Pentagons And Pentagrams

Author : Eli Maor,Eugen Jost
Publisher : Princeton University Press
Page : 201 pages
File Size : 52,8 Mb
Release : 2022-09-27
Category : Mathematics
ISBN : 9780691238555

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Pentagons and Pentagrams by Eli Maor,Eugen Jost Pdf

A fascinating exploration of the pentagon and its role in various cultures The pentagon and its close cousin, the pentagram, have inspired individuals for the last two and half millennia, from mathematicians and philosophers to artists and naturalists. Despite the pentagon’s wide-ranging history, no single book has explored the important role of this shape in various cultures, until now. Richly illustrated, Pentagons and Pentagrams offers a sweeping view of the five-sided polygon, revealing its intriguing geometric properties and its essential influence on a variety of fields. Traversing time, Eli Maor narrates vivid stories, both celebrated and unknown, about the pentagon and pentagram. He discusses the early Pythagoreans, who ascribed to the pentagon mythical attributes, adopted it as their emblem, and figured out its construction with a straightedge and compass. Maor looks at how a San Diego housewife uncovered four previously unknown types of pentagonal tilings, and how in 1982 a scientist’s discovery of fivefold symmetries in certain alloys caused an uproar in crystallography and led to a Nobel Prize. Maor also discusses the pentagon’s impact on many buildings, from medieval fortresses to the Pentagon in Washington, D.C. Eugen Jost’s superb illustrations provide sumptuous visual context, and the book’s puzzles and mazes offer fun challenges for readers, with solutions given in an appendix.

Author : Eli Maor,Eugen Jost
Publisher : Princeton University Press
Page : 184 pages
File Size : 54,5 Mb
Release : 2022-09-27
Category : Mathematics
ISBN : 9780691201122

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Pentagons and Pentagrams by Eli Maor,Eugen Jost Pdf

A fascinating exploration of the pentagon and its role in various cultures The pentagon and its close cousin, the pentagram, have inspired individuals for the last two and half millennia, from mathematicians and philosophers to artists and naturalists. Despite the pentagon’s wide-ranging history, no single book has explored the important role of this shape in various cultures, until now. Richly illustrated, Pentagons and Pentagrams offers a sweeping view of the five-sided polygon, revealing its intriguing geometric properties and its essential influence on a variety of fields. Traversing time, Eli Maor narrates vivid stories, both celebrated and unknown, about the pentagon and pentagram. He discusses the early Pythagoreans, who ascribed to the pentagon mythical attributes, adopted it as their emblem, and figured out its construction with a straightedge and compass. Maor looks at how a San Diego housewife uncovered four previously unknown types of pentagonal tilings, and how in 1982 a scientist’s discovery of fivefold symmetries in certain alloys caused an uproar in crystallography and led to a Nobel Prize. Maor also discusses the pentagon’s impact on many buildings, from medieval fortresses to the Pentagon in Washington, D.C. Eugen Jost’s superb illustrations provide sumptuous visual context, and the book’s puzzles and mazes offer fun challenges for readers, with solutions given in an appendix.

Author : Frederickson Greg N
Publisher : World Scientific
Page : 432 pages
File Size : 47,5 Mb
Release : 2017-11-24
Category : Mathematics
ISBN : 9789813220492

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Ernest Irving Freese's "Geometric Transformations": The Man, The Manuscript, The Magnificent Dissections! by Frederickson Greg N Pdf

