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