April is both Mathematics Awareness Month and National Poetry Month. Merging them together, as suggested by Stephen Ornes, results in Mathematical Poetry month. The union of these two fields is nicely showcased in this blog.
In order to celebrate this special month, I thought I’d share with you three instances in which these two seemingly unrelated fields have crossed paths.
Archimedes’ Cattle Problem
In the third century BC, Greek mathematician Archimedes issued a challenge to the Alexandrian mathematicians headed by Eratosthenes. He described, in poetic language, a certain herd of cattle, consisting of four types, with bulls and cows of each type. The number of cattle in each of the eight categories is not given, but these numbers are related by nine simple conditions which Archimedes outlines. The Archimedes’ cattle problem was discovered by Gotthold Ephraim Lessig in 1773 in a Greek Manuscript containing a 44 line poem (pictured below).
The Solution of the Cubic Equation
A cubic equation is of the form:
Although the solution for quadratic equations was known to the ancient Babylonians and medival Islamic mathematicians, the solution to the cubic equation was unknown for many years. The whole story of its discovery is extensive, but the part that concerns poetry is when Niccolò Tartaglia had discovered a way to solve certain types of cubic equations. Girolamo Cardano wanted to learn the formula, promising not to publish it. Tartaglia eventually shared the formula as a poem (and Cardano ended up publishing it). The poem goes as follows:
“When the cube with the cose beside it <x3+px >
Equates itself to some other whole number, <=q>
Find two other, of which it is the difference. <u–v=q>
Hereafter you will consider this customarily
That their product always will be equal <uv=>
To the third of the cube of the cose net. 3/3, instead of (p/3)3>
Its general remainder then
Of their cube sides , well subtracted, < >
Will be the value of your principal unknown. <=x>
In the second of these acts,
When the cube remains solo , <x3=px+q>
You will observe these other arrangements:
Of the number <q> you will quickly make two such parts, <q=u+v>
That the one times the other will produce straightforward <uv=>
The third of the cube of the cose in a multitude, <p3/3, instead of (p/3)3>
Of which then, per common precept,
You will take the cube sides joined together. < >
And this sum will be your concept. <=x>
The third then of these our calculations <x3+q=px>
Solves itself with the second, if you look well after,
That by nature they are quasi conjoined.
I found these, & not with slow steps,
In thousand five hundred, four and thirty
With very firm and strong foundations
In the city girded around by the sea.
Note: this is the English translation, which does not rhyme like the original Italian version. For more on the poem, read here.
The Sator Square can be described as a mathematical pattern poem, and is a word square containing a Latin palindrome:
These five words can be read from top-to-bottom, bottom-to-top, left-to-right, or right-to-left.
The oldest Sator Square was found in the ruins of Pompeii. However, its translation has no clear consensus and is subject of much speculation.
So what do you think of Math Poetry Month? M x