Rock Paper Scissors

ROCKPAPERSCISSORS

An O

de to the Circle, the Triangle, and the SquareFinal Thesis D

ocument by M

artina Hw

ang

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Table of Contents

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Preface and Acknowledgements

A research document that explores and examines the three shapes.They are geometrical, mathematical, and abstract. ultimately they are an abstract creation of the human mind...

What can the shapes reveal about us?an exploration of the mysterious fact that these shapes are an abstract creation of the human mind, yet they are so applicable to almost every aspect of our physical universe: from nature, math, science...Abstract forms that has been transformed by humans into tangible, prac-tical forms to make our lives easier.

Beginning with the ancient mathematicians and culminating in 20th century theories of space and time, the mathematicians of the circle has pointed many investigators in fruitful directions in their quest to unravel nature’s secrets.

I want to create a discussion of the three shapes in technology, culture, history, and science. Look around you, they are everywhere.

This document is not meant to be a complete history on the three shapes, as it would be impossible for the duration of BDes thesis. How-ever, it is an initial attempt of exploring the shapes that seem to be uni-versally constant and surrounded. Although they are figments of our imagination, however they are the keys and connectors to the physical universe we live in. They are the constant links to our past and future, and this newspaper-like opus makes a tribute.

This may speak to a connection of such work and current preoccupa-tions with, say, the re-enactment of historical events and the layering of fiction and reality in documentary.

Form and content.

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Primitive Instinct The Drive to Create

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Man’s heritage is of two different kinds. One has been

accumulated through perhaps two billion years of

evolution and is encoded in the molecular structure of

his genetic make-up. The other has been built up during

approximately one million years of communication and

is encoded in the symbolic structure of his knowledge.

While man evolved as a result of interplay

between genetic mutability and environmental selec-

tivity, his self-made symbols evolved as a result of

interplay between his flexibility in expressing and

his sensitivity in distinguishing. This observa-

tion links these two evolutionary processes in a

not too obvious way, and gives rise to the formi-

dable problem of demonstrating this link by trac-

ing structure and function of the symbols he uses

back to the cellular organization of his body.

―Heinz Von Foerster

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The symbols of primitive art are rooted in the primary

demands of human existence, in the idea of the conti-

nuity of life and death. The main purpose of primi-

tive existence was to obtain food. Food implied the

animal. Where direct attack on the animal was not

successful, rituals, magic signs, and magic symbols

were invented, by which man hoped to be invested

with power to bewitch the animal. But the kill-

ing of beasts was not enough to ensure a continu-

ous food supply. That depended also on the fecun-

dity of the stock; to ensure this, primitive man was

even more powerless. Only magic held out hope.

―S. Geidon

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001 Blombos Ochre. 70,000 bce.

The engraved piece of ochre is regarded as the oldest

known artwork. The use of abstract symbolism on the

engraved pieces of ochre and the presence of a com-

plex tool kit suggests Middle Stone Age people were

behaving in a cognitively modern way and had the

advantages of syntactical language at least 80,000

years ago.

002 The Lascaux Cave Painting. 27,000 bce.

Some theories hold that the cave paintings are a way

of communicating with others, and/or that they are

part of religious or ceremonial rituals.

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003 The Ishango Bone. 25,000 bce – 20,000 bce.

Paleolithic tally sticks are among the earliest known

mathematical objects. The groupings of notches indi-

cate a mathematical understanding that goes beyond

counting. Some scientists think that the tool was used

to construct a numeral system, and possibly to repre-

sent a six-month lunar calendar.

004 Neolithic Geometric Tokens. Circa 8000 bce.

This invention is thought to have been used for 5000

years prior to the use of abstract numbers which led

to writing about 3500 bce, and then to mathematics

about 2600 bce.

005 Sundials. Date Unknown.

Prehistoric sundials found in South West Leicester-

shire. These artifacts have been dated to be older

than Stonehenge (2500 bce) by the stone tools which

were found in the area. The length and position of the

shadow created by the upright flint gnomon enabled

people to gauge the passing of time for ritual needs.

