In this enjoyable and lightheaded volume, he gathers a plethora of cultural, biological, geometrical, algebraic, and planetary phenomena of our lives related to the number five. He investigates these occurrences in various facets of life on earth and seeks plausible explanations for some of them and hypothesizes about some others while widening your horizon.

If you have ever wondered how the universe physically works, then this book focusing on the central role that rotational motion plays in our daily lives will lead you to new discoveries, knowledge, and wisdom.

Rotation is found everywhere but often overlooked. There are rotating wheels on cars, wheels that spin in games of chance, Ferris wheels at city carnivals, and other manifestations of rotation that play an essential role in virtually everything we do. Even more important is how everyday phenomena driven by rotation make up life's intrinsic components.

Supported by historical information about the lives of individuals who have contributed to the understanding of rotation, this book delves into the physical principles that explain hurricanes, trade winds, gravity measurements, and much more.

Rotation continues to play a large role in the world, and it's possible that the universe itself rotates. Take a journey defined by new ideas and little-known facts in Wheels in the Sky, a must read for anyone interested in the origin and workings of the universe.

We eat three meals a day and use three utensils. There are three branches of the military. We use three letter acronyms such as NBC, FDR, JFK, FBI, and IRS. We eat BLTs, and we learn the ABCs. The number "three" permeates our lives. In Three of Life, author Louis Komzsik examines the unique role that this number plays in life.

Three of Life focuses on the diverse mathematical roles of the number as a geometric and arithmetic building block as well as a gatekeeper of, or a gateway to, infinity. It also discusses appearances of the number in places ranging from historical occurrences, to archaeological finds, to religious symbols, and to biology and physics.

In this light-hearted narrative, Komzsik describes the spectacular role that the number three plays in our physical lives-from biology to the mechanical world to the planetary motions. The number three has occupied a prominent role in human history for thousands of years and has demonstrated an intrinsic presence in our physical life.

In Cycles of Time, author Louis Komzsik offers a comprehensive study of time, its relation to astronomy, and its relative nature. He reviews interesting tidbits of the historical evolution of our understanding of time and discusses some philosophical ideas about the topic. He explores the history of time, its origins in the celestial cycles observed by ancient cultures, and the expansion of our time horizon into cosmic cycles. He examines and debunks the doomsday predictions about the year 2012, and discusses the large scale measuring of time, gradually refined by humankind with medium scale instruments of calendars bringing time to the horizon of a human lifetime. While investigating the physical aspects of time, Cycles of Time examines time's relativity and ponders the possibility of time travel. Influencing one's past, an attractive idea to all of us and the potential cause of the grandfather paradox, may not be theoretically possible, but also merits speculation. Cycles of Time explains time's very strong trichotomy of past, present, and future in their simplest definitions: the past we remember, the present we experience now, and the future we anticipate.

Gravity is the most detectable physical phenomenon of the universe. Nothing or nobody can escape its grasp, even in very large, astronomical distances. It is manifested in many aspects of our lives. Yet we are still not really sure what carries it. The gradually increasing understanding of gravity throughout history and its observed effects in various physical fields are the subjects of this book. This is an enlightening read about one of the most misterious phenomena of our lives that is still far from being fully understood, presenting a historical journey through several millennia of encountering and understanding gravity's mysteries.

In this easily readable volume, the author explains some of the reasons for our preference toward the number seven. He reviews its occurrences in our cultural, biological, chemical, physical, algebraic and geometrical world in an attempt to find the reasons behind them.

Calculus of variations has a long history. Its fundamentals were laid down by icons of mathematics like Euler and Lagrange. It was once heralded as the panacea for all engineering optimization problems by suggesting that all one needed to do was to state a variational problem, apply the appropriate Euler-Lagrange equation and solve the resulting differential equation. This, as most all encompassing solutions, turned out to be not always true and the resulting differential equations are not necessarily easy to solve. On the other hand, many of the differential equations commonly used in various fields of engineering are derived from a variational problem. Hence it is an extremely important topic justifying the new edition of this book. This third edition extends the focus of the book to academia and supports both variational calculus and mathematical modeling classes. The newly added sections, extended explanations, numerous examples and exercises aid the students in learning, the professors in teaching, and the engineers in applying variational concepts.

Primary care practitioners are often the first medical professionals to see patients after an injury, making it critical for them to stay up to date on the latest developments in sports medicine. Musculoskeletal and Sports Medicine for the Primary Care Practitioner contains the most current information on major topics in sports science and clinical medicine. It is a valuable resource for primary care physicians and allied health professionals who practice, teach, and hold specialty certifications in sports medicine and related fields. The book discusses key concepts related to the diagnosis, treatment, and prevention of sports injuries. This edition adds new sections on pro-inflammatory treatments, field-side acupuncture, and brief musculoskeletal ultrasound as well as a new chapter on wellness and video illustrations of important musculoskeletal maneuvers at www.crcpress.com/9781482220117. The book follows the Strength of Recommendation Taxonomy (SORT), which addresses the quality, quantity, and consistency of evidence. It recommends levels of patient-oriented evidence to assist physicians in their diagnoses. Also included is a link to videos that demonstrate important musculoskeletal maneuvers used in sports medicine. As exercise and sports move beyond the realm of leisurely activity to a necessary component of good health, this book has become an important resource for all those involved in sports medicine.