A geometric dissection is a cutting of a geometric figure (such as a regular polygon, or a star, or a cross) into pieces that we can rearrange to form another geometric figure. The best dissections are beautiful and possess economy (few pieces), symmetry, or hingeability. They are often challenging to discover. Ernest Irving Freese was an architect who lived and worked in Los Angeles until his death in 1957. Shortly before he passed away, he completed a 200-page manuscript on geometric dissection, the first book-length treatment on that subject. Freese included elegant drawings of dissections that were both original and clever. After his death the manuscript lay forgotten in his former house until Greg Frederickson set in motion its recovery in 2003. What a treat that it was rescued! Frederickson's book sketches a history of geometric dissections and a biography of Freese, followed by a refurbished copy of Freese's manuscript interleaved with a commentary that highlights Freese's major contributions as well as singular improvements made by Frederickson and others after Freese. This book introduces Freese and his creations to math puzzle enthusiasts, by way of his engaging manuscript, his wild adventures, and his lovely dissections. Frederickson also includes remarkable designs that improve on Freese's work, and packs this book with nifty illustrations and tidbits that may well leave you speechless! Contents: The Rich History of Geometric DissectionsThe "Wild Adventures" of Ernest FreeseTechniques, Special Properties, HardnessFreese's Title Page and IndexIsosceles TrianglesEquilateral TrianglesSquares, Crosses, RectanglesPentagons and PentagramsHexagons and HexagramsOctagons and OctagramsEnneagons (Nonagons)Decagons and DecagramsDodecagons, DodecagramsMany-sided PolygonsMiscellaneous FiguresMore CrossesMore Miscellaneous FiguresMixed Polygons to OneSpecial Triangles Readership: General public and math puzzle enthusiasts. Keywords: Geometric Dissections;Hinged Dissections;Ernest Irving Freese;Henry E Dudeney;Mathematical Recreations;Polygons;Stars;Tessellations;Rhombuses;SymmetryReview: Key Features: The book is a feast for the eyes: Freese's manuscript displays exquisite drawings in an architect's style, while the commentary presents outstandinging dissections that illustrate a brilliant visual one-ups-man-shipThe book stretches the boundaries of dissection: Freese's manuscript explores a remarkable variety of here-to-fore unseen geometric dissections, including those that demonstrate nontrivial numerical identities. The commentary pushes his exploratory use of hinges in extraordinary ways, and drastically improves on his pioneering dissections of many-sided polygons to squaresThe book provides not only historical perspectives on geometric dissection, but also summarizes current mathematical characterizations of the hardness of minimizing the number of pieces in a dissection and of verifying motion planning of hinged dissections

Author : I. Hargittai
Publisher : Elsevier
Page : 1084 pages
File Size : 47,5 Mb
Release : 2016-02-25
Category : Science
ISBN : 9781483299495

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Symmetry 2 by I. Hargittai Pdf

Symmetry 2 aims to present an overview of the contemporary status of symmetry studies, particularly in the arts and sciences, emphasizing both its role and importance. Symmetry is not only one of the fundamental concepts in science, but is also possibly the best unifying concept between various branches of science, the arts and other human activities. Whereas symmetry has been considered important for centuries primarily for its aesthetic appeal, this century has witnessed a dramatic enhancement of its status as a cornerstone in the sciences. In addition to traditionally symmetry-oriented fields such as crystallography and spectroscopy, the concept has made headway in fields as varied as reaction chemistry, nuclear physics, and the study of the origin of the universe. The book was initiated in response to the success of the first volume, which not only received good reviews, but received the award for "The Best Single Issue of a Journal" by the Association of American Publishers for 1986. The second volume extends the application of symmetry to new fields, such as medical sciences and economics, as well as investigating further certain topics introduced in Symmetry. The book is extensively illustrated and with over 64 contributions from 16 countries presents an international overview of the nature and diversity of symmetry studies today.

Author : M.A Hann,I.S. Moxon
Publisher : Routledge
Page : 276 pages
File Size : 45,5 Mb
Release : 2018-09-26
Category : Design
ISBN : 9781351977258

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Patterns by M.A Hann,I.S. Moxon Pdf

In Patterns: Design and Composition, M. A. Hann and I. S. Moxon present guidelines for the original design and composition of regular patterns alongside an understanding of the inherent structures of these patterns. Starting with the compositional elements, Hann and Moxon take the reader through patterns in the environment, early forms of patterns and aspects of classification based on circles, squares, triangles and symmetry. With 250 images sourced from past examples as well as student work, this essential read for design students and researchers demonstrates how simplicity begets complexity in the design and composition of regular patterns.

