Vitruvian Man
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The Beautiful Cubit System I Douglas 2019 the Beautiful Cubit System
The Beautiful Cubit System I Douglas 2019 The Beautiful Cubit System Ian Douglas, B.Sc [email protected] 30 June 2019 Version 1.0.0 DOI: https://doi.org/10.5281/zenodo.3263864 This work is licensed under the Creative Commons Attribution 4.0 International License. Abstract An analysis of the Egyptian Royal cubit, presenting some research and opinions flowing from that research, into what I believe was the original cubit, and how it was corrupted. I show various close arithmetic approximations and multiple ways of getting the divisions of the cubit, as well as some related measures. The cubit also encapsulates the basic components for the metric system. Keywords: Egyptology, metrology, royal cubit, cubit, metre, foot, metric system Contents 1. Introduction 2. Overview of current understanding 3. An alternative origin 4. Different ways of approximating the royal cubit 5. Different ways of getting the cubit divisions 6. Geometry, the Royal Cubit and the metric system 7. Bibliography 1. Introduction The cubit is a well-know ancient measure of length, used around various places in the Middle East and Mediterranean region in the distant past. 1 The Beautiful Cubit System I Douglas 2019 It is allegedly based on the length of a human (male) fore-arm. It is typically measured from the back of the elbow to some point between the wrist and the end of the outstretched middle finger, or in some variants, a point beyond that. The problem with this approach is that everyone’s arm is a different length. If the heights of the dynastic Egyptians is taken as representative, then their arms would have been too short to justify the accepted lengths. -
12 Huggins CAA 1983.Pdf
103 SAXON BUILDI NG MEASUREMENTS P.J.Hu99 ins 27 Grange Court, Waltham ~bbey, ~ssex. Abstract The medieval ~nglish rod of 5.OJ m has been shown to have been in use back to the 6th c~ntury.The sub-divi'sions so fa.r detected are thirds and sixths of this .rod. '1',10 particular a.spects are considered in this paper. The first is vhether the rod was divided further into feet; it is suggested that the manupes-the foot measured by hand-at 15 to the rod is the likely contender. The second aspect concerns building data from r-Juckine. At least 66 Saxon post-hole buildings have been analysed and, provisionally, it appears that 40 were set out using a rod of about 4.65 m and 25 using the 5.03 m rod. Extant rods in the Saxon bomeland likewise have a mean value of 4.65 m suggesting this measure Has brought over by the original Saxon settlers at Bucking. Introduction In a developing sub'ject new ideas are formula.ted and old ideas rightly questioned and possibly discarded. Ne," data may support established hypotheses or change or add to the picture. At any particular time one or hvo aspects of a developing subject will appear to be of special importance in a \vorker t s mind. Such is the position at the present time. The first as~ect of current interest is whether or not the 5.03 m rod, used in the Saxon period, was divided into feet. The second aspect concerns a site '''here two measuring systems appear to have been in use. -
Simple Rules for Incorporating Design Art Into Penrose and Fractal Tiles
Bridges 2012: Mathematics, Music, Art, Architecture, Culture Simple Rules for Incorporating Design Art into Penrose and Fractal Tiles San Le SLFFEA.com [email protected] Abstract Incorporating designs into the tiles that form tessellations presents an interesting challenge for artists. Creating a viable M.C. Escher-like image that works esthetically as well as functionally requires resolving incongruencies at a tile’s edge while constrained by its shape. Escher was the most well known practitioner in this style of mathematical visualization, but there are significant mathematical objects to which he never applied his artistry including Penrose Tilings and fractals. In this paper, we show that the rules of creating a traditional tile extend to these objects as well. To illustrate the versatility of tiling art, images were created with multiple figures and negative space leading to patterns distinct from the work of others. 1 1 Introduction M.C. Escher was the most prominent artist working with tessellations and space filling. Forty years after his death, his creations are still foremost in people’s minds in the field of tiling art. One of the reasons Escher continues to hold such a monopoly in this specialty are the unique challenges that come with creating Escher type designs inside a tessellation[15]. When an image is drawn into a tile and extends to the tile’s edge, it introduces incongruencies which are resolved by continuously aligning and refining the image. This is particularly true when the image consists of the lizards, fish, angels, etc. which populated Escher’s tilings because they do not have the 4-fold rotational symmetry that would make it possible to arbitrarily rotate the image ± 90, 180 degrees and have all the pieces fit[9]. -