006 Quipus. 1438–1533.

Quipus or khipus (or ‘talking knots’) were recording

devices used in the Inca Empire and its predecessor

societies in the Andean region. A quipu usually con-

sisted of colored spun and plied thread or strings from

llama or alpaca hair. It could also be made of cotton

cords. The cords contained numeric and other values

encoded by knots in a base ten positional system.

Quipus might have just a few or up to 2000 cords.

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Measuring the Everyday Seeking the Absolute Truth

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The waves at the beach, the chariot wheels of the

ancient Egyptians, the swirling of millions of stars in

distant galaxies, the shaps of puffball musrooms, the

structure of the atoms in our own bodies—all these

and many other diverse physical entities become

connected when we reduce their descriptions to math-

ematical languge. But are the connections really

there, and historically valid, or are they just artifacts

of our limited way of thinking mathematically?

—Ernest Zebrowski

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The primitive utensil (sharpened flint, hand ax,

arrow, knife) or the most refined precision instrument

(compass, microscope, transistor) each possesses a

twofold aspect: that of being invested with a ‘specific

function’ (to wound, to cut, to perform a mechanical

operation); and that of ‘containing,’ summing up repre-

senting that function by means

of an external aspect which has to assume a more

or less constant characteristic and which amounts

to an ‘aesthetic’ aspect.

—Gillo Dorfles

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007 Babylonian Mathematics. 1800 bce.

The majority of recovered Babylonian clay tablets

cover topics such as fractions, algebra, quadratic and

cubic equations, the Pythagorean theorem, the cal-

culation of Pythagorean triples and possibly trigono-

metric functions.

This particular tablet (ybc 7289) gives an approxi-

mation to the square root of 2, accurate to five decimal

places.

008 Rhind Mathematial Papyrus. Circa 1650 bce.

Written in the hieratic script, this Egyptian manuscript

shows a basic awareness of composite and prime

numbers; arithmetic, geometric and harmonic means;

a simplistic understanding of the Sieve of Eratos-

thenes, and perfect numbers.

This document is one of the main sources of our

knowledge of Egyptian mathematics.

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009 Zhou Bi Suan Jing, 1046 – 256 bce.

A diagram for the (3, 4, 5) triangle. The Zhou Bi Suan

Jing (the Arithmetical Classic of the Gnomon and

the Circular Paths of Heaven) is one of the oldest

and most famous Chinese mathematical texts. The

book contains one of the first recorded proofs of the

Pythagorean Theorem, but focuses more on astro-

nomical calculations.

010 Oxyrhynchus papyrus, 75 – 125 ce.

One of the oldest surviving fragments of Euclid’s Ele-

ments. The text reads “If a straight line be cut into

equal and unequal segments, the rectangle contained

by the unequal segments of the whole together with

the square on the straight line between the points of

section is equal to the square on the half.”

011 The School of Athens, Raphael, 1509 – 1510

Euclid of Alexandria, a great Greek mathematician,

is depicted in one of the most famous paintings by

Raphael. It is one of a group of four main frescoes

on the walls in the Stanze di Raffaello, located in the

Apostolic Palace in the Vatican.

012 Painting of Luca Pacioli, unknown, 1495

In the painting, the table is filled with geometrical

tools: slate, chalk, compass, a dodecahedron model.

A rhombicuboctahedron half-filled with water is sus-

pended from the ceiling. Pacioli is demonstrating a

theorem by Euclid.

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013 Progress of Determining the Value of Pi

The table shows the historical progress of determining

the value of Pi, from analog attempts by important

mathematicians to digital capabilities of computer

processing. We have come a long way all thanks to the

great mathematicians in the past whom never gave up

in seeking ultimate truth.

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014 Three Angles, Józef Robakowski. 1975.

Józef Robakowski is one of the famous Polish art-

ists and filmmakers associated with the Neo-Avant-

Garde movement of the 1960s. The Three Angles

piece is part of his Energetic Angles series: a discourse

and exploration on whether the practical qualities of

geometry can be expressively transformed to art.

Using his arms, Robakowski cleverly represents

the definition of an angle, which simply is the figure

formed by two rays sharing a common endpoint (the

vertex of the angle).

