idea no. 3 – geometry stuart e.b. hughes moray house 26 november 2014
TRANSCRIPT
100 Great Ideas
Idea No. 3 – GEOMETRYStuart E.B. Hughes
Moray House26 November 2014
IDEAS FORUM 2014
Prehistoric measurementEarly GeometryEuclidian geometryCartesian geometry Geometry in art and architectureSpiritual 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 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 - 300BCEarly 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 AlexandriaEuclid as ‘father of geometry’Legacy is twofold:1. Mathematical2. Introduction of logical reasoning in
problem solving
Euclid’s Mathematical LegacyEuclid’s ElementsIt 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 GeometryDescartes brought algebra into geometry
Geometry in the Modern EraGPS Technology
Geometry in the Modern EraLand title – setting out and definition Personal satnavs/GPSMarine navigationAviationConstruction – setting out Without geometry in todays world we
basically would know where we are!
Geometry in Art and ArchitectureArtists 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