This second edition includes eleven new sections based on the approximation of matrix functions, deflating the solution space and improving the accuracy of approximate solutions, iterative solution of initial value problems of systems of ordinary differential equations, and the method of trial functions for boundary value problems. The topics of the two new chapters are integral equations and mathematical optimization. The book provides alternative solutions to software tools amenable to hand computations to validate the results obtained by "black box" solvers. It also offers an insight into the mathematics behind many CAD, CAE tools of the industry. The book aims to provide a working knowledge of the various approximation techniques for engineering practice.

Calculus of variations has a long history. Its fundamentals were laid down by icons of mathematics like Euler and Lagrange. It was once heralded as the panacea for all engineering optimization problems by suggesting that all one needed to do was to state a variational problem, apply the appropriate Euler-Lagrange equation and solve the resulting differential equation. This, as most all encompassing solutions, turned out to be not always true and the resulting differential equations are not necessarily easy to solve. On the other hand, many of the differential equations commonly used in various fields of engineering are derived from a variational problem. Hence it is an extremely important topic justifying the new edition of this book. This third edition extends the focus of the book to academia and supports both variational calculus and mathematical modeling classes. The newly added sections, extended explanations, numerous examples and exercises aid the students in learning, the professors in teaching, and the engineers in applying variational concepts.

This second edition includes eleven new sections based on the approximation of matrix functions, deflating the solution space and improving the accuracy of approximate solutions, iterative solution of initial value problems of systems of ordinary differential equations, and the method of trial functions for boundary value problems. The topics of the two new chapters are integral equations and mathematical optimization. The book provides alternative solutions to software tools amenable to hand computations to validate the results obtained by "black box" solvers. It also offers an insight into the mathematics behind many CAD, CAE tools of the industry. The book aims to provide a working knowledge of the various approximation techniques for engineering practice.

In this easily readable volume, the author explains some of the reasons for our preference toward the number seven. He reviews its occurrences in our cultural, biological, chemical, physical, algebraic and geometrical world in an attempt to find the reasons behind them.

Gravity is the most detectable physical phenomenon of the universe. Nothing or nobody can escape its grasp, even in very large, astronomical distances. It is manifested in many aspects of our lives. Yet we are still not really sure what carries it. The gradually increasing understanding of gravity throughout history and its observed effects in various physical fields are the subjects of this book. This is an enlightening read about one of the most misterious phenomena of our lives that is still far from being fully understood, presenting a historical journey through several millennia of encountering and understanding gravity's mysteries.

In this enjoyable and lightheaded volume, he gathers a plethora of cultural, biological, geometrical, algebraic, and planetary phenomena of our lives related to the number five. He investigates these occurrences in various facets of life on earth and seeks plausible explanations for some of them and hypothesizes about some others while widening your horizon.

In Cycles of Time, author Louis Komzsik offers a comprehensive study of time, its relation to astronomy, and its relative nature. He reviews interesting tidbits of the historical evolution of our understanding of time and discusses some philosophical ideas about the topic. He explores the history of time, its origins in the celestial cycles observed by ancient cultures, and the expansion of our time horizon into cosmic cycles. He examines and debunks the doomsday predictions about the year 2012, and discusses the large scale measuring of time, gradually refined by humankind with medium scale instruments of calendars bringing time to the horizon of a human lifetime. While investigating the physical aspects of time, Cycles of Time examines time's relativity and ponders the possibility of time travel. Influencing one's past, an attractive idea to all of us and the potential cause of the grandfather paradox, may not be theoretically possible, but also merits speculation. Cycles of Time explains time's very strong trichotomy of past, present, and future in their simplest definitions: the past we remember, the present we experience now, and the future we anticipate.

We eat three meals a day and use three utensils. There are three branches of the military. We use three letter acronyms such as NBC, FDR, JFK, FBI, and IRS. We eat BLTs, and we learn the ABCs. The number "three" permeates our lives. In Three of Life, author Louis Komzsik examines the unique role that this number plays in life.

Three of Life focuses on the diverse mathematical roles of the number as a geometric and arithmetic building block as well as a gatekeeper of, or a gateway to, infinity. It also discusses appearances of the number in places ranging from historical occurrences, to archaeological finds, to religious symbols, and to biology and physics.

In this light-hearted narrative, Komzsik describes the spectacular role that the number three plays in our physical lives-from biology to the mechanical world to the planetary motions. The number three has occupied a prominent role in human history for thousands of years and has demonstrated an intrinsic presence in our physical life.

If you have ever wondered how the universe physically works, then this book focusing on the central role that rotational motion plays in our daily lives will lead you to new discoveries, knowledge, and wisdom.

Rotation is found everywhere but often overlooked. There are rotating wheels on cars, wheels that spin in games of chance, Ferris wheels at city carnivals, and other manifestations of rotation that play an essential role in virtually everything we do. Even more important is how everyday phenomena driven by rotation make up life's intrinsic components.

Supported by historical information about the lives of individuals who have contributed to the understanding of rotation, this book delves into the physical principles that explain hurricanes, trade winds, gravity measurements, and much more.

Rotation continues to play a large role in the world, and it's possible that the universe itself rotates. Take a journey defined by new ideas and little-known facts in Wheels in the Sky, a must read for anyone interested in the origin and workings of the universe.