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

Prehistoric Measurement

Early Geometry ( BC) Stonehenge UK

Early Geometry ( BC) Avebury Stone Circles

Stone circles in Southern and Western Africa

N & S America and India

Early Geometry ( BC) Celestial Measurement

Early Geometry ( BC) 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 BC 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 BC 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 – a 2 +b 2 =c 2 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 2 nd 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