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Thymaridas of Paros (ca. 400 BCE - ca. 350 BCE)
was an ancient Greek
mathematician and Pythagorean noted for his work on prime numbers and simultaneous linear equations.
Although little is known about the life of Thymaridas, it is
believed that he was a rich man who fell into poverty. It is said
that Thestor of Poseidonia traveled to Paros in order to help Thymaridas with the money
that was collected for him.
that Thymaridas called prime numbers "rectilinear" since they can
only be represented on a one dimensional line. Non-prime numbers,
on the other hand, can be represented on a two dimensional plane as
a rectangle with sides that, when multiplied, produce the non-prime
number in question. He further called the number one a "limiting quantity", or
as we might say a "limit of fewness".
Iamblichus in Introductio arithmetica tells us that
Thymaridas also worked with simultaneous linear equations.
In particular, he created the then famous rule that was known as
the "bloom of Thymaridas" or as the "flower of Thymaridas", which
If the sum of n quantities be given, and also the sum
of every pair containing a particular quantity, then this
particular quantity is equal to 1/(n + 2) of the
difference between the sums of these pairs and the first given
or using modern notation, the solution of the following system
of n linear equations in n unknowns,
x + x1 + x2 + …
+ xn−1 = s
x + x1 = m1
x + x2 = m2
x + xn−1 =
is given by
Iamblichus goes on to describe how some systems of linear
equations that are not in this form can be placed into this
- Heath, Thomas Little (1981). A History
of Greek Mathematics. Dover publications. ISBN
- Flegg, Graham (1983). Numbers:
Their History and Meaning. Dover publications. ISBN
Citations and footnotes
- ^ a
Heath (1981). "The ('Bloom') of
Thymaridas". pp. 94–96. "Thymaridas of Paros, an ancient
Pythagorean already mentioned (p. 69), was the author of a rule for
solving a certain set of n simultaneous simple equations
connecting n unknown quantities. The rule was evidently
well known, for it was called by the special name [...] the
'flower' or 'bloom' of Thymaridas. [...] The rule is very obscurely
worded , but it states in effect that, if we have the following
n equations connecting n unknown quantites
x, x1, x2 ...
xn-1, namely [...] Iamblichus, our informant on
this subject, goes on to show that other types of equations can be
reduced to this, so that the rule does not 'leave us in the lurch'
in those cases either."
- ^ Flegg (1983). "Unknown Numbers".
pp. 205. "Thymaridas (fourth century) is said to have had this
rule for solving a particular set of n linear equations in
If the sum of n quantities be given, and also the sum of
every pair containing a particular quantity, then this particular
quantity is equal to 1/(n + 2) of the difference between the sums
of these pairs and the first given sum."