Saturday

VIDEO: Modern View of Ancient Texts

Hidden by Greek monks in the Middle Ages (by a process embedded amongst the parchment of the Archimedes prayerbook) an amazing discovery reveals hidden text of at least seven treatises by Archimedes...
-These treatises: The Equilibrium of Planes, Spiral Lines, The Measurement of the Circle, Sphere and Cylinder, On Floating Bodies, The Method of Mechanical Theorems, and the Stomachion!

As scientists revealed the ancient texts beneath, it was said to be
'just like receiving a fax from the 3rd century BC'...
-View imagery at the Scientist's site
Modern Technology Reveals Ancient Science!
Click-image-view-VIDEO - Live webcast (Stanford) of 8/4/06!

-Using the latest Scientific techniques with cutting edge physics to view treatises of Archimedes palimpsest...
-View Palimpsest Viewer
SCIENTISTS: Roger Easton, Professor of Imaging Science at The Rochester Institute of Technology, Keith Knox, of the Boeing Corporation, based in Maui, and William A. Christens-Barry of Equipoise Imaging, LLC; who in cooperation, via the use of imaging techniques, made these remarkable discoveries, by the use of a (only copy of its kind) Archimedes palimpsest...

Of the number of techniques applied, confocal microscopy, magnetic resonance imaging, however, multispectral imaging was the most successful..
- Process of Imagery techniques
-An excellent Archimedes biography
-A few of the Accomplishments of Archimedes
-Illustrations from Archimedes' Claw- (invention)

-Of the many inventions...there was also warfare made at King Hieron's request, designed to strike the Syracusans dumb with fear...

War Inventions:

Archimedes created catapults to hurl burning balls of fire and grappling cranes to tip over ships. And, additionally, he invented a system of mirrors that reflected and directed the sun at warships causing them to set fire. It appears that Archimedes actually assembled a group of soldiers with polished shields into a large parabola shape and then focused the reflection from their shields onto the rigging of the ships and igniting them.
~~~~~~

Of all of his inventions, I consider the ratio of the volume of the cylinder to that of the sphere-- to be Archimedes’s greatest achievement.

Archimedean property:

Theorem 2.4.6: Properties of R and Q
The set of real numbers satisfies the Archimedean Property:
Let a and b be positive real numbers. Then there is a natural number n such that n * a > b
The set of rational numbers satisfies the following Density Property:
Let c < d be real numbers. Then there is a rational number q with c < q < d.

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