Page

**2**

Developed system to express equations

Established quantitative calculations

Believed geometry and math could describe all truth and beauty

Truth is described by small whole numbers

Symmetry of the "perfect" body

Example today: Quantum chemistry

Developed a school and "ideal" society

Key geometric relationships

Pythagorean law

Golden mean

Principles of music

Slide 8

“The Golden Mean defines the proportions of the Parthenon, the shape of playing cards and credit cards, and the proportions of the General Assembly Building at the United Nations in New York. The horizontal member of most Christian crosses separates the vertical member by just about the same ratio: the length above the crosspiece is 61.8% of the length below it. The Golden Mean also appears throughout nature – in flower patterns, the leaves of an artichoke, and the leaf stubs on a palm tree. It is also the ratio of the length of the human body above the navel to its length below the navel (in normally proportioned people, that is). The length of each successive bone in our fingers, from tip to hand, also bears this ratio.”

– Peter L. Bernstein, Against the Gods, 1996, XXVI

Slide 9

Parthenon

Latin Cross

Slide 10

Slide 11

Golden Triangle

Isosceles with 72 and 36 degree angles

Used to construct the Golden Spiral

Dodecahedron forms a 5 pointed star made of Golden Triangles

Symbol of the Pythagoreans

Slide 12

Music rules discovered and quantified

Hammers had different tones according to weight

String length relationships (octaves, fifths, etc.)

Principle of harmonic vibration

Music's relationship to mathematics became basis of the study of nature

Music applied to medicine and astronomy

Good health resulted from harmony in the body

Motions of the planets were harmonic multiples

Pythagoras

Slide 13

Heraclitus

"No man steps into the same river twice"

Two worlds

Material = changing

Spiritual = unchanging

Xeno

Motion is not possible (1/2 way)

Democritus

Atomic Theory

Action of atoms determines all events

Solves the Xeno problem

Wrote over 70 books

Plato wanted to burn them all

Slide 14

- Early Greece
- Thales of Miletus 625 BC
- Thales
- Golden Mean
- Golden Spiral
- Pythagoras
- Other Pre-Socratics
- Creativity
- Pythagoras

- Soil and Plant Nutrition
- Magnetic field uses sound waves to ignite sun's ring of fire
- Newton’s third law of motion
- Solar Thermal Energy
- Radiation
- Resource Acquisition and Transport in Vascular Plants
- Buoyancy

© 2010-2021 powerpoint presentations