV of the connection between lower circle and upper parabola, it is possible to identify the unique right-angled triangle TQC — with its right-angle at point Q — one cathetus of which coincides with the segment TQ, whereas the second is orthogonal to it, and intercepts the lower circle centre C at the springing quote, guaranteeing the tangency continuity condition of the two curves at point Q; at the same time the parabola amplitude depends on the distance of point Q from the symmetry axis.