Exercises of Flat Geometry E-Book

Simone Malacrida

• Herausgeber: Simone Malacrida
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Veröffentlichungsjahr: 2022

Beschreibung

In this book, exercises are carried out regarding the following mathematical topics:
angles, lines and segments
circumference and curves
triangles, quadrilaterals and polygons
Initial theoretical hints are also presented to make the performance of the exercises understood.

Leseprobe

Table of Contents

"Exercises of Flat Geometry"

INTRODUCTION

THEORETICAL OUTLINE

EXERCISES

"Exercises of Flat Geometry"

SIMONE MALACRIDA

In this book, exercises are carried out regarding the following mathematical topics:

angles, lines and segments

circumference and curves

triangles, quadrilaterals and polygons

Initial theoretical hints are also presented to make the performance of the exercises understood.

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 – THEORETICAL OUTLINE

Elementary concepts

Circumference

Ellipse

Parable

Polygons: definitions

Triangle

Quadrilaterals

More polygons

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II – EXERCISES

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Exercise 6

Exercise 7

Exercise 8

Exercise 9

Exercise 10

Exercise 11

Exercise 12

Exercise 13

INTRODUCTION

In this workbook some examples of calculations related to plane geometry are carried out.

Geometry is characterized as one of the main fields of mathematics and the study of plane geometry is the basis for understanding any other evolution.

In order to understand in more detail what is presented in the resolution of the exercises, the theoretical reference context is recalled in the first chapter.

What is presented in this workbook is generally addressed during the first two years of high school.

I

THEORETICAL OUTLINE

Elementary concepts

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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.

A segment can therefore be seen as part of a straight line.

Two consecutive segments are adjacent if they belong to the same line.

Lines, segments and semi-lines are characterized by a single dimension called length.

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The geometric entity characterized by two dimensions, called length and height, is the plane , while the one characterized by three dimensions (in addition to those mentioned there is the width) is called space . Plane geometry deals with the study of the two-dimensional case, solid geometry with the three-dimensional case.

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Two straight lines or two segments are said to be coplanar if they lie in the same plane, otherwise they are called skew .

In geometry, points are indicated with capital letters, segments with capital letters of the two extremes barred at the top by a line, while straight lines and semi-lines with small letters.

Furthermore, all geometric dimensions are, by definition, positive.

Two segments, two straight lines or two semi-lines are said to coincide if and only if all the points present in the first geometric element are exactly the same as in the second geometric element.

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In plane geometry, in the case of two half-lines having a common end point, the concept of angle can be defined .