015 How to Draw an Equilateral Triangle

An equilateral triangle is a triangle in which all three

sides are equal, and all three internals angles are also

congruent to each other and are each 60 .̊

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016 Properties of a Rectangle.

In Euclidean geometry, the term rectangle normally

refers to a quadrilateral with four right angles. This is a

simple rectangle, achieved by folding equal margins all

around on a long and irregular piece of paper.

017 Squaring the Rectangle.

Squaring the rectangluar piece of paper by folding the

corner to the opposite side to form a triangle. Trim

along the vertical line of the rectangle. Note that the

rectangular strip left over can alsp be used for making

smaller squares.

018 Squares Within Squares.

The center of the square is the center of its circum-

scribed and inscribed circles.

Any crease through the center of the square

divides it into two trapezoids which are congruent. A

second crease through the center at right angles to the

first divides the square into four congruent quadrilat-

erals, of which two opposite angles are right angles.

The quadrilaterals are concyclic, which means the ver-

tices of each lie in a circumference.

019 The Equilateral Triangle.

The equilateral triangle can be folded from a square.

Any intersections made based on the middle fold will

also create isosceles triangles. Note the two right-

angled triangles with in the equilateral triangle.

020 The Nonagon.

Any angles can be trisected fairly accurately by paper

folding, and in this way regular nonagon can be con-

structed. A circle can be inscribed in a regular polygon,

and a circle can also be circumscribed round it. Note

the equal radii within the nonagon.

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021 Measuring Distances with a Rope.

The ancient Egyptians were probably the first civiliza-

tion to develop special tools to make rope. The use of

ropes for hunting, pulling, fastening, attaching, car-

rying, lifting, and climbing dates back to prehistoric

times. Rope is also a good tool to measure, especially

for longer distances.

The photograph below is taken by Michael

Gerzon and is part of his Tetrahedral Recording series.

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022 Property of a Straight Line.

A straight line is simply the shortest path between

one point to another point. One of the ways to get a

straight line is to stretch a thread between two points

(fixed by pins).

023 Drawing a Circle Without a Compass.

Drawing circles can be done without a compass. Use

a thumb tack and some string and tie one end of the

string to the tack and pin it wherever the center of the

circle will be. Tie the other end to a pencil. Keep the

string stretched and move the pencil around the pin to

draw a circle.

024 Drawing an Ellipse.

An ellipse can be drawn using two pins, a length of

string, and a pencil: push the pins into the paper at

two points, which will become the ellipse’s foci. Tie the

string into a loose loop around the two pins. Pull the

loop taut with the pencil’s tip, so as to form a triangle.

Move the pencil around, while keeping the string taut,

and its tip will trace out an ellipse.

025 Practical Uses of Drawing an Ellipse

Using the string to draw shapes can be very helpful

and economical for everyday situations like making a

shape for a flower bed.

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026 Sea Island Survey Diagram, Liu Hui

The Sea Island Mathematical Manual was written by

the Chinese mathematican Liu Hui of the Three King-

doms era (220–280 bce). The manual contained many

practical problems of surveying using trignometry

and geometry. Comprehensively, it provided detailed

instructions on how to measure distances and heights,

espeically in inaccessible places.

027 Shadows Measure Height

To determine the height of a tree: one can place a

staight stick nearby the tree, and measure the length

of the stick and its shadow, and the shadow of the tree

with a tape measurer (or rope). Then, the height of the

tree is found by multiplying the length of the stick by

the length of the tree’s shadow, and dividing this result

by the lenght of the stick’s shadow.

028 A Diagram of the Direction of Sun Rays

This diagram illustrates that sun rays come from the

same direction in making shadows, therefore the two

triangles have exactly the same shape and are dif-

ferent only in size.

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031 A Satellite View of Earth in Google Maps

The principle behind the unprecedented navigational

capabilities of Global Positioning System (gps) is trian-

gulation. To triangulate, a gps receiver precisely mea-

sures the time it takes for a satellite signal to make

its brief journey to Earth to obtain the corresponding

distance between it and the satellite. This puts the

receiver somewhere on the surface of an imaginary

sphere with a radius equal to its distance from the

satellite. When signals from three other satellites are

similarly processed, the receiver’s built-in computer

calculates the point at which all four spheres intersect,

effectively determining the user’s current longitude,

latitude, and altitude.

