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Author: Jorge Angeles
Publisher: Springer Nature
ISBN: 3030431312
Category : Technology & Engineering
Languages : en
Pages : 182
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Book Description
The textbook provides both beginner and experienced CAD users with the math behind the CAD. The geometry tools introduced here help the reader exploit commercial CAD software to its fullest extent. In fact, the book enables the reader to go beyond what CAD software packages offer in their menus. Chapter 1 summarizes the basic Linear and Vector Algebra pertinent to vectors in 3D, with some novelties: the 2D form of the vector product and the manipulation of “larger" matrices and vectors by means of block-partitioning of larger arrays. In chapter 2 the relations among points, lines and curves in the plane are revised accordingly; the difference between curves representing functions and their geometric counterparts is emphasized. Geometric objects in 3D, namely, points, planes, lines and surfaces are the subject of chapter 3; of the latter, only quadrics are studied, to keep the discussion at an elementary level, but the interested reader is guided to the literature on splines. The concept of affine transformations, at the core of CAD software, is introduced in chapter 4, which includes applications of these transformations to the synthesis of curves and surfaces that would be extremely cumbersome to produce otherwise. The book, catering to various disciplines such as engineering, graphic design, animation and architecture, is kept discipline-independent, while including examples of interest to the various disciplines. Furthermore, the book can be an invaluable complement to undergraduate lectures on CAD.
Author: Jorge Angeles
Publisher: Springer Nature
ISBN: 3030431312
Category : Technology & Engineering
Languages : en
Pages : 182
Get Book Here
Book Description
The textbook provides both beginner and experienced CAD users with the math behind the CAD. The geometry tools introduced here help the reader exploit commercial CAD software to its fullest extent. In fact, the book enables the reader to go beyond what CAD software packages offer in their menus. Chapter 1 summarizes the basic Linear and Vector Algebra pertinent to vectors in 3D, with some novelties: the 2D form of the vector product and the manipulation of “larger" matrices and vectors by means of block-partitioning of larger arrays. In chapter 2 the relations among points, lines and curves in the plane are revised accordingly; the difference between curves representing functions and their geometric counterparts is emphasized. Geometric objects in 3D, namely, points, planes, lines and surfaces are the subject of chapter 3; of the latter, only quadrics are studied, to keep the discussion at an elementary level, but the interested reader is guided to the literature on splines. The concept of affine transformations, at the core of CAD software, is introduced in chapter 4, which includes applications of these transformations to the synthesis of curves and surfaces that would be extremely cumbersome to produce otherwise. The book, catering to various disciplines such as engineering, graphic design, animation and architecture, is kept discipline-independent, while including examples of interest to the various disciplines. Furthermore, the book can be an invaluable complement to undergraduate lectures on CAD.
Author: Andrew Sutton
Publisher: Bloomsbury Publishing USA
ISBN: 0802717764
Category : Mathematics
Languages : en
Pages : 65
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Book Description
Presents an introduction to the origins and principles of geometry, describing geometric constructions that can be achieved through the use of rulers and compasses.
Author: David Hilbert
Publisher: Read Books Ltd
ISBN: 1473395941
Category : History
Languages : en
Pages : 139
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Book Description
This early work by David Hilbert was originally published in the early 20th century and we are now republishing it with a brand new introductory biography. David Hilbert was born on the 23rd January 1862, in a Province of Prussia. Hilbert is recognised as one of the most influential and universal mathematicians of the 19th and early 20th centuries. He discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.
Author: Alberto Lastra
Publisher: Springer Nature
ISBN: 3030813177
Category : Mathematics
Languages : en
Pages : 293
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Book Description
This textbook provides a thorough introduction to the differential geometry of parametrized curves and surfaces, along with a wealth of applications to specific architectural elements. Geometric elements in architecture respond to practical, physical and aesthetic needs. Proper understanding of the mathematics underlying the geometry provides control over the construction. This book relates the classical mathematical theory of parametrized curves and surfaces to multiple applications in architecture. The presentation is mathematically complete with numerous figures and animations illustrating the theory, and special attention is given to some of the recent trends in the field. Solved exercises are provided to see the theory in practice. Intended as a textbook for lecture courses, Parametric Geometry of Curves and Surfaces is suitable for mathematically-inclined students in engineering, architecture and related fields, and can also serve as a textbook for traditional differential geometry courses to mathematics students. Researchers interested in the mathematics of architecture or computer-aided design will also value its combination of precise mathematics and architectural examples.
