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He proposed the theory of the apeiron in direct response to the earlier theory of his teacher, Thales, who had claimed that the primary substance was water. The notion of temporal infinity was familiar to the Greek mind from remote antiquity in the religious concept of immortality, and Anaximander's description was in terms appropriate to this ...
Anaximander (Greek: Ἀναξίμανδρος, Anaximandros) (c. 610 – c. 546 BCE) wrote a cosmological work, little of which remains.From the few extant fragments, we learn that he believed the beginning or first principle (arche, a word first found in Anaximander's writings, and which he probably invented) is an endless, unlimited mass (), subject to neither old age nor decay, which ...
Flux F through a surface, dS is the differential vector area element, n is the unit normal to the surface. Left: No flux passes in the surface, the maximum amount flows normal to the surface.
Anaximenes's views have been interpreted as reconciling those of his two predecessors, Thales and Anaximander. Air as the arche is a limitless concept, which resembled Anaximander's theory that the arche was the abstract infinite that he called apeiron (Ancient Greek: ἄπειρον, lit. 'unlimited, 'boundless').
In mathematics, a flow formalizes the idea of the motion of particles in a fluid. Flows are ubiquitous in science, including engineering and physics. The notion of flow is basic to the study of ordinary differential equations. Informally, a flow may be viewed as a continuous motion of points over time.
The assumptions for the stream function equation are: The flow is incompressible and Newtonian. Coordinates are orthogonal. Flow is 2D: u 3 = ∂u 1 / ∂x 3 = ∂u 2 / ∂x 3 = 0; The first two scale factors of the coordinate system are independent of the last coordinate: ∂h 1 / ∂x 3 = ∂h 2 / ∂x 3 = 0 ...
Anaximander posited that every element had an opposite, or was connected to an opposite (water is cold, fire is hot). Thus, the material world was said to be composed of an infinite, boundless apeiron from which arose the elements (earth, air, fire, water) and pairs of opposites (hot/cold, wet/dry). There was, according to Anaximander, a ...
The primitive equations may be linearized to yield Laplace's tidal equations, an eigenvalue problem from which the analytical solution to the latitudinal structure of the flow may be determined. In general, nearly all forms of the primitive equations relate the five variables u , v , ω, T , W , and their evolution over space and time.