This chapter elaborates the research pentagon as a diagram for reflecting on research. Examples show how the pentagon may represent specific aspects of research, how it allows for (re-)structuring the inquiry process in research, and finally the pentagon is used as an analytic tool to visualize...
I show that a fifth century BCE Uruk tablet employs the Ancient method, but possibly with very strange consequences, and that a Ptolemaic Egyptian papyrus that checks this method by comparing the area of a circle calculated from the sum of a regular inscribed polygon and the areas of the segm...
Ptolemy began his discourse by calculating the chord lengths for the central angles corresponding to the sides of a regular inscribed decagon, hexagon, pentagon, square, and triangle. He determined the first three of these chords using the figure below with the following proof3....
In that work it was argued on "physical" grounds that the only divergence arises from a simple pole. Here we undertake and complete the argument by summing to zero all the non-leading logarithmic terms (which are potentially new divergences) in the pentagon diagram. Certain aspects of our ...
If conditions 1 ° and 2 ° are not valid, then the solution (4) is stable in a linear setting, and nonlinear analysis is required to solve the stability problem. 4.3. Stability Diagram of a Regular Vortex N-gon Let’s introduce the following notation Γ ˜ 0 k = d e f − 1...
The phasor diagram of a PMASynRM with respect to the rotor reference frame is shown in Figure 6a, considering the steady-state condition. Generally, the torque in an m-phase SynRM can be expressed as Equation (2) where Xd, Xq, Ld, Lq, Id, and Iq are the d and q axes reactance, ...
Additive manufacturing (AM) is one of the fastest-growing markets of our time. During its journey in the past 30 years, its key to success has been that it can easily produce extremely complex shapes and is not limited by tooling problems when a change in geometry is desired. This flexibil...
Hard-anodized is a widely used method in the aeronautical sector to improve aluminum alloys abrasion and corrosion resistance. Aim of this work was to characterize the mechanical properties and resistance hard-anodized aluminum 6061 in citric acid solution as a replacement sulfuric acid solution were ...
Moreover, the pentacle connection has the finest qualities in regular operation. As a result, it would be most desirable to run a five-phase motor in a pentacle connection and switch to a pentagon connection during fault operation. Other papers [13] provide simulations of a five-phase ...