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The wall paintings and reliefs of ancient Egyptian tombs and temples record a continuity of customs and beliefs over nearly 3000 years. Even the artistic style of the scenes seems unchanged from century to century, but this appearance is deceptive. In this work, the author proves - with the help of her original research into grid systems and proportions - that innovation and stylistic variation played a significant role in ancient Egyptian art. This book presents a comprehensive account of the squared grids used by the artists of these lost millennia to achieve acceptable proportions for standing, sitting and kneeling human figures. The author traces the system from its Old Kingdom origins through its development in the Middle Kingdom and its continued employment in the Late and Ptolemaic periods. She explores for the first time its use to reflect physical differences between men and women. Also included are a detailed account of the canon of proportions discovered by the author - the Amarna canon - which accompanied the revolutionary changes instituted by the heretic king Akhenaten, and the first full analysis of how the grid system influenced composition as a whole. The text is illustrated by numerous line drawings of paintings and reliefs with superimposed grids, either derived from actual traces surviving on monuments or calculated according to the methods used by the ancient Egyptians themselves.

This handbook provides readers with a well-illustrated and readable comparative guide to proportion systems in architecture, setting out the mathematical principles that underlie the main systems and illustrating these with examples of their use in historical and modern buildings. The main body of the text traces the interplay of abstraction and empathy through the history of science, philosophy and architecture from the early Greeks through to the two early twentieth-century architects who made proportion the focus of their work: Le Corbusier and Van der Laan. The book ends with a reflection on the present and future role of proportion in architecture.

This handbook provides readers with a well-illustrated and readable comparative guide to proportion systems in architecture, setting out the mathematical principles that underlie the main systems and illustrating these with examples of their use in historical and modern buildings. The main body of the text traces the interplay of abstraction and empathy through the history of science, philosophy and architecture from the early Greeks through to the two early twentieth-century architects who made proportion the focus of their work: Le Corbusier and Van der Laan. The book ends with a reflection on the present and future role of proportion in architecture.

The painted and relief-cut walls of ancient Egyptian tombs and temples record an amazing continuity of customs and beliefs over nearly 3,000 years. Even the artistic style of the scenes seems unchanging, but this appearance is deceptive. In this work, Gay Robins offers convincing evidence, based on a study of Egyptian usage of grid systems and proportions, that innovation and stylistic variation played a significant role in ancient Egyptian art. Robins thoroughly explores the squared grid systems used by the ancient artists to proportion standing, sitting, and kneeling human figures. This investigation yields the first chronological account of proportional variations in male and female figures from the Early Dynastic to the Ptolemaic periods. Robins discusses in detail the proportional changes underlying the revolutionary style instituted during the Amarna Period. She also considers how the grid system influenced the composition of scenes as a whole. Numerous line drawings with superimposed grids illustrate the text.

This handbook provides readers with a well-illustrated and readable comparative guide to proportion systems in architecture, setting out the mathematical principles that underlie the main systems and illustrating these with examples of their use in historical and modern buildings. The main body of the text traces the interplay of abstraction and empathy through the history of science, philosophy and architecture from the early Greeks through to the two early twentieth-century architects who made proportion the focus of their work: Le Corbusier and Van der Laan. The book ends with a reflection on the present and future role of proportion in architecture.

The wall paintings and reliefs of ancient Egyptian tombs and temples record a continuity of customs and beliefs over nearly 3000 years. Even the artistic style of the scenes seems unchanged from century to century, but this appearance is deceptive. In this work, the author proves - with the help of her original research into grid systems and proportions - that innovation and stylistic variation played a significant role in ancient Egyptian art. This book presents a comprehensive account of the squared grids used by the artists of these lost millennia to achieve acceptable proportions for standing, sitting and kneeling human figures. The author traces the system from its Old Kingdom origins through its development in the Middle Kingdom and its continued employment in the Late and Ptolemaic periods. She explores for the first time its use to reflect physical differences between men and women. Also included are a detailed account of the canon of proportions discovered by the author - the Amarna canon - which accompanied the revolutionary changes instituted by the heretic king Akhenaten, and the first full analysis of how the grid system influenced composition as a whole. The text is illustrated by numerous line drawings of paintings and reliefs with superimposed grids, either derived from actual traces surviving on monuments or calculated according to the methods used by the ancient Egyptians themselves.

