names of Archimedes and Bernoulli are inextricably associated with
National Curve Bank is delighted to welcome a deposit on spirals from
|For the student . . . .
Click on the icons to see Panagiotis' web work.
On spirals from
have more of the writings of Archimedes than of any other great
mathematician from antiquity. Moreover, he was quite
prolific. Over the centuries, scholars have sought to preserve
his work for it has been held in highest
esteem. As he lived in Syracuse, but
communicated frequently to the mathematics community in Alexandria, his
large treasure of letters have become a fount of mathematical reasoning.
The NCB now quotes from Fauvel and Gray's The History of
Mathematics:A Reader,p. 160. Fauvel and Gray used Sir Thomas
Heath's translation. Today's student may find either of this
treatises in the university library.
On spirals: A
Letter to Dositheus. ca. 200 BC.
[...] "After these came the following
propositions about the spiral, which are as it were another
sort of problem
having nothing in common with the foregoing; and I have written
out the proofs of them for you in this book. They are as
If a straight line of which one extremity
remains fixed be made to revolve at a uniform rate in a plane until it
returns to the position from which it started, and if, at the same time
as the straight line revolves, a point moves at a uniform rate along
the straight line, starting from the fixed extremity, the point will
describe a spiral in the plane. I say then that the area bounded
by the spiral and the straight line which has returned to the position
from which it started is a third part of the circle described with the
fixed point as centre and with radius the length traversed by the point
along the straight line during the one revolution."
Archimedes, ca. 200 BC.
Archimedes' Tomb near Syracuse in
| Please see < http://www.stefanides.gr/pdf/PROPOSED_GEOMETRY_OF_THE_PLATONIC_TIMAEUS_GREEK.pdf.pdf
Please see < http://www.mcs.drexel.edu/~crorres/Archimedes/contents.html
> for a comprehensive web site devloted to Archimedes.
Please see < http://curvebank.calstatela.edu/lemniscate/lemniscate.htm
> for more on the lives of the Bernoulli family.
The Gewerbemuseum in Basel,
had a famous exhibit on Spirale WUNDER der Welt in 1985.
you read German, try to see Die Spirale published by
John Fauvel and Jeremy Gray, The
History of Mathematics ~A Reader~. The Open University, 1987.
T. L. Heath, The Works
of Archimedes, Cambridge, 1897.
In 1982, Stefanides Panagiotis
was awarded a Silver Medal, the "Archimedes," given by the Hellenic
Society of Research and Inventions for his solar tracking system.
He named his experimental unit the "Heliotropio Stefanides." The
invention uses optical signals, differential amplifiers, and electronic
filters to capture reflected sun rays. The signals are relayed
using Boolean algebra. Click on the image at the right for a
For a complete list of Panagiotis
Stefanides' work see < http://www.stefanides.gr