Basel, Switzerland
The names of Archimedes and
Bernoulli are inextricably associated with
spirals.
The National Curve Bank is
delighted to welcome a deposit on spirals from
Athens, Greece.
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the student . . . .
Click on the icons to see Panagiotis' web
work.
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On
spirals from Archimedes
We 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 follows.  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.
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Archimedes' Tomb
near Syracuse in Sicily, Italy
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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 < ..//lemniscate/lemniscate.htm
>
for more on the lives of the
Bernoulli family.
Printed
References
The
Gewerbemuseum in Basel,
Switzerland had a famous exhibit
on Spirale WUNDER der Welt in
1985. If you read German,
try to see Die Spirale published
by Birkhäuser, ISBN 3-85700-058-9.
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 larger view.
For a
complete list of Panagiotis
Stefanides' work see < http://www.stefanides.gr
>
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