Author: Michael S. Schneider
Publisher: Harper Collins
ISBN: 0062043161
Category : Science
Languages : en
Pages : 523
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Book Description
Discover how mathematical sequences abound in our natural world in this definitive exploration of the geography of the cosmos You need not be a philosopher or a botanist, and certainly not a mathematician, to enjoy the bounty of the world around us. But is there some sort of order, a pattern, to the things that we see in the sky, on the ground, at the beach? In A Beginner's Guide to Constructing the Universe, Michael Schneider, an education writer and computer consultant, combines science, philosophy, art, and common sense to reaffirm what the ancients observed: that a consistent language of geometric design underpins every level of the universe, from atoms to galaxies, cucumbers to cathedrals. Schneider also discusses numerical and geometric symbolism through the ages, and concepts such as periodic renewal and resonance. This book is an education in the world and everything we can't see within it. Contains numerous b&w photos and illustrations.
Author: Nathan Altshiller-Court
Publisher: Dover Publications
ISBN: 9780486788470
Category :
Languages : en
Pages : 336
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Book Description
The standard university-level text for decades, this volume offers exercises in construction problems, harmonic division, circle and triangle geometry, and other areas. 1952 edition, revised and enlarged by the author.
Author: Sidney M Levy
Publisher: Butterworth-Heinemann
ISBN: 0123822440
Category : Technology & Engineering
Languages : en
Pages : 701
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Book Description
Construction Calculations is a manual that provides end users with a comprehensive guide for many of the formulas, mathematical vectors and conversion factors that are commonly encountered during the design and construction stages of a construction project. It offers readers detailed calculations, applications and examples needed in site work, cost estimation, piping and pipefitting, and project management. The book also serves as a refresher course for some of the formulas and concepts of geometry and trigonometry. The book is divided into sections that present the common components of construction. The first section of the books starts with a refresher discussion of unit and systems measurement; its origin and evolution; the standards of length, mass and capacity; terminology and tables; and notes of metric, U.S, and British units of measurements. The following concepts are presented and discussed throughout the book: Conversion tables and formulas, including the Metric Conversion Law and conversion factors for builders and design professionals Calculations and formulas of geometry, trigonometry and physics in construction Rudiments of excavation, classification, use of material, measurement and payment Soil classification and morphology, including its physicochemical properties Formulas and calculations needed for soil tests and evaluations and for the design of retaining structures Calculations relating to concrete and masonry Calculations of the size/weight of structural steel and other metals Mechanical properties of wood and processing of wood products Calculations relating to sound and thermal transmission Interior finishes, plumbing and HVAC calculations Electrical formulas and calculations Construction managers and engineers, architects, contractors, and beginners in engineering, architecture, and construction will find this practical guide useful for managing all aspects of construction. - Work in and convert between building dimensions, including metric - Built-in right-angle solutions - Areas, volumes, square-ups - Complete stair layouts - Roof, rafter and framing solutions - Circle: arcs, circumference, segments
Author: Andreĭ Petrovich Kiselev
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 192
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Book Description
This volume completes the English adaptation of a classical Russian textbook in elementary Euclidean geometry. The 1st volume subtitled "Book I. Planimetry" was published in 2006 (ISBN 0977985202). This 2nd volume (Book II. Stereometry) covers solid geometry, and contains a chapter on vectors, foundations, and introduction in non-Euclidean geometry added by the translator. The book intended for high-school and college students, and their teachers. Includes 317 exercises, index, and bibliography.
Author: California. Curriculum Development and Supplemental Materials Commission
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 356
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Book Description
Author: Michael Serra
Publisher:
ISBN: 9781559535885
Category : Mathematics
Languages : en
Pages : 34
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Book Description
