Glimpses of History: Olden Times
editby Martin Huxley
editFirst traces of Maths that we find,
Old bones in a cave left behind,
With patterns of nicks,
Babylonian tricks,
And the fruitful Papyrus of Rhind.
We don't have a board game of Thera's'
Chaturanga's from subsequent eras,
But a race game is known,
Bets and dice being thrown,
And its catchphrase, `Apekho s'ap'hieras!'.
[I take you off the Sacred Way. Chaturanga gave rise to chess and cards. The Drowned City of Thera is one source of the Atlantis story.]
"The squares on the legs as a pair
Add up to the underside square,"
But PYTHAGORAS' battle,
Root two is irrat'l,
No cattle were sacrificed there. (about 550BC)
"What ratio seen in the square
Does the side to diagonal bear?
Can the numbers of GOD
Be both even and odd?"
Impetuous student, beware! (about 550BC)
PYTHAGORAS' numbers were wholes
With losable, breathable souls,
And the student who knew
About square root of two
Was sent down, charged with kicking own goals. (about 550 BC)
The pentagon HIPPASOS saw
Has a small one inside when you draw
The diagonal lines.
Repetition defines
The irrational nature of tau. [1]
Doctor EUCLID the mathematician
Was also a noted magician.
While hymning to Demeter
He proved several lemmata,
And almost invented division. (about 300BC)
So EUCLID's first proof was acquired
By assumption of what was desired:
"Either a or else b
Is a product of p."
There's a modern text equally mired. [2]
"Did they make something fake for a crown?
It would take sort of `density' down…
I've found it! Heureka!"
He ran as a streaker
From his bath through the town with no gown. (ARCHIMEDES)
Was bubble bath known to the Greeks?
ARCHIMEDES relaxes and seeks
An assay for the crown,
Blowing foam up and down…
He'd've not found the answer for weeks. (about 220BC)
"Consider the flocks of the sun…"
Was how ARCHIMEDES begun.
For counting the fleeces,
Even ant'hyp'hairesis
Leaves plenty of work to be done. (about 220BC)
The ancient Sicilian Don,
ARCHIMEDES, could be living on.
When his life should be spared,
He went: "Halve it if paired,
If unpaired, go to ". (212BC; the 'Syracuse Algorithm')
When forming an area mapping
With tangents and segments and capping,
The historical Greeks
Were constrained in techniques:
They had to avoid overlapping. (thanks to ROGERS)
How the Emperors exercise might,
What the West calls the move of a knight:
Tread the Paces of Yu
Around the Lo Shu
Magic square, South to North, left to right. (MING TANG 23)
LIU HUI, a name to recall,
Got pi with an error that's small.
He was able to vary a
Treatment of area
So triangles fill almost all. (about 300; thanks to ROGERS)
DIOPHANTUS's book: if you buy it,
Twelve chapters, then everything's quiet;
HYPATIA's edition
Cut short by sedition,
With the editor killed in a riot. (415)
The inscrutable Chinaman SSUN TSU
Gave a rule for when someone presents two
Remainder conditions
With co-prime divisions.
You pronounce him however you wants to. (about 450; but see CHIN CHIU-SHAO)
When you look for a name for your thesis
On how to take numbers to pieces,
There's more satisfaction
From "cut-taker fraction"
Than original "ant'hyp'hairesis". (BHATTACHARYA, EUDOXUS)
The story of solving the PELL:
The Greeks had techniques, but they fell.
BHATTACHARYA was random,
Then BHASKARA tandem;
Till LAGRANGE, "if it works, all is well".
A merchant asleep in his tent
At a halt on the road to Tashkent
Awoke from his slumbers
With negative numbers,
So, rather than coming, he went.
He set Algebra off on its way,
But the name AL-GORITHMI today
Was taken in vain
As "Maths is a pain",
In Greek "ho arithmos algeï". (AL-KHOWRIZMI, about 825)
The son of BONACCIO knew
What one pair of rabbits can do,
Their awful potential
To grow exponential,
First England, Australia too. (FIBONACCI 1202)
CHIN CHIU-SHAO fulfilled many goals,
Wrote a Treatise on Maths in nine scrolls;
In his elegant library,
Furnished by bribery,
He took wine, women, pork casseroles. (1247)
Who first combined residue classes?
In a country here nothing new passes,
CHIN gave Master SONG
His discovery (Strong
'Proximation), and called for the lasses. (1247)
A name, all the same, what is in?
Consider what happened to CHIN.
Although he attained a
High rank, his remainder
'S `Chinese', with no credit to him. (1247)
Was Madhava first to define
The series for cosine and sine?
Such command of technique!
In the land of the leek,
In his name, ev'ry week, let us dine! (at the Madhav; about 1400)
Has the magic departed from squares
Since DÜRER depicted black cares?
No emperor paces,
No astrologer traces,
No lawgivers leap from their chairs. (1514; MINGTANG, KEPLER, FRANKLIN)
References
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