Converting Waste Oil Palm Trees Into a Resource R O G R a M M E P N V I R O N M E N T E
w w w . u n ep. o r g United Nations Environment Programme P.O. Box 30552 Nairobi, 00100 Kenya Tel: (254 20) 7621234 Fax: (254 20) 7623927 E-mail: [email protected] web: www.unep.org CONVERTING WASTE OIL PALM TREES INTO A ESOURCE R ROGRAMME P NVIRONMENT E ATIONS N NITED U Copyright © United Nations Environment Programme, 2012 This publication may be reproduced in whole or in part and in any form for educa- tional or non-profit purposes without special permission from the copyright holder, provided acknowledgement of the source is made. UNEP would appreciate receiv- ing a copy of any publication that uses this publication as a source. No use of this publication may be made for resale or for any other commercial purpose whatsoever without prior permission in writing from the United Nations Environment Programme. Disclaimer The designations employed and the presentation of the material in this publication do not imply the expression of any opinion whatsoever on the part of the United Na- tions Environment Programme concerning the legal status of any country, territory, city or area or of its authorities, or concerning delimitation of its frontiers or boundar- ies. Moreover, the views expressed do not necessarily represent the decision or the stated policy of the United Nations Environment Programme, nor does citing of trade names or commercial processes constitute endorsement. Acknowledgement This document was developed by a team led by Dr. Wan Asma Ibrahim Head of Bioen- ergy Programme, Forest Products Division, Forest Research Institute Malaysia (FRIM) under the overall guidance and supervision of Surya Prakash Chandak, Senior Pro- gramme Officer, International Environmental Technology Centre, Division of Technol- ogy, Industry & Economics, United Nations Environment Programme. -
Leonardo Universal
Leonardo Universal DE DIVINA PROPORTIONE Pacioli, legendary mathematician, introduced the linear perspective and the mixture of colors, representing the human body and its proportions and extrapolating this knowledge to architecture. Luca Pacioli demonstrating one of Euclid’s theorems (Jacobo de’Barbari, 1495) D e Divina Proportione is a holy expression commonly outstanding work and icon of the Italian Renaissance. used in the past to refer to what we nowadays call Leonardo, who was deeply interested in nature and art the golden section, which is the mathematic module mathematics, worked with Pacioli, the author of the through which any amount can be divided in two text, and was a determined spreader of perspectives uneven parts, so that the ratio between the smallest and proportions, including Phi in many of his works, part and the largest one is the same as that between such as The Last Supper, created at the same time as the largest and the full amount. It is divine for its the illustrations of the present manuscript, the Mona being unique, and triune, as it links three elements. Lisa, whose face hides a perfect golden rectangle and The fusion of art and science, and the completion of the Uomo Vitruviano, a deep study on the human 60 full-page illustrations by the preeminent genius figure where da Vinci proves that all the main body of the time, Leonardo da Vinci, make it the most parts were related to the golden ratio. Luca Pacioli credits that Leonardo da Vinci made the illustrations of the geometric bodies with quill, ink and watercolor. -
Art and Anatomy: the Vitruvian Teen
Curriculum Units by Fellows of the Yale-New Haven Teachers Institute 2006 Volume VI: Anatomy and Art: How We See and Understand Art and Anatomy: The Vitruvian Teen Curriculum Unit 06.06.01 by Wendy Decter, M.D. Justification Ultimately, learning becomes interdisciplinary as we mature and have opportunities for varied experiences. As adults and teachers it is our responsibility to facilitate growth and provide opportunity for different experiences. Meaningful interpretation and integration of experience must be modeled for our students as well. In grade school children build reading, writing, computational and analytical skills in a step by step fashion usually with one teacher each year. The next teacher uses the previous years' accomplishments as building blocks. Gradually vocabulary expands and students read more complex books. Perspective expands as we start to learn about countries and cultures other than our own, and examine the physical world around us. A sense of community and of the value of education is a necessary ingredient, both in school and at home. Throughout the grades, our students' required readings are set in the historical setting that is being explored from a social standpoint. Our students are acquiring the computational skills needed in their current scientific studies. They move from learning about their town, to their state, to their country and finally to their world and beyond. In middle school and high school courses and the school day becomes compartmentalized. English, now dubbed Language Arts, Social Studies, Science, Math, Art, and Foreign Language are separate departments with differentiated courses taught by many teachers in many ways. -
