Plane and Solid Geometry: Concepts and Tools

Plane geometry:


part of the geometry that considers the figures whose points are all on a plane.

Geometry of space, which considers the figures whose points are not all on the same plane.

Descriptive geometry:

that is to resolve problems the geometry of space by means of cash transactions in a plane and it figures represent solids.

Projective geometry:

that is the projection of figures on a plane.

Analytic geometry:

a study of figures which uses a coordinate system and methods of mathematical analysis.

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Technical Drawing: Projections, Sections, and Views

Overview and Sections

Cuts

A cut is the artifice by which, in the representation of a piece, we remove some of it to clarify and make the representation and annotation easier.

Section is the shear plane intersection with the part (the area indicated in red). When representing a section, unlike a cut, we do not represent the rest of the piece left behind. Whenever possible, we prefer to represent the section since it is a clearer and simpler representation.

Cuts are standard devices that we use imaginatively

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Technical Drawing: An Overview of Projections and Sections

Overview and Sections

A cut is the artifice by which, in the representation of a piece, we remove some of the same, in order to clarify and make easier the representation and annotation. A section is called the shear plane intersection with the part (the area indicated in red), as shown when he represents a section, unlike a court, not representing the rest of the piece left behind same. Whenever possible, we prefer to represent the section, since it is clearer and simpler representation.

Cuts are

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Textiles, Carpets, Glass, Enamel & Drawing: A Comprehensive Guide

Textiles and Carpets

Fabrics

Fabrics are fundamental materials for clothing, fashion, and various applications. They consist of two main components:

a) Yarn:

Yarn is the result of intertwining threads, which can be derived from animal origins (wool, silk), vegetable sources (flax, hemp, cotton), or synthetic chemicals (rayon, polyester). Animal and plant fibers require preparation before spinning.

Yarn Production:

  • Early Methods: Wrapping fibers around a nail, using a distaff and spindle.
  • Spinning Wheel:
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Textiles, Carpets, and Drawing: A Comprehensive Guide to Materials and Techniques

Textiles and Carpets. FABRICS Fabrics are the media for paintings and fundamental materials for clothing, fashion, and all types of fabrics. The fabrics are going to see mainly two things: a) Yarn: The tissue is the result of several threads we can have animal origin (wool, silk), vegetable (flax, hemp, cotton) or synthetic chemicals (rayon and polyester). Animal and plant fibers require prior preparation (up to the eighteenth century these operations were not mechanized). Yarn: conversion of fibers

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Geometry Postulates and Theorems: A Comprehensive Guide

Geometry Postulates and Theorems

Postulates

1.1 Ruler Postulate

The points on a line can be matched one to one with the real numbers. The real number that corresponds to a point is the coordinate of the point. The distance between points A and B, written as AB, is the absolute value of the difference of the coordinates of A and B.

1.2 Segment Addition Postulate

If B is between A and C, then AB + BC = AC. If AB + BC = AC, then B is between A and C.

1.3 Protractor Postulate

Consider a ray OB and a point

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