Author : Greg N. Frederickson,Greg Norman Frederickson
Publisher : Cambridge University Press
Page : 334 pages
File Size : 53,8 Mb
Release : 1997
Category : Mathematics
ISBN : 0521525829

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Dissections by Greg N. Frederickson,Greg Norman Frederickson Pdf

A comprehensive, beautifully illustrated survey accessible to anyone familiar with high school geometry.

Author : Mario Livio
Publisher : Crown
Page : 305 pages
File Size : 55,9 Mb
Release : 2008-11-12
Category : Mathematics
ISBN : 9780307485526

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The Golden Ratio by Mario Livio Pdf

Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market! The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist.

Author : Eli Maor,Eugen Jost
Publisher : Princeton University Press
Page : 206 pages
File Size : 45,6 Mb
Release : 2017-04-11
Category : Art
ISBN : 9780691175881

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Beautiful Geometry by Eli Maor,Eugen Jost Pdf

An exquisite visual celebration of the 2,500-year history of geometry If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configurations involving infinity. The result is a delightful and informative illustrated tour through the 2,500-year-old history of one of the most important branches of mathematics.

Author : István Hargittai
Publisher : World Scientific
Page : 580 pages
File Size : 52,7 Mb
Release : 1992-03-24
Category : Science
ISBN : 9789814522403

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Fivefold Symmetry by István Hargittai Pdf

Fivefold symmetry is common in flowers, fruits, molecules, logos, and buildings, but it is a forbidden symmetry in the world of crystals. A few years ago, the so-called quasicrystals were discovered displaying fivefold symmetry, and it caused a minirevolution in crystallography. There has been increased awareness of fivefold symmetry in all domains of human interest ever since. The present book brings together authors and ideas on a common theme from mathematics, the sciences, design, and anthropology to history, literature, and the arts. Its 29 chapters are an offering by scientists and humanists from 13 countries to a broad readership of professionals and laypersons about fivefold symmetry and the areas that are being bridged by this unique concept. Contents: Fivefold Symmetry in Mathematics, Physics, Chemistry and Beyond (J Brandmüller)800 Year Old Pentagonal Tiling from Maragh(, Iran, and the New Varieties of Aperiodic Tiling it Inspired (E Makovicky)Fivefold Symmetry in Hyperbolic Crystallography (D Dunham)Pentagonal Chaos (C A Pickover)The Discovery of Space Frames with Fivefold Symmetry (S Baer)The Icosahedral Design of the Great Pyramid (H F Verheyen)A Mystic History of Fivefold Symmetry in Japan (K Miyazaki)Albrecht Dürer and the Regular Pentagon (D W Crowe)Fivefold Symmetry in the Graphic Art of M C Escher (R A Dunlap)Hawaiian Flowers with Fivefold Symmetry (M Hargittai)The Relationship between Mathematics and Mysticism of the Golden Mean Through History (J Kappraff)An Islamic Pentagonal Seal (W K Chorbachi & A L Loeb)and other papers Readership: Scientists, humanists, artists and laypersons. keywords:

Author : Opher Liba,Bat-Sheva Ilany
Publisher : Springer Nature
Page : 174 pages
File Size : 53,8 Mb
Release : 2023-05-08
Category : Education
ISBN : 9783030976002

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From the Golden Rectangle to the Fibonacci Sequences by Opher Liba,Bat-Sheva Ilany Pdf

The book takes us on a fascinating journey through one of the most beautiful and fascinating topics of mathematics. It presents a wealth of information about the golden ratio and the Fibonacci sequence. The book introduces the reader to novel perspectives to classic mathematical concepts and problems. The book’s structure engages with the reader actively, leading to more profound understanding, satisfaction and deep insights in learning mathematics. The book strengthens and expands the readers' mathematical knowledge, allowing them a glimpse of several advanced academic concepts. It demonstrates and instils the essence of mathematical research, along the lines of George Polya: observation, conjecture, proof, implementation, generalization and raising new questions.

