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Proof! : how the world became geometrical
\"An eye-opening narrative of how geometric principles fundamentally shaped our world\"-- Provided by publisher.
Book
N-Dimensional Space and Perspective: The Mathematics Behind the Interpretation of Ancient Perspective
The discoveries of Herculaneum and Pompeii and the broadened scope of geography in the eighteenth century, and developments in mathematics and physics that began in the nineteenth and continued into the twentieth, renewed studies of ancient works of art led to the creation of opposing factions regarding the “question of perspective”: those who maintained the existence of a single possible perspective, and those who upheld the existence of multiple perspective constructions. To shed light on the debate, this present paper examines some of the factors behind the two positions.
Journal Article
Shape : the hidden geometry of absolutely everything
How should a democracy choose its representatives? How does disease spread? How do computers teach themselves chess, and why is chess easier for them than analyzing a sentence? What should your kids study in school if they really want to learn to think? All of these are questions about geometry. Jordan Ellenberg reveals the mathematics behind some of the most important scientific, political, and philosophical conundrums we face. The word 'geometry', from the Greek, means 'measuring the world'. If anything, geometry doesn't just measure the world - it explains it. Shape shows us how.
Book
Transformation of Geometry from 2D to 3D: Revisiting Origami in a Digital Design Course
In this study, the importance of origami in transforming 2D patterns into 3D objects is highlighted. Within a design workshop, projects of architecture graduate students were evaluated, focusing on the conversion of 2D patterns to 3D using various tools. The workshop consisted of two stages. In the first stage, students created basic geometric shapes such as spheres, cubes, and ellipses using the origami technique with A4 and A5 papers, and transformed them from 2D to 3D through practical tessellation processes. In the second stage, students were instructed in basic folding techniques using Rhino-Grasshopper software, enabling them to digitally model the transformation from 2D tessellation to 3D structures using the origami technique. The study examined these processes, considering variations in tessellation methods, the influence of material knowledge on tessellation processes, and the impact of material characteristics on form finding.
Journal Article
Experimental Structural Model: From Manual Paper Garment to Fabrication as an Architectural Practice-Based Approach for Fashion Design Education
The study presents the integration of architectural design approaches in the fashion design process suggesting a new educational method based on structural model fabrication. The paper addresses the output of an experimental collaborative practice-based workshop titled ‘Fashion Clash’ that mixes both architects and fashion designers. The workshop focused on testing self-structural garments following a manual workflow which is divided into three main phases, (1) modeling and form-finding, (2) assembly, and (3) fabrication. Paper-based materials are used for transforming full-scale garments into textiles. The results presented seven garments displayed at a fashion show that show the effect of the folding techniques in reaching stability and highlighting the interdisciplinary integration of architects and fashion designers. The study concludes that implementing a parametric design logic based on architectural perspective in fashion would generate innovative ways of testing self-supporting geometry. Digitally computing the forces and structure before fabrication are left for further research.
Journal Article
Mathematics Art Music Architecture Education Culture
The international annual Bridges conference exploring Mathematical Connections in Art, Music, Architecture, Education and Culture was founded by Reza Sarhangi (1952–2016) in 1998 at a private liberal arts college in Kansas, Southwestern College. It is an annual conference, which has provided a remarkable multi-disciplinary model of collaboration between mathematics, arts and other cultural activities. The genuine efforts of many founding members of this organization provided an inspirational model throughout the past 20 years that has shaped the Bridges into one of the premier interdisciplinary conferences in the world. The conference has travelled across North America to Europe, and Asia, and hosts participants from dozens of countries around the world.
Journal Article
Epidermis: Algorithmic Design Based on Biomimetic Morphology
The paper discusses the possibilities and challenges that arise when teaching algorithmic design to students with no previous experience in computational processes. It describes the educational approach and methodology of an introductory algorithmic design workshop which employed biomimetic morphological references. In the workshop, the research on the formation processes of natural patterns and the study of the geometric principles that govern their form, triggered an algorithmic design approach where the morphogenetic strategy is abstracted and implemented for biomimetic design using computational design tools. The paper suggests a series of guidelines based on examples of good practice and identifies potential risks that arise from the use of digital design tools. The workshop methodology aimed to address the challenges of complex parametric geometry employing new digital techniques while studying the underlying algorithmic logic of natural systems. The workshop took place at the Aristotle University of Thessaloniki, in Greece.
Journal Article
Advances in Architectural Geometry (AAG) 2016 Symposium
The Advances in Architectural Geometry (AAG) symposia serve as a unique forum where developments in the design, analysis and fabrication of building geometry are presented. With participation of both academics and professionals from the fields of architecture, engineering, computer science and mathematics, each symposium aims to gather and present practical work and theoretical research that responds to contemporary design challenges and expands opportunities for architectural form. This report summarizes the AAG2016, the fifth edition of the symposia hosted by the Swiss National Centre of Competence in Research (NCCR) Digital Fabrication at ETH Zurich from 9 to 13 September 2016.
Journal Article
Math for real life for dummies
The easy way to brush up on the math skills you need in real life Not everyone retains the math they learned in school. Like any skill, your ability to speak \"math\" can deteriorate if left unused. From adding and subtracting money in a bank account to figuring out the number of shingles to put on a roof, math in all of its forms factors into daily life. Math For Real Life For Dummies provides you with the simple formulas and theorems that you're likely to encounter in the workplace, the kitchen, and even when playing games. You can turn to Math For Real Life For Dummies to brush up on your math skills or to handle everyday encounters, like calculating restaurant tips, understanding interest rates, and figuring out percentages and odds. Packed with real-world examples that make sense, Math For Real Life For Dummies takes the stress out of your daily calculation encounters. Provides tips for understanding and using basic mathematical concepts Shows you how math helps the mind to reason and organize complicated situations or problems into clear, simple, and logical steps Covers all of the math skills you're likely to need in everyday situations If you're looking for a practical, plain-English guide to mastering everyday math skills, Math For Real Life For Dummies has you covered.
eBook
Projecting an Architectural Perspective: Euclidean Propositions and Common Practices at Gonçalves Sena’s Workshop
The projection of architectural perspectives, from the drawing plane to the tectonic support, might be the central problem of
quadratura
. However, specialized treatises tend to treat it through ideal statements. Highlighting the materialization of abstract reasoning, those demonstrations serve the scientific legitimation of
quadratura
practice, possibly circumscribed to enlightened scientific and artistic circles, rather than the dissemination of procedures aiming to train people in the projection craftsmanship. This may even be the best-kept secret of the
quadratura
painters. In this context, this paper is focused on Sena’s
quadratura
(1754), at the church of Santarém’s Jesuit College, where under Vieira’s statements exposed in his treatise on perspective (
Tractado de Prospectiva
, Codex 5170, Biblioteca Nacional de Lisboa,
1716
), we will disclose procedures based upon common practices of the painter’s workshop concerning the outline and projection of the image.
Journal Article