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Stefanides Panagiotis
Head of Standards and Certification,
  EMC HELLAS SA
  Athens Offices:
  2-4, Mesogion Ave.(AthensTower)
115 27 Athens -Greece

panamars@otenet.gr
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Logarithmic Spirals

NCB Deposit #20

Bernoulli spiral in Cathedral
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.

For the student . . . .

Click on the icons to see Panagiotis' web work.
Nautilus
Logarithmic Spiral
Why_Logarithm?

Log equations
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.  spiral 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.
Nautilus
 
Archimedes' Tomb

Archimedes' Tomb near Syracuse in Sicily, Italy


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.
 

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 >

Solar tracking system

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