Idea No. 3 – GEOMETRY
Stuart E.B. Hughes
Moray House
26 November 2014
 Prehistoric measurement
 Early Geometry
 Euclidian geometry
 Cartesian geometry
 Geometry in art and architecture
 Spiritual geometry
Mrs. Jagan’s Geometry Class
Mrs Jagan’s Geometry Class
Mrs Jagan’s Geometry Class
Prehistoric Measurement
Early Geometry (6000-3000BC)
Stonehenge UK
Early Geometry (6000-3000BC)
Avebury Stone Circles
Stone circles in Southern and
Western Africa
N & S America and India
Early Geometry (6000-3000BC)
Celestial Measurement
Early Geometry (6000-3000BC)
 Geometry – geo earth metry measurement
 Origins of geometry developing within a social context
i.e. the need for measurement
 Celestial calendars developed out of need to predict
the seasons and regulate the pursuits of early
civilisations.
Geometry 3000 - 300BC
 Development of geometry in this era driven by the
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need for measurement of lines and angles for:
(i) Tax purposes
(ii) Resolving land disputes i.e. re-establishing
boundaries after flooding
(iii) Construction of the pyramids
(iv) Marine navigation
Geometry 3000 - 300BC
 Early geometers had already mastered ways of
calculating areas of the basic geometric shapes
 Thales: volume of a pyramid, distance from land to sea
 Pythagoras – a2+b2=c2
 Egyptian and Greek had amassed a great collection of
empirical principles about basic geometric shapes
Euclidian Geometry
 Ancient library and Museum of Alexandria
 Euclid as ‘father of geometry’
 Legacy is twofold:
 1. Mathematical
 2. Introduction of logical reasoning in problem solving
Euclid’s Mathematical Legacy
 Euclid’s Elements
 It was 2nd most printed book in the western world after
the Bible.
 13 volumes – collection of axioms, proofs and theorems
Euclid’s Logical Reasoning Legacy
If A=B and B=C therefore A=C
 Daily problem solving
 Western reductionism
 Legal system
Cartesian Geometry/coordinate
geometry or analytical geometry
Cartesian/Coordinate Geometry
 Descartes brought algebra into geometry
Geometry in the Modern Era
GPS Technology
Geometry in the Modern Era
 Land title – setting out and definition
 Personal satnavs/GPS
 Marine navigation
 Aviation
 Construction – setting out
 Without geometry in todays world we basically would
know where we are!
Geometry in Art and Architecture
 Artists have been fascinated by geometry for as
long as mathematicians have.
 Geometric ratios, and geometric figures were often
employed in the design of Egyptian, ancient
Indian, Greek and Roman architecture.
 Medieval European cathedrals also incorporated
symbolic geometry
Islamic Architecture
Architecture in Guyana
Expressionism and Cubism
Fractal Art
Spiritual Geometry
 “The laws of nature are but the mathematical thoughts
of God” – Euclid
 “The great book of nature lies ever open before our
eyes and the true philosophies reveal it, but we cannot
read it unless we have first learned the language and
the characters in which it is written. It is written in the
mathematical language and the characters are
triangles, circles and other geometric figures” – Galileo
Spiritual Geometry
 “In nature, we find patterns, designs and structures from
the most minuscule particles, to expressions of life
discernible by human eyes, to the greater cosmos. These
inevitably follow geometrical archetypes, which reveal to us
the nature of each form and its vibrational resonances.”
 “The strands of our DNA, the cornea of our eye, snow
flakes, pine cones, flower petals, diamond crystals, the
branching of trees, a nautilus shell, the stars, the galaxy,
the air and all life forms as we know them emerge out of
timeless geometric codes.”
 “5 perfect 3-dimensional forms - the tetrahedron,
hexahedron, octahedron, dodecahedron, and icosahedron
... collectively known as the Platonic Solids; and that these
form the foundation of everything in the physical world.”
Thank You