MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

150 Biographical Vignettes
Forms which gave rise to the mathematical philosophy we now call Platonism.
Through his emphasis on proof, Plato strongly influenced the subsequent development
of Hellenic Mathematics. It was in his Timaeus that he propounded
a mathematical theory of the composition of the universe on the basis of the
five Platonic solids (see Chapter 1). Plato’s Academy flourished until 529 A.D.
when it was closed by Christian Emperor Justinian as a pagan establishment.
At over 900 years, it is the longest known surviving university. Plato died in
Athens, aged 80. Source material for Plato is available in [42, 221].
Vignette 3 (Euclid of Alexandria: Circa 325-265 B.C.).
Little is known of the life of Euclid except that he taught at the Library of
Alexandria in Egypt circa 300 B.C. [165]. When King Ptolemy asked him if
there was an easy way to learn Mathematics, he reportedly replied “There is
no royal road to Geometry!”. It is likely that he studied in Plato’s Academy
in Athens since he was thoroughly familiar with the work of Eudoxus and
Theaetetus which he incorporated into his masterpiece on geometry and number
theory, The Elements [164]. This treatise begins with definitions, postulates
and axioms and then proceeds to thirteen Books. Books one to six
deal with plane geometry (beginning with the construction of the equilateral
triangle, see opening of Chapter 1); Books seven to nine deal with number
theory; Book ten deals with irrational numbers; and Books eleven through
thirteen deal with three-dimensional geometry (ending with the construction
of the regular polyhedra and the proof that there are precisely five of them).
More than one thousand editions of The Elements have been published since
it was first printed in 1482. The opening passages of Book I of the oldest extant
manuscript of The Elements appear in the frontispiece. It was copied by
Stephen the Clerk working in Constantinople in 888 A.D. and it now resides
in the Bodleian Library of Oxford University. Euclid also wrote Conics, a lost
work on conic sections that was later extended by Apollonius of Perga. Source
material for Euclid is available in [164].
Vignette 4 (Archimedes of Syracuse: 287-212 B.C.).
Archimedes is considered by most, if not all, historians of Mathematics to
be one of the greatest (pure or applied) Mathematicians of all time [80, 166]. (I
am told that physicists also feel likewise about him.) He was born in Syracuse,
Sicily, now part of Italy but then an important Greek city-state. As a young
man, he studied with the successors of Euclid in Alexandria but returned to
Syracuse for the remainder of his life. Among his many mathematical accomplishments
were his use of infinitesimals (method of exhaustion) to calculate
areas and volumes, a remarkably accurate approximation to π, and the discovery
and proof that a sphere inscribed in a cylinder has two thirds of the
volume and surface area of the cylinder. He regarded the latter as his greatest