Linking Math with Art Through the Elements of Design
2007 Asilomar Mathematics Conference Linking Math With Art Through The Elements of Design Presented by Renée Goularte Thermalito Union School District • Oroville, California www.share2learn.com [email protected] The Elements of Design ~ An Overview The elements of design are the components which make up any visual design or work or art. They can be isolated and defined, but all works of visual art will contain most, if not all, the elements. Point: A point is essentially a dot. By definition, it has no height or width, but in art a point is a small, dot-like pencil mark or short brush stroke. Line: A line can be made by a series of points, a pencil or brush stroke, or can be implied by the edge of an object. Shape and Form: Shapes are defined by lines or edges. They can be geometric or organic, predictably regular or free-form. Form is an illusion of three- dimensionality given to a flat shape. Texture: Texture can be tactile or visual. Tactile texture is something you can feel; visual texture relies on the eyes to help the viewer imagine how something might feel. Texture is closely related to Pattern. Pattern: Patterns rely on repetition or organization of shapes, colors, or other qualities. The illusion of movement in a composition depends on placement of subject matter. Pattern is closely related to Texture and is not always included in a list of the elements of design. Color and Value: Color, also known as hue, is one of the most powerful elements. It can evoke emotion and mood, enhance texture, and help create the illusion of distance. -
Decoding the Last Supper
HOUSE OF TRUTH | TOTUUDEN TALO Decoding the Last Supper The Great Year and Men as Gods House of Truth | www.houseoftruth.education 21.6.2013 Table of Contents Introduction ....................................................................................................................................................... 2 The Last Supper and the Great Year .................................................................................................................. 3 36 engravings on the roof ............................................................................................................................. 4 Elements of the Last Supper .......................................................................................................................... 5 Hands of Christ .............................................................................................................................................. 6 The Lesser Conclusion ................................................................................................................................... 7 Men as Gods in the Last Supper ........................................................................................................................ 8 Roman trio of gods ........................................................................................................................................ 9 Evidence number 153 ................................................................................................................................. -
English Customary Weights and Measures
English Customary Weights and Measures Distance In all traditional measuring systems, short distance units are based on the dimensions of the human body. The inch represents the width of a thumb; in fact, in many languages, the word for "inch" is also the word for "thumb." The foot (12 inches) was originally the length of a human foot, although it has evolved to be longer than most people's feet. The yard (3 feet) seems to have gotten its start in England as the name of a 3-foot measuring stick, but it is also understood to be the distance from the tip of the nose to the end of the middle finger of the outstretched hand. Finally, if you stretch your arms out to the sides as far as possible, your total "arm span," from one fingertip to the other, is a fathom (6 feet). Historically, there are many other "natural units" of the same kind, including the digit (the width of a finger, 0.75 inch), the nail (length of the last two joints of the middle finger, 3 digits or 2.25 inches), the palm (width of the palm, 3 inches), the hand (4 inches), the shaftment (width of the hand and outstretched thumb, 2 palms or 6 inches), the span (width of the outstretched hand, from the tip of the thumb to the tip of the little finger, 3 palms or 9 inches), and the cubit (length of the forearm, 18 inches). In Anglo-Saxon England (before the Norman conquest of 1066), short distances seem to have been measured in several ways. -
This Kinetic World: Rethinking the Grid (Neo-Baroque Calls)
