### A Ton of Wonders

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.