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Greek Science and The Golden Section |
Ancient Science and Mathematics
Selections
from Julia E. Diggins, String, Straightedge, and
Shadow Viking Press, New York
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)
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.
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 Britton’s excellent slide show introduction to the Golden Mean.
Fibonacci
Numbers and The Golden Section
One of the best and most extensive sites I’ve found. Ron Knott's
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
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
by Norman Shapiro
Fibonacci
Numbers in Nature
Another excellent slide presentation from Jill Bretton’s 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
Infinite Ink: The Continuum
Hypothesis by Nancy McGough
Zeno_of_Elea
Basic Ideas in
Greek Mathematics
from the Math Forum at Drexel U.
Mid Atlantic Geomancy Sacred geometry site.
Some very nice resources here. Sections on Sqaring the Circle and Pi.
Plato and Aristotle
Some
Main Points of Aristotle's Thought
Selections from Aristotle's Physics
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