**EUCLID**
[334? - 280 B.C.] or [325 - 270 B.C.]
By
Arun Kumar Tripathi
Darmstadt University of Technology, Germany
WHO has not heard of Euclid during his first lessons in geometry in the School? He created the geometry of the universe on which Newton built his laws
of gravitation and motion. It was only in the 19th century that the limitation of Euclid's geometry as applied to space was first discovered by Nicholas Lobatchevsky, and later by Einstein who completely repudiated the Euclidean geometry in his Relativity Theory. However, Euclidean geometry and the Newtonian laws are the one which are most valid on earth.
The great Greek mathematician Euclid, whose book on geometry has struck fear into teenagers' hearts for two millennia. Although he apparently studied at Plato's Academy in Athens, Euclid's home was Alexandria, Egypt, where he worked during the reign of King Ptolemy -- one of many Egyptian kings of the same name. (By the way, Ptolemy was not the astronomer Claudius Ptolemaeus known for the "Ptolemaic system" that identified the Earth as the center of the universe.)
EARLY DAYS
Euclid seemed to have studied in Plato's Academy, the then best known school of Mathematics a "Cambridge of Greece". He was believed to be a "Phoenician" with a "Greek outlook". It was the period when Alexander of Macedonia, after his world conquest, had established the township of Alexandria in Egypt. Ptolemy, the
governor of Alexandria in Egypt, was a great learned man and he founded the great university of Alexandria which surpassed even Plato's Academy. There Euclid
was invited to teach geometry.
A GREAT EXPERIMENTER
He learned more through applications like construction of pumps, fountains, and steam driven motors. Euclid achieved things which were then thought impossible. For example, his fellow professors thought it impossible to measure the height of the great pyramid. But Euclid found a way. He waited near the pyramid measuring his own shadow. At the hour when it became equal to his own height, he quickly measured the length of the shadow cast by the pyramid and offered it as the height of the same. This was one of the consequences of his study of the propagation
of light in straight lines, the other being his discovery of the laws of formation of images by mirrors.
Euclid did his work in the great library and university King Ptolemy built called the Museum -- because it was a temple in honor of the "Muses"
or goddesses who inspired practitioners of the arts and sciences. At the Museum, Euclid churned away at points and lines and axioms and postulates, and of course his special proof of the Pythagorean theorem, which is that in any right-angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.
The Great Geometrician
Euclid raised geometry to the highest level and he published 13 books called 'Elements' which contained the basic principles, the statements and proofs of theorems. Even after two and half millennia, these books remain the standard texts in geometry, and wherever geometry is taught, there resides Euclid.
Euclid and the Infinity
Euclid tried to solve the three classical problems of trisecting an angle, doubling a cube and squaring
a circle. The first problem has a cubic equation 4x*3-3x-a=0, where 'a' is a given number. The problem of
doubling the cube can also be resolved into a cubic equation (2x*3=y*3)
Greeks of Euclid's time were not equipped with graduated instruments which alone could solve a cubic equation. The story is that once the Delphian Oracle predicted a military victory, provided the Athenians would double the siege of the altar of Apollo. The expedition was lost because instead of doubling the siege, they doubled the length, breadth and height of the altar which meant an eight fold enlargement.
The third problem of squaring the circle involves the finding of the exact value of pi --the ratio between the cirumference of a circle and its diameter. Pi belongs to the irrational or unspeakable number of Pythagoras and Euclid proved that it was a waste
of time to expect an exact value of pi, because his solutions ended up in absurd contradictions showing that no exact ratio existed between the entities sought.
Euclid's work with the primes and the irrational numbers dissuaded him from the investigation of infinity and even today, after 2500 years no one can exactly define the role of infinity in mathematics.
Of course, some of this stuff is heady going, which is exactly what King Ptolemy once said in a complaint to Euclid. Euclid's disdainful reply
was: "There is no royal road to geometry."
Copyright
@ Copyright, Science Master Magazine, 1983
@ updated 10th March, 2001
The above article was published first time in Science Master Magazine in the year 1983
The author Arun Kumar Tripathi is working as a Research Assistant at the Telecooperation Research Group, Darmstadt University of Technology, Germany and is a Global Educator and National Advisory Board Member for AmericaTakingAction, a National Network.
Please send your thoughts, ideas and references regarding *Euclid* and *its research* to Arun Kumar Tripathi