PERFORMANCE PHILOSOPHY THIS KINETIC WORLD: RETHINKING THE GRID (NEO-BAROQUE CALLS) LARA D. NIELSEN IE UNIVERSITY—MADRID Distance is not a safety zone but a field of tension. Theodor Adorno, Minima Moralia (2005, 127) Changing course and moving to Spain got me thinking about the grid again. I thought I’d left it, but I was heading right back into it. Truth is, there’s no getting out of it. Some things are for real. It is in Spain that the city grid (la cuadrícula) renewed its license, so to speak, on modernity. Ruins of 2nd century BCE cities like Baelo Claudia, for instance, a Roman municipality doing trade with the Maghreb, imprint the grid’s heterogeneous and syncretic leave (complete with basilica, forum, amphitheatre, temples of Juno, Minerva and the Egyptian Isis). The Alhambra in Granada was built over Roman ruins, its fine interior courts and muqarnas (geometrical, or honeycomb vaulting) the signature of Moorish architecture and design. On the exterior, the grand scale of its organic layout piles quadrangular additions across the mountain ridge in a manner reminiscent of ramshackle medieval cities throughout the Mediterranean, with passages going this way and that. Thus it is noteworthy that among the first known cuadrículas implemented in early modern Spain was a military encampment built in Santa Fe de Granada, in 1491, by Catholic armies forcing out the Muslim Emirate of Granada in the Reconquista. For the Romans as for the Emirates and the Spanish, city grid regimes are conditioned by contact with its “others.” PERFORMANCE PHILOSOPHY VOL 3, NO 1 (2017):285–309 DOI: https://doi.org/10.21476/PP.2017.31127 ISSN 2057–7176 For some 200 years, Granada was the last Emirate standing in Iberia. -
1 Math Action Figures- Human Body Proportion 11-18-14 AO
ARTS IMPACT LESSON PLAN Visual Arts and Math Infused Lesson Lesson One: Math Action Figures: Human Body Proportion Author: Meredith Essex Grade Level: Seventh Enduring Understanding Ratio and proportional relationships can guide accurate portrayal of human figures of any size. Lesson Description (Use for family communication and displaying student art) Students apply understandings of fractions, scale, and ratio to create a human figure in proportion. Head and total height of a human figure is drawn on grid paper based on a 1:8 ratio multiplied by a scale factor. Students then divide the figure horizontally into 8 equal parts and place parts of the figure in those fractional areas guided by a proportion diagram. Last, students use math tools and colorful pens to transform their figure into a “Math Action Figure” character with special math powers. Learning Targets and Assessment Criteria Target: Uses understanding of ratio and scale to map out a human figure. Criteria: Uses ratio of 1:8 (head to body) multiplied by a scale factor to establish proportional head and body height in drawing. Target: Documents proportion calculations. Criteria: Records ratio multiplied by scale factor equation on drawing. Target: Uses understanding of proportion to represent additional parts of a human figure. Criteria: Divides height of figure into 8 equal parts. Sketches head in top 1/8 and sketches parts of figure in other fractional areas guided by diagram and prompts. Target: Creates a math action figure using craftsmanship. Criteria: Defines contour of figure and adds invented geometric elements using pen, grid squares, and straight edge to suggest human and math-inspired characteristics. -
Francis Bacon's Challenge to the Figurative
FIGURE AND FLESH: FRANCIS BACON’S CHALLENGE TO THE FIGURATIVE TRADITION IN WESTERN ART A THESIS SUBMITTED TO THE DEPARTMENT OF GRAPHIC DESIGN AND THE INSTITUTE OF FINE ARTS ¡ ¢ £ ¤ ¥ ¦ § ¨ © § ¦ ¨ IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF FINE ARTS By Müge Telci May, 2002 I certify that I have read this thesis and in my opinion it is fully adequate, in scope and quality, as a thesis for the degree of Master of Fine Arts. _________________________________________________ Assist. Prof. Dr. Mahmut Mutman (Thesis Supervisor) I certify that I have read this thesis and in my opinion it is fully adequate, in scope and quality, as a thesis for the degree of Master of Fine Arts. __________________________________________________ Assoc. Prof. Dr. Emel Aközer I certify that I have read this thesis and in my opinion it is fully adequate, in scope and quality, as a thesis for the degree of Master of Fine Arts. ____________________________________________________ Assist. Prof. Dr. Asuman Suner I certify that I have read this thesis and in my opinion it is fully adequate, in scope and quality, as a thesis for the degree of Master of Fine Arts. _____________________________________________________ Zafer Aracagök Aproved by the Institute of Fine Arts ______________________________________________________ Prof. Dr. Bülent Özgüç Director of the Institute Of Fine Arts ii ABSTRACT FIGURE AND FLESH: FRANCIS BACON’S CHALLENGE TO FIGURATIVE TRADITION IN WESTERN ART Müge Telci M.F.A in Graphical Arts Supervisor: Assist. Prof. Dr. Mahmut Mutman June, 2002 When figuring the body is at stake within the Western tradition of art, figuration comes up as a question of framing and controlling the mass of body (flesh, bones, body liquids etc…).