029 Surveying Using Theodolite, 1915

Over time, foresters, builders, surveyors, map makers

and scientists have created special tools to help them

measure the height of trees, buildings and other tall

structures very accurately. In this photo, one surveyor

looks through the telescope of a theodolite while his

partner records angle measurements.

030 Bilby Triangulation Tower, 1920

The ingenuity of Jasper Bilby in designing a tower that

allowed surveyors to obtain needed clear lines-of-

sight and accurate survey observations was enduring:

the last Bilby Tower was built in 1984, over 50 years

after it was first conceived by Bilby.

The towers represent important tools in sur-

veying the world around us. The surveys were manully

conducted by real people in the past, which became

the backbone of our spatial reference framework.

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Order and Choas The Macro and Micro Qualities of LIfe

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What is chaos, if forms emerged from it? How

much order must be ascribed to the ‘initial condi-

tions’ of the cosmos? Do the laws of nature describe

the production of order, or only timeless order?

—Lancelot L. Whyte

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Measuring the Everyday The Macro and Micro Qualities of LIfe

Everything that we can see, everything that we can

understand, is related to structure, and as the Gestalt

psychologists have so beautifully shown, percep-

tion itself is in patterns, not fragments. All awareness

or mental activity seem to involve the comparison of

a sensed or thought pattern with a pre-existing one,

a pattern fromed in the brain’s physical structure by

biological inheritance and the imprint of experience.

—Cyril Stanley Smith

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032 Vitruvian Man, Leonardo da Vinci. 1487.

The world-renowned drawing is accompanied by

notes based on the work of the famed architect, Vit-

ruvius Pollio. The drawing, which is in pen and ink on

paper, depicts a male figure in two superimposed posi-

tions with his arms and legs apart and simultaneously

inscribed in a circle and square. The drawing and text

are sometimes called the Canon of Proportions or, less

often, Proportions of Man.

Tradtionally, the circleis the shape assigned to

the heavens, and the square to the Earth. ‘Squaring

the cirlce’ means unifying the two shapes into equal

area or perimeter; thus symbolically combining

Heaven and Earth as spirit and matter.

If the Earth is fitted inside a square, then the

equal perimeter circle defines the relative size of the

Moon to 99.9 percent accuracy. The Earth and the

heavenly Moon thus square the circle.

033 The Full Moon, taken by Lick Observatory.

Earth has one moon. A symbol in famous love songs,

movies, poems, and folklore, many myths about the

Moon date back to ancient history. In fact, the name

Monday originates from Moon-day.

The Moon glows by light it reflects from the Sun

and is frequently the brightest object in the night

sky. The Moon orbits the Earth about once a month

(moon-th) from about one light second away. The pic-

ture on the left occurs when the Moon is nearly oppo-

site to the Sun in its orbit.

Recent evidence indicates that the Moon formed

from a colossal impact on the Earth about 4.5 billions

of years ago, and therefore has a similar composition

to the Earth. Humans walked on the Moon for the first

time in 1969.

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034 A Diagram of the Solar System.

All of the planets are nearly spherical, and so are all of

the larger planetary moons. The governing agent is the

force of gravity. A large amount of gas will generate

sufficient gravity to pull it together into a dense sphere

of minimum surface area.

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035 Kungelbild, k100b, Paul Talman. 1968.

A kinetic sculpture by artist Paul Talman. In the panels

of rotatable, half black and half white balls, the partic-

ipant is encouraged to rearrange and alter the design.

The semi-circular curve of the Kungelbild

spheres also illustrate the orbiting and rotational

quality of planets in space. Particularily, the Moon

and its phases. From observing the lunar phases from

earth, ancient mathematicians were able to logically

conclude that Earth orbits the Sun, while the Moon

orbits Earth. The logic is that little round objects are

seen to cast circular shawdows, a big circular shadow

suggests the presence of a big round object.

