Introduction to Flat and Solid Geometry E-Book

Simone Malacrida

• Herausgeber: BookRix
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Veröffentlichungsjahr: 2023

Beschreibung

The theoretical assumptions of the following mathematical topics are presented in this book: plane geometry (elementary concepts and figures) solid geometry note to non-Euclidean geometries. In addition, the main applications of these topics are mentioned and some exercises are carried out.

Leseprobe

Simone Malacrida

Introduction to Flat and Solid Geometry

BookRix GmbH & Co. KG81371 Munich

Table of Contents

Table of Contents

“Introduction to Flat and Solid Geometry”

INTRODUCTION

PLANE GEOMETRY: BASIC CONCEPTS

PLANE GEOMETRY: FIGURES

SOLID GEOMETRY

NOTE ON NON-EUCLIDEAN GEOMETRIES

“Introduction to Flat and Solid Geometry”

“Introduction to Flat and Solid Geometry”

SIMONE MALACRIDA

The theoretical assumptions of the following mathematical topics are presented in this book:

plane geometry (elementary concepts and figures)

solid geometry

nod to non-Euclidean geometries.

In addition, the main applications of these topics are mentioned and some exercises are carried out.

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Simone Malacrida (1977)

Engineer and writer, has worked on research, finance, energy policy and industrial plants.

ANALYTICAL INDEX

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INTRODUCTION

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I – PLANE GEOMETRY: BASIC CONCEPTS

Definitions

Euclid's postulates

Other definitions

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II – PLANE GEOMETRY: FIGURES

Definitions

Circumference

Ellipse

Parable

Polygons: definitions

Triangle

Quadrilaterals

More polygons

Exercises z i

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III – SOLID GEOMETRY

Definitions

Sphere

Cone

Cylinder

Polyhedra: definitions

Pyramid

Prism

Exercises

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IV – NOTE ON NON-EUCLIDEAN GEOMETRIES

Introduction

Elliptical geometry

Spherical geometry

Hyperbolic geometry

Other non-Euclidean geometrics

INTRODUCTION

INTRODUCTION

This book presents the main results of Euclidean geometry, declined in the form of plane geometry and solid geometry.

Like arithmetic and algebra, geometry represents one of the cornerstones of mathematical knowledge, necessary not only for understanding any sector of this discipline (analytical geometry, trigonometry, mathematical and functional analysis), but above all for solving concrete problems related to every aspect of science and human life.

Precisely because of the importance of geometry, the majority of the results presented in this manual were already known in antiquity, especially among the Greeks.

Each chapter will be accompanied by some final exercise. This manual is not a workbook and, precisely for this reason, you will not find hundreds of exercises.

The questions proposed were considered significant for understanding the main rules and for their application.

In addition, particular emphasis has been given to the method of solving them since the real leap in quality between the study of a rule and its application is given precisely by the method, i.e. by the quality of the reasoning, and not by the quantity of calculations.

The program presented in this manual expands what is taught in technical institutes and high schools, generally in the first two years, for the exposure of non-Euclidean geometries, usually omitted in the programmes.

I

PLANE GEOMETRY: BASIC CONCEPTS

PLANE GEOMETRY: BASIC CONCEPTS

Definitions

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Geometry is that branch of mathematics that deals with shapes and figures in a given setting.

Below we give the foundations of elementary geometry, largely developed already in ancient Greece.

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The primitive concept of geometry is the point, conceived as a dimensionless and indivisible entity, which characterizes the position and is characterized by it .

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An infinite and successive set of points is called a segment , if this set is delimited by two points called extremes.

Two segments are consecutive if they have an end point in common, while they are external if they have no point in common.

Two segments are said to be incident if they have only one point in common, called the point of intersection , which however is not an extreme.

The midpoint of a segment is the point that exactly divides the segment in half.

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An infinite and successive set of points is called a straight line , if this set is not bounded by any end point, while it is called a semi-line if there is only one end point.