This is the first paperback edition of Roy Howat's stimulating and provocative study of Debussy's unorthodox use of musical form. Throught detailed analyses of the piano pieces Reflets dans l'eau and L'isle joyeuse and the symphonic poem La mer, Dr Howat shows how the pieces are built precisely and intricately around the two ratios of Golden Section and bisection so that the music is organised in various geometrical patterns which contribute substantially to its expansive and dramatic impact. The final chapter traces evidence of whether the proportional systems were designed consciously, and if so, where and why Debussy might have learnt such techniques. The evidence includes his involvement in the Symbolist movement and in esotericism.

This is the first paperback edition of Roy Howat's stimulating and provocative study of Debussy's unorthodox use of musical form. Throught detailed analyses of the piano pieces Reflets dans l'eau and L'isle joyeuse and the symphonic poem La mer, Dr Howat shows how the pieces are built precisely and intricately around the two ratios of Golden Section and bisection so that the music is organised in various geometrical patterns which contribute substantially to its expansive and dramatic impact. The final chapter traces evidence of whether the proportional systems were designed consciously, and if so, where and why Debussy might have learnt such techniques. The evidence includes his involvement in the Symbolist movement and in esotericism.

This revolutionary book establishes new foundations for trigonometry and Euclidean geometry. It shows how to replace transcendental trig functions with high school arithmetic and algebra to dramatically simplify the subject, increase accuracy in practical problems, and allow metrical geometry to be systematically developed over a general field. This new theory brings together geometry, algebra and number theory and sets out new directions for algebraic geometry, combinatorics, special functions and computer graphics. The treatment is careful and precise, with over one hundred theorems and 170 diagrams, and is meant for a mathematically mature audience. Gifted high school students will find most of the material accessible, although a few chapters require calculus. Applications include surveying and engineering problems, Platonic solids, spherical and cylindrical coordinate systems, and selected physics problems, such as projectile motion and Snell's law. Examples over finite fields are also included.

This revolutionary book establishes new foundations for trigonometry and Euclidean geometry. It shows how to replace transcendental trig functions with high school arithmetic and algebra to dramatically simplify the subject, increase accuracy in practical problems, and allow metrical geometry to be systematically developed over a general field. This new theory brings together geometry, algebra and number theory and sets out new directions for algebraic geometry, combinatorics, special functions and computer graphics. The treatment is careful and precise, with over one hundred theorems and 170 diagrams, and is meant for a mathematically mature audience. Gifted high school students will find most of the material accessible, although a few chapters require calculus. Applications include surveying and engineering problems, Platonic solids, spherical and cylindrical coordinate systems, and selected physics problems, such as projectile motion and Snell's law. Examples over finite fields are also included.

Illustrated, in full colour, this third book of the "MEMENTO 13" series gives a historical review on the most famous of all proportions - also named the divine. The geometrical ways to determine this proportion are given, and the family of so-called golden shapes and Fibonacci series is introduced. Further on, the author explores the golden proportion's presence in numerous areas of life: its significance to human DNA, body proportions, distances to the Moon and Sun, inner states of bliss and love, as well as its appearance in music, poetry, paintings and architecture (with a focus on the Great Pyramid in Egypt). After reading this book, reader will never again look at the world and their own self with the same eyes.

Proportion sketching allows the artist to develop head-to-body ratios to differentiate the various characters and distinguish between the two genders. It also allows the artist to draw characters in dynamic or striking poses and design characters that suit a variety of genres and settings. This volume explains to the reader how to use manga sketching to devise head-to-body ratios that make each character distinct. It also covers how to proportion realistic, attractive characters as well as adorable, ultra-stylized chibi characters and teaches how to stylize figures.

