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Lissajous Figures are produced by combining two oscillations at right angles to each other. The figures, drawn by mechanical devices called Harmonographs, have scientific uses, but are also enjoyed for their own beauty. The author has been working with harmonographs since his undergraduate days, has built several of them, lectured about them and has written articles about them. This book is intended for people who enjoy physics or art or both. Certainly physics professionals, both students and faculty members, will enjoy reading about an interesting byway of physics. The book is mainly designed for the reader who has some scientific literacy, but who may not be a scientist. If your mathematics is rusty, a preliminary section on mathematics supplies the necessary background for reading the rest of the book.
Lissajous Figures are produced by combining two oscillations at right angles to each other. The figures, drawn by mechanical devices called harmonographs, have scientific uses, but are also enjoyed for their own beauty. The author has been working with harmonographs since his undergraduate days, building several of them, lecturing on them and has written articles about them. This book is intended for people who enjoy physics or art or both
Lissajous figures are produced by combining two oscillations at right angles to each other. The figures, drawn by mechanical devices called harmonographs, have scientific uses, but are also enjoyed for their own beauty. The author has been working with harmonographs since his undergraduate days, building several of them, lecturing on them and has written articles about them. This book is intended for people who enjoy physics or art or both.
Lissajous Figures are produced by combining two oscillations at right angles to each other. The figures, drawn by mechanical devices called Harmonographs, have scientific uses, but are also enjoyed for their own beauty. The author has been working with harmonographs since his undergraduate days, has built several of them, lectured about them and has written articles about them. This book is intended for people who enjoy physics or art or both. Certainly physics professionals, both students and faculty members, will enjoy reading about an interesting byway of physics. The book is mainly designed for the reader who has some scientific literacy, but who may not be a scientist. If your mathematics is rusty, a preliminary section on mathematics supplies the necessary background for reading the rest of the book.
For many years I was organizing a weekly seminar on dynamical astronomy, and I used to make some historical remarks on every subject, including some anecdotes from my contacts with many leading scientists over the years. I described also the development of various subjects and the emergence of new ideasindynamicalastronomy. Thenseveralpeoplepromptedmetowritedown these remarks, which cannot be found in papers, or books. Thus, I decided to write this book, which contains my experiences over the years. I hope that this book may be helpful to astronomy students all over the world. During my many years of teaching, as a visiting professor, in American Universities (1962-1994, Yale, Harvard, MIT, Cornell, Chicago, Maryland and Florida) I was impressed by the quality of my graduate students. Most of them were very bright, asking penetrating questions, and preparing their homework in a perfect way. In a few cases, instead of a ?nal examination, I assigned to them some small research projects and they presented their results at the end of the course. They were excellent in preparing the appropriate slides and in presenting their results in a concise and clear way.
This book covers essential Microsoft EXCEL®'s computational skills while analyzing introductory physics projects. Topics of numerical analysis include; multiple graphs on the same sheet, calculation of descriptive statistical parameters, a 3-point interpolation, the Euler and the Runge-Kutter methods to solve equations of motion, the Fourier transform to calculate the normal modes of a double pendulum, matrix calculations to solve coupled linear equations of a DC circuit, animation of waves and Lissajous figures, electric and magnetic field calculations from the Poisson equation and its 3D surface graphs, variational calculus such as Fermat's least traveling time principle and the least action principle. Nelson's stochastic quantum dynamics is also introduced to draw quantum particle trajectories.
The first quantum revolution started in the early 20th century and gave us new rules that govern physical reality. Accordingly, many devices that changed dramatically our lifestyle, such as transistors, medical scanners and lasers, appeared in the market. This was the origin of quantum technology, which allows us to organize and control the components of a complex system governed by the laws of quantum physics. This is in sharp contrast to conventional technology, which can only be understood within the framework of classical mechanics. We are now in the middle of a second quantum revolution. Although quantum mechanics is nowadays a mature discipline, quantum engineering as a technology is now emerging in its own right. We are about to manipulate and sense individual particles, measuring and exploiting their quantum properties. This is bringing major technical advances in many different areas, including computing, sensors, simulations, cryptography and telecommunications. The present collection of selected papers is a clear demonstration of the tremendous vitality of the field. The issue is composed of contributions from world leading researchers in quantum optics and quantum information, and presents viewpoints, both theoretical and experimental, on a variety of modern problems.
"A coloring book that reveals math's hidden beauty and contemplative power as never before with 78 coloring designs and games that explore symmetry, fractals, tessellations, randomness, and more."--
Literature is uncertain. Literature is good for us. These two ideas are often taken for granted. But what is the relationship between literature’s capacity to perplex and its ethical value? Seven Modes of Uncertainty contends that literary uncertainty is crucial to ethics because it pushes us beyond the limits of our experience.