JOURNEY THROUGH THE WONDERS OF PLANE GEOMETRY, A

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Geometry is one of the most beautiful aspects of mathematics. This beauty is because you can "see" geometry at work. Most people are exposed to the very basic elements of geometry throughout their schooling with the most concentrated study in the secondary school curriculum. High schools in the United States offer one year of concentrated study of geometry that shows students how a mathematician functions, since everything that is accepted beyond the basic axioms must be proved. Unfortunately, as the course is only one year long, there is still very much in geometry left unexplored for the general audience. That is the challenge of this book, in which we will present a plethora of amazing geometric relationships. We begin with the special relationships of the Golden Ratio, before considering unexpected concurrencies and collinearities. Next, we present some surprising results that arise when squares and similar triangles are placed on triangle sides, followed by a discussion of concyclic points and the relationships between circles and various linear figures. Moving on to more advanced aspects of linear geometry, we consider the geometric wonders of polygons. Finally, we address geometric surprises and fallacies, before concluding with a chapter on the useful concept of homothety, which is not included in the American year-long course in geometry. Request Inspection Copy Sample Chapter(s) Introduction Chapter 9: Geometric Surprises Contents: About the Authors Introduction The Golden Ratio in Geometry Unexpected Concurrencies Unexpected Collinearities Squares on Triangle Sides Similar Triangles on Triangle Sides Discovering Concyclic Points Circle Wonders Polygons and Polygrams Geometric Surprises Geometric Fallacies Homothety, Similarity, and Applications Index Readership: This book is suitable for secondary/high school level students and teachers, as well as a general readership, particularly those interested in bridging the gaps in their knowledge of geometry.

Prevention and Early Treatment of Depression Through the Life Course (1版)

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This book presents current evidence of new perspectives for the prevention and appropriate management of depression in people across the life course. Special attention has been dedicated to facilitating factors for the development of health system capacity and the effectiveness of the different types of interventions. The first part of the book reviews the innovations in global prevention and non-pharmacological treatments for children, adolescents, and youths. The second part reviews interventions for adults across the lifespan, including older adults and caregivers. Despite the efforts to tackle depression, the COVID-19 pandemic directly or indirectly affected the mental health of the population, including an increase in the incidence of depressive disorders, which are underdiagnosed and undertreated in young and older people. Because of the characteristics of adolescence and older adulthood, people can consider depression signs and symptoms as natural, neglecting a proper diagnosis. To address these challenges in the clinical management of depression, Prevention and Early Treatment of Depression Through the Life Course presents a life course perspective on the analysis and treatment of depression to help clinical psychologists, psychiatrists and other mental health professionals understand the mechanisms associated with the onset of depression and identify/develop proper evidence-based treatments for different ages and in different circumstances.