# Glimpses 1

### From Rhaworth

## Glimpses of History: Olden Times

### by *Martin Huxley*

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)

"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. (thanks to K.M. SCHMIDT)

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. (thanks to NARKIEWICZ)

"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 3n + 1". (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 algeî". (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)