036 Aerial photo of the Large Hadron Collider.

The Large Hadron Collider (lhc) is the world’s largest

and highest- energy particle accelerator. It was built

by the European Organization for Nuclear Research

(cern) with the intention of proving the existence or

non-existence of the Higgs boson: a hypothetical mas-

sive scalar elementary particle predicted to exist by

the Standard Model in particle physics.

The lhc is a synchrotron, a particular type of

cyclic particle accelerator in which the magnetic field

(to turn the particles so they circulate) and the electric

field (to accelerate the particles) are carefully synchro-

nized with the travelling particle beam.

The lhc impressively lies in a tunnel 27 kilome-

tres in circumference, as much as 175 metres beneath

the Franco-Swiss border near Geneva, Switzerland.

On March 30th 2010, the first planned collisions

took place between two 3.5 TeV beams, which set a

new world record for the highest-energy man-made

particle collisions.

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037 Vector Equilibrium

A structural system in which the radial vectors and the

circumferential vectors are of equal magnitude. Equi-

librium is a ‘dangerous’ condition because—due to

entrophy—something is always about to be added or

subtracted to change the balance. It consists of four

symmetrically interdisposed tetrahedral planes.

038 The Great Pyramid in Egypt

The most well-known and moumental ‘geometric

object’ on Earth: the square pyramids.

039 Bubbles.

Froth of irregular soap bubbles showing a cellular

structure analogous to that of metals.

040 Salt Crystals, photo by C.W. Mason.

A group of polyhedral salt crystals growing individu-

ally from solution. Taken under magnification x 200.

The form of the crystals are naturally porportionate

and square; the struture is orderly, yet it looks like as

if though someone carefully arranged them so.

041 Human Fat Tissue, photo by F. T. Lewis.

The shape of cells in human fat tissue. Taken under

magnification x 400. Note how geometric the pentag-

onal faces of the cells are.

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042 A section of an Unknown Mineral.

A classic example of geometry balance and porportion

in nature. The beauty of pattern is breathtaking. Like

a tree ring growth, one can understand the mineral's

progress in formation through looking at its 'triangle

ring growth'.

043 A Cross-section of a Nautilus Shell

Cross-section of a nautilus shell with a plastic repro-

duction (on the right). This very ancient species of mol-

lusk has developed a magnificent, geometrically pure

spiral to accommodate the animal’s need for more

living space. In a living mautilus, a closed tube runs

through curved partitions, through which the animal

can increase or decrease the supply of air in order to

raise or lower itself.

044 A Cross-section of an Apple

Cross-section of an apple showcases the five-sided

regularity that occus or just happens to most plants

and flowers.

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Modularity The Form and Structure Around Us

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It is human consciousness itself that is the great arti-

fact of man. The making and shaping of conscious-

ness from moment to moment is the supreme artis-

tic task of all individuals. To qualify and to perfect

this process on a world environmental scale is

the inherent potential of each new technology.

—Marshall McLuhan

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Measuring the Everyday The Form and Structure Around Us

Roundness must surely be a phenomenon of the

perceiving eye’s experience of itself. Do we not live

visually in a spherical world? No doubt this remains

an unconscious component of our vision, but perhaps,

for that, nonetheless dominant. With our extraor-

dinary human eye we have the capacity to see both

things close at hand and also objects and forms at great

distances. When this capacity is finally fully devel-

oped we are able to see the remote stars, the waxing

and waning of moon, the rising and setting usn.

Awesome in their remoteness and divinely pursu-

ing their slow progress through the spaciousskies

with regularity and development, man has ever-

where reverently propitiated the sun, the moon,

and the stars. They were his day and his night, his

months and his years. He sought to win their benev-

olent attention by all the magical means he could

devise. He made round forms, disks and spheres, and

wore them on his person, symbols of great venera-

tion. Are they magic microcosms of the remote light-

giving forms of the macrocosm of the universe?

—Joan M. Erikson

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045 Golden Section

Egyptians

046 University of South Carolina.

Architect Edward Stone built this dormitory based on

jazz rhythems. A very cubic façade, with no differcian-

tion between top to bottom and left to right.