This is a comprehensive studio guide to human proportions listing over one hundred measurements of both male and female figures with head and face details. Measurements are in both inch and metric systems and fractions are in columns from heroic to 1/12 life size. Section are included on relative and comparative proportions and of dynamic symmetry.

Jain 108 of Australia has distilled the last 30 years of his research towards the re-introduction of Sacred Geometry back into the public school curriculum. 100 years ago, topics like the 5 Platonic Solids, the Fibonacci Sequence and the Golden Mean Spiral were highlights of a national curriculum handed down to us for over 2,000 years since the Greek empire. To our detriment, heads of government made the decision, 100 years ago, to remove this legacy from the national curriculum. Since then, students world-wide have shut down from learning mathematics dur to its current dry factory-style content. Jain Mathemagics is merely putting back into the curriculum that which was already there! Jain succeeds in communicating to Youth in a highly visual Language permitting the Students to understand the in-depth meanings of concepts like: Fractality, Infinite Series, Scale Invariancy etc.

Great learning tools! Contemporary's popular Number Sense series encourages students to explore number relationships to build a concrete understanding of mathematical operations, problem-solving strategies, and real-life applications, using a highly visual and active approach to introduce basic mathematics concepts. Lessons are carefully designed to simultaneously build students' mastery and self-confidence. Each text illustrates a basic math skill with a step-by-step approach, and follows with lots of practice.

Jain 108 of Australia has distilled the last 30 years of his research towards the re-introduction of Sacred Geometry back into the public school curriculum. 100 years ago, topics like the 5 Platonic Solids, the Fibonacci Sequence and the Golden Mean Spiral were highlights of a national curriculum handed down to us for over 2,000 years since the Greek empire. To our detriment, heads of government made the decision, 100 years ago, to remove this legacy from the national curriculum. Since then, students world-wide have shut down from learning mathematics dur to its current dry factory-style content. Jain Mathemagics is merely putting back into the curriculum that which was already there! Jain succeeds in communicating to Youth in a highly visual Language permitting the Students to understand the in-depth meanings of concepts like: Fractality, Infinite Series, Scale Invariancy etc.

The symposium held to celebrate the achievements of Albert Einstein is here provided to you in text. Among the many participants are: Felix Gilbert, Harry Woolf, Ernest Nagel, Gerald Holton, Arthur I. Miller.

Combining W.D. Gann’s Square-of-9 and R.N. Elliott’s Wave Principle into one analytical method, this volume uses W.D. Gann's "Time Factor", "Law of Vibration" and Elliott’s cycles to unveil the 3000 BCE Chaldean study into the motion of time. They divided time into years, months, weeks, days, hours, minutes and seconds and devised calendars which helped them predict, and therefore survive, their two rivers' ravaging floods. Inadvertently, their findings also solved the mystery behind the ups and down of money markets. From ancient Sumer to Egypt, ancient China to the native peoples of Central and North America, civilisations unlikely to have had contact with each other built remarkably similar monuments according to geometrical proportions designed to embody cosmic knowledge that would last for all time. Each deciphered time cycles, created calendars and made long term projections of natural phenomena. The Square-of-9 is a matrix embodying nature's cosmic clock. Pauline Novak-Reich takes the reader through ancient math, sacred geometry and lore demonstrating the extraordinary achievements of people who lived in tandem with nature. Each one of these civilisations discovered Nature's "Black Box". Gann often reiterated that: "Everything in existence is based on exact proportion and perfect relationship. There is no chance in nature; because mathematical principles of the highest order lie at the foundation of all things...Vibration is fundamental: nothing is exempt from this law. It is universal, therefore applicable to every class of phenomena on the globe."

, 176 pages with diagrams in the text

Discusses the concept of modularity as a general principle of order in the universe and as applied to architecture, the plastic arts, and music. Bibliogs