Greek Science and The Golden Section

Ancient Science and Mathematics

Selections from Julia E. Diggins, String, Straightedge, and Shadow Viking Press, New York , 1965. (Illustrations by Corydon Bell)

Now back in print! Purchase at http://wholespiritpress.com/string.htm

Chapters 8, 9: Thales
Chapters 11, 12: Pythagoras and his Theorem
Chapter 13: Platonic Solids
Chapter 14: The Irrationals
Chapter 15: The Golden Mean
Chapter 16: Archimedes
Chapter 17: Eratosthenes

Selection from Plato's Timaeus

Pythagoras of Samos (ca. 560-ca. 480 BC)

Homage to Pythagoras

One of the most comprehensive sets of resources on Pythagoras on the net
Selection from Burnet's Early Greek Philosophy on Pythagoras from the site above.

A collection of ancient quotes and sources on Pythagoras from the same site, originally from Arthur Fairbanks, ed. and trans. The First Philosophers of Greece, 1898.

Harmony and Proportion
Plato and Pythagoras on Music; Alberti and Palladio on architectural space.

Pythagoras on Proportion in Music
From the above site,

MathGYM Pythagoreans activity pages.
The Pythagorean Theorem††††††† essay
Activity†††††††††††††††††††††††††††††††††††† Prove the theorem graphically.

Another applet that proves the theorm graphically from U. of British Columbia

43 proofs of the Theorem from the Cut the Kot site by Alex Bogomolny

Here is an applet that demonstrates the method used in the Diggins book from this site.

Math and Music. Has Pythagorean music theory.
from the Darmouth site.

History of Greek Mathematics

Basic Ideas in Greek Mathematics

History of Mathematics Home Page

Euclid:

D.E. Joyce's Hypertext version of the Elements


The Golden Section

The Golden Mean
An extensive site on the Golden Section in architecture and art.
Lots of diagrams and links. A good place to start.

The Golden Section in Art and Architecture
Jill Brittonís excellent slide show introduction to the Golden Mean.

Fibonacci Numbers and The Golden Section
One of the best and most extensive sites Iíve found. Ron Knott's Surrey University Site

Museum of Harmony. A beautiful site with a nice introduction to the Golden Section.
by Alexey Stakhov and Anna Sluchenkova

The Golden Proportion
Examples of the proportion in nature, art, and architecture, and even dental aesthetics. Sells a gauge to measure the proportion.

Golden Number.net. A well-designed site with a wealth of applications of the Golden Section.

by Gary Meisner. Site has ads.

The Golden Grid. A printable template to check if items are in the golden section. From same site

Fib-Phi Link page

A Nicely annotated and comprehensive list of links on the Fibonnacci Sequence and the Golden Section. Most strong in the former.

Sacred Geometry Home Page
A more general account of the relationship of geometric form to beauty. The page is very well done and gives a good idea of the Neoplatonic view of form and beauty.

 

Mid_Atlantic Geomancy Sacred Geometry Page
A very nice simple account of some of the most persistent mathematical forms in Art and Nature. Nice Images!!

The Divine Proportion
Another nice short account of the Golden Section and where it shows up in Art.
Some nice images.

 

The Mathematics of the Golden Mean
A mathematical account of the Golden Section. Not for those who hate math!

Phi: That Golden Number

A nice short essay on the simple math of the Golden Section by Mark Freitag. Especially good on the relation of phi to other geometrical figures.

Mid Atlantic Geomancy  Sacred geometry site.

Some very nice resources here.

A nice animated construction of the Golden section from this site.

Squaring the Circle: Geometry in Art and Architecture 
By Paul Calter from Darmouth. Highly Recommended!

Flat geometry and the Golden Section.

By Ron Knott. Many activities and applications related to the Golden Section. Look here for constructions.

Here is the construction to divide a given line in the section.

Here is another construction by Robin Hu from her Geometric Constructions with Compass site

The Golden Ration in the Great Pyramid  from the same site.

Deriving a Golden Rectangle from a square.
A nice applet from Textism site, but the applet takes you to the main page when it finishes.

Another applet on the Fibonacci series from the same site

Power Retouch: A Photoshop Plugin for the Golden Section. Has a tutorial as well.

A French site on Pacioli's Divine Proportion.   Has some of the original figures.

Luca Pacioli. The Famous Portrait and some discussion

Leonardo Da Vinci's Platonic Solids from The Divine Proportion

Mozart and the Golden Section
from American Scientist Magazine


A student art project on the Golden Section

Geometry through Art

by Norman Shapiro

 

Fibonacci Numbers in Nature
Another excellent slide presentation from Jill Brettonís site.

Fibonacci Number
Golden Ratio
Phyllotaxis
These three pages are from the Wolfram mathworld site.

 

Polyhedral Models. Includes the Platonic Solids
by Douglas Zongker

3D Models of the Platonic Solids from the U. of Sheffield UK site.

Paper models of Polyhedra. Includes templates for the Platonic Solids

Tesselated Polyhedra. More templates of Platonic Solids to make. From Jill Britton's site.

More on Folding Polyhedra from the Geometry Junkyard


Infinity and Continuity

Aristotle's account of Zeno's paradoxes

Basic Ideas in Greek Mathematics with section on Zeno

Infinity -- A Platonic Realms Mini-Text

Numbers -- A Platonic Realms Mini-Text

Transfinite Numbers

Squaring the Circle

From the Perseus Tufts site

Infinite Ink: The Continuum Hypothesis by Nancy McGough
Zeno_of_Elea
Basic Ideas in Greek Mathematics

Famous Paradoxes: Has sections on Zeno and Cantor
from the Math Forum at Drexel U.

The Value of Pi   from the same site

Mid Atlantic Geomancy  Sacred geometry site.

Some very nice resources here. Sections on Sqaring the Circle and Pi.

The rise of calculus


Plato and Aristotle

Plato's Theory of Forms

Some Main Points of Aristotle's Thought

Selections from Aristotle's Physics


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