047 Finnish Interior.

Cross-section of an apple showcases the five-sided

regularity that occus or just happens to most plants

and flowers.

048 A Metal Sculpture, Walter Gropius.

Walter Adolph Georg Gropiu, founder of the Bauhaus

School who, along with Ludwig Mies van der Rohe and

Le Corbusier, is widely regarded as one of the pio-

neering masters of modern architecture.

In this picture, a metal sculpture part of the

Deutsches Volk, Deutsche Arbeit exhibition in Berlin.

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Composition with Triangles, Rectangles and Circles,

Sophie Taeuber-Arp. 1916.

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Olavi Arjas. Sarvis plastic pail.

Dissatified with ordinary round pails, Arjas designed

a square one so it can be carried closer to the body.

The square form also allows for easy pouring. Another

bonus is that the pail fits snuggly between the user’s

legs when used as a general disposal bin.

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the Chinese Pi, a jade disk varying in size, generally

between 10 and 20 cm. in diameter, and pierced in the

center with a circular hole. The pi symbolizes heaven

and was used in sacrificial ceremonials. It was also a

token of rank and one of the emblematic objects used

in burial sites.






in burial sites.

Horse-drawn chariot carved onto the mandapam of

Airavateswarar temple, Darasuram (left), c.a. 12th cen-

tury AD. The chariot and its wheel (right) are so finely

sculpted that they include even the faintest details

The chariot is the earliest and simplest type of horse carriage, used in both

peace and war as the chief vehicle of many ancient peoples. Ox-carts, proto-

chariots, were built in Mesopotamia as early as 3000 BC. The original horse

chariot was a fast, light, open, two or four-wheeled conveyance drawn by two

or more horses hitched side by side. The car was little else than a floor with

a waist-high semicircular guard in front. The chariot, driven by a charioteer,

was used for ancient warfare during the Bronze and Iron Ages, armor being

provided by shields. The vehicle continued to be used for travel, processions

and in games and races after it had been superseded for military purposes.

Militarily, the chariot became obsolete as horse breeding efforts produced an

animal that was large enough to ride into battle.[citation needed]

The word “chariot” comes from Latin carrus, which itself was a loan from

Gaulish. A chariot of war or of triumph was called a car. In ancient Rome and

other ancient Mediterranean countries a biga was a two-horse chariot, a triga

used three horses and a quadriga was drawn by four horses abreast. Obsolete

terms for chariot include chair, charet and wain.

The critical invention that allowed the construction of light, horse-drawn

chariots for use in battle was the spoked wheel. The earliest spoke-wheeled

chariots date to ca. 2000 BC and their usage peaked around 1300 BC (see

Battle of Kadesh). Chariots ceased to have military importance in the 4th

century BC, but chariot races continued to be popular in Constantinople until

the 6th century CE (AD).

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in burial sites.

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Symbolism in Art Mystical Forces

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In writing, signs, symbols, and abstraction flow

together. Thousands of years of abstract representation

lie behind the development of writing. Without this the

discovery would have been unthinkable. Abstraction

shaped its direct development and its final consistency.

In primitive times, abstract representation remained

in the magical and symbolical realms. With writing,

abstraction took on the aspect of everyday currency.

Just like the animal whic, when deprived of its free-

dom, becomes domesticated, so the magical meaning

of abstraction was put to everyday use through writing.

—S. Giedion

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Man and other mammals respond to signals

and signs. But only man communicates

through symbols. Symbols are exclusive

human creations for a world of meaning.

Symbols are created by man to commu-

nicate with others and with himself.

—Rudolf Modley

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Unku

This shows the whole of an unku; note the rectangular band at the top.

These are designs composed of a rectangle and geometric figures woven in strong colours, found mainly in textiles but also in ce-ramics. It is thought that these designs contain coded information which could be “read” by the Inca elite. Some Japanese reserach-ers believe that they form the basis of a writing system, in the same way as the quipu represented an accounting system.

Inca Culture: 1200-1532 AD

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Slide 13-26: Donatello: Madonna of the Clouds c. 1427

The square is a special case of the rectangle, and art-ists have used some of the same devices, such as using the diagonal to separate a picture into two zones. But unlike the rectangle, the diagonal of a square is an axis of symmetry.