Author : George Sarton
Publisher : Courier Corporation
Page : 688 pages
File Size : 49,5 Mb
Release : 2012-10-16
Category : Science
ISBN : 9780486144986

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Ancient Science Through the Golden Age of Greece by George Sarton Pdf

Remarkably readable, thoroughly documented, and well illustrated, this fascinating book by an eminent science historian covers problems of mathematics, astronomy, physics, and biology.

Author : Alan Rogerson
Publisher : WTM-Verlag Münster
Page : 476 pages
File Size : 42,5 Mb
Release : 2015-07-01
Category : Education
ISBN : 9783942197861

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The Mathematics Education for the Future Project. Proceedings of the 13th International Conference Mathematics Education in a Connected World by Alan Rogerson Pdf

This volume contains the papers presented at the International Conference on Mathematics Ed-ucation in a Connected World held from September 16-21, 2015 in Catania, Italy. The Con-ference was organized by The Mathematics Education for the Future Project – an international educational project founded in 1986.

Author : Roger Herz-Fischler
Publisher : Wilfrid Laurier Univ. Press
Page : 208 pages
File Size : 42,6 Mb
Release : 1987
Category : Geometry
ISBN : 9780889201521

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A Mathematical History of Division in Extreme and Mean Ratio by Roger Herz-Fischler Pdf

Author : Greg N. Frederickson
Publisher : Cambridge University Press
Page : 314 pages
File Size : 50,6 Mb
Release : 2002-08-26
Category : Mathematics
ISBN : 0521811929

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Hinged Dissections by Greg N. Frederickson Pdf

These novel and original dissections will be a gold mine for math puzzle enthusiasts and for math educators.

Author : Enrique Maciá
Publisher : CRC Press
Page : 364 pages
File Size : 53,9 Mb
Release : 2015-05-05
Category : Science
ISBN : 9789814463539

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Thermoelectric Materials by Enrique Maciá Pdf

Environmental and economic concerns have significantly spurred the search for novel, high-performance thermoelectric materials for energy conversion in small-scale power generation and refrigeration devices. This quest has been mainly fueled by the introduction of new designs and the synthesis of new materials. In fact, good thermoelectric materials must simultaneously exhibit extreme properties: they must have very low thermal conductivity values and both electrical conductivity and Seebeck coefficient high values as well. Since these transport coefficients are interrelated, the required task of optimization is a formidable one. Thus, thermoelectric materials provide a full-fledged example of interdisciplinary research connecting fields such as solid-state physics, materials science engineering, and structural chemistry and raise the need of gaining proper knowledge of the role played by the electronic structure in the thermal and electrical transport properties of solid matter. This book presents a detailed, updated introduction to the field of thermoelectric materials in a tutorial way, focusing on both basic notions and fundamental questions and illustrating the abstract concepts with suitable application examples. It discusses thermoelectric effects, the transport coefficients and their mutual relations, the efficiency of thermoelectric devices, and some notions on the characterization and related industry standards. It also reviews the two basic strategies for optimizing the thermoelectric performance of materials: the control of thermal conductivity and the power factor enhancement. It discusses structural complexity approach, focusing on complex enough lattice structures with heavy atoms in the unit-cell or nanostructured systems characterized by low-dimensional effects, and introducing different kinds of bulk materials of growing chemical and structural complexity. It also discusses the electronic structure engineering approach that focuses on obtaining a guiding principle, in terms of an electronic band structure tailoring process, and describes the role played by the electronic structure in the thermoelectric performance of different materials.