Every number is interesting. Suppose there were uninteresting numbers. Then there would be a smallest one. But this is an interesting property, contradicting the supposition. By *reductio ad absurdum*, there are none!

This is the hundredth “That’s Maths” article to appear in *The Irish Times* [TM100, or search for “thatsmaths” at irishtimes.com]. To celebrate the event, we have composed an ode to the number 100.

** A Ton of Wonders**

The number familiarly known as a ton

Comprises two zeros appended to one.

It holds, in its five score of units, great store

Of marvel and mystery and magic and more.

Take 1, 2, 3, 4; add them up to make 10.

Then square to one, zero and zero again.

Now square 1, square 7 and double the deuce;

The four squares together one hundred produce.

Pythagoras knew, with sides 6, 8 and 10,

A trigon would have a right angle and then,

The squares of the 6 and the 8 being paired,

Make a century for the hypotenuse squared.

The cubes of the first four whole numbers combine

To total one hundred, and not ninety-nine.

With Goldbach to guide us, a century splits

as a sum of two primes, with a half-dozen fits.

The nine smallest primes up to twenty-and-three

Will sum to precisely a ton, you’ll agree.

Now add all odd numbers from 1 to 19:

A sum of a centum again will be seen.

A number is ‘Leyland’ if *m* to the *n*

Plus *n* to the *m* gives the number again.

One hundred is such, as we easily shew,

When *m* equals 6, and *n* equals 2.

One hundred is thrice thirty-three-and-a-third

With many more forms that are much more absurd:

Take a ton from its square: then the iterate root

Brings you back to one hundred without any doubt.

A ton can be made from irrationals too

And even the powers of transcendents will do:

One hundred is *e* plus the fourth power of *π*

(albeit this estimate’s slightly too high).

And what of partitions? Of sums there are more

than one-ninety million to make up five score.

This number produces, when broken asunder,

A cornucopia of wealth and of wonder.

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