But the square format has one property that the rectangular does not; it gives a scene stillness and serenity, a calm and dignity which we’ll see again in the round format. This makes it ideal for a subjects such as a Madonna

According to Augusto Marinoni, ‘The problem in geometry that engrossed Leonardo interminably was the squaring of the circle. From 1504 on, he devoted hundreds of pages in his notebooks to this question of quadrature ... that so fascinated his mentor Pacioli ... While his investigations produced no appreciable gain for mathematics, it did create a multiplicity of complex and pleasing designs.”

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Abstraction in Art Looking at Art in a Post Modern Landscape

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Indeed, architecture, like every art, begins to exist

with abstraction: it abstracts man from the earth and

put him on an artificial, geometrically horizontal

plane; architecture, in order to make its own abstract

world, creates artificial interiors, in which man feels

removed from his natural environment. All structural

elements—walls, floors, columns, ceilings, arches,

and domes—are no more than artificial forms, prod-

ucts of intellectual abstraction, no matter whether

they sometimes evoke a natural form, as a dome, for

instance, evokes the vault of the sky. As soon as this

artificial world is created, however, a contrary phase

sets in: the approach to the natural, whether by the

limitation of forms, or by interpenetration of inte-

rior and exterior space, or by the diffusion of light,

or by colours. The dialectics of artificial and natu-

ral world never cease, and indeed never must, for

then art would lose its enchatment. Indeed they do

not cease even today when architecture has reached

maximum of abstraction and refuses every imita-

tion. Rather in contemporary architecture the value

of form, space, and light in themselves is vindicated.

—P. A. Michelis

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I no longer believe in the possibility of ‘demostrat-

ing’ what form is. To be capable of this would mean

to be capable of demonstrating what life is. Today, I

am interested only in examining how form is born,

that is how a reality becomes perceivable. Therefore,

excluded the possibility of making an abstract contri-

bution, the only possibility which remains to me is

that of documenting an experience: my experience in

painting and in architecture, my two professions.

Form is nothing other than the tangible expression

of a reality and when this truly coincides with reality it

is in consequence true, it is in consequence beautiful.

—Leonardo Ricci

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Klassiek Barok Modern

(transcript of a lecture by TvD)

Cover design by TvD

De Sikkel, Em. Querido

first edition, 1920

Proponents of De Stijl sought to express a new

utopian ideal of spiritual harmony and order. They

advocated pure abstraction and universality by a

reduction to the essentials of form and colour; they

simplified visual compositions to the vertical and hori-

zontal directions, and used only primary colors along

with black and white

this new plastic idea will ignore the particulars of

appearance, that is to say, natural form and colour.

On the contrary, it should find its expression in the

abstraction of form and colour, that is to say, in the

straight line and the clearly defined primary colour.

Theo van Doesburg, Composition IX. 1920. oil on

canvas W.853.1.467B: Geometric Design

Artist: Anonymous (Islamic)

Date (Period): 13th century AH/AD 19th century

Medium: ink and pigments on laid European paper

(probably Italian)

Measurements: H: 4 5/16 x W: 4 5/16 in. (11 x 11 cm)

Description

This folio from Walters manuscript W.853.1 contains a

geometric design.

Additional Information

Text Title: Qur’an: First Volume: Suras 1-18

Title: Leaf from Qur’an

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“Slit Tapestry Red/Green” 1927/28

Stölzl considered the workshop a place for experimen-tation and encouraged improvisation. She and her stu-dents, especially Anni Albers, were very interested in the properties of a fabric and in synthetic fibers. They tested materials for qualities such as color, texture, structure, resistance to wear, flexibility, light refraction and sound absorption. Stölzl believed the challenge of weaving was to create an aesthetic that was appropri-ate to the properties of the material

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bauhaus

bauhaus principles

child, play, study of form, REDUCTION

reintroduction of modularity, tesellation, motion but in the graphic and sense

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Rock Paper Scissors

Documents

magic symbols

abstract forms

primitive man

abstract creation

selfmade symbols

human mind

result of interplay

squarefinal thesis document