Glimpses 1

From Rhaworth

Glimpses of History: Olden Times

First 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)

\medskip

\goodbreak

"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)

\medskip

\goodbreak

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)

\medskip

\goodbreak

The pentagon HIPPASOS saw Has a small one inside when you draw

The diagonal lines.

Repetition defines

The irrational nature of tau. (thanks to K.M. SCHMIDT)

\medskip

\goodbreak

Doctor EUCLID the mathematician Was also a noted magician.

While hymning to Demeter

He proved several lemmata,

And almost invented division. (about 300BC)

\medskip

\goodbreak

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. (thanks to NARKIEWICZ)

\medskip

\goodbreak

"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)

\medskip

\goodbreak

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)

\medskip

\goodbreak

"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)

\medskip

\goodbreak

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 $3n + 1$". (212BC; the `Syracuse Algorithm')

\medskip

\goodbreak

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)

\medskip

\goodbreak

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)

\medskip

\goodbreak

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)

\medskip

\goodbreak

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)

\medskip

\goodbreak

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)

\medskip

\goodbreak

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)

\medskip

\goodbreak

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".

\medskip

\goodbreak

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.

\medskip

\goodbreak

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 alge\^i". (AL-KHOWRIZMI, about 825)

\medskip

\goodbreak

The son of BONACCIO knew What one pair of rabbits can do,

Their awful potential

To grow exponential,

First England, Australia too. (FIBONACCI 1202)

\medskip

\goodbreak

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)

\medskip

\goodbreak

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)

\medskip

\goodbreak

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)

\medskip

\goodbreak

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)

\medskip

\goodbreak

Has the magic departed from squares Since D\"URER depicted black cares?

No emperor paces,

No astrologer traces,

No lawgivers leap from their chairs. (1514; MINGTANG, KEPLER, FRANKLIN) </poem>