**The Kiss Precise by Frederick Soddy** For pairs of lips to kiss maybe

Involves no trigonometry.

This not so when four circles kiss

Each one the other three.

To bring this off the four must be

As three in one or one in three.

If one in three, beyond a doubt

Each gets three kisses from without.

If three in one, then is that one

Thrice kissed internally.

Four circles to the kissing come.

The smaller are the benter.

The bend is just the inverse of

The distance form the center.

Though their intrigue left Euclid dumb

There's now no need for rule of thumb.

Since zero bend's a dead straight line

And concave bends have minus sign,

The sum of the squares of all four bends

Is half the square of their sum.

To spy out spherical affairs

An oscular surveyor

Might find the task laborious,

The sphere is much the gayer,

And now besides the pair of pairs

A fifth sphere in the kissing shares.

Yet, signs and zero as before,

For each to kiss the other four

The square of the sum of all five bends

Is thrice the sum of their squares.

The Kiss Precise (generalized) by Thorold Gosset

And let us not confine our cares

To simple circles, planes and spheres,

But rise to hyper flats and bends

Where kissing multiple appears,

In n-ic space the kissing pairs

Are hyperspheres, and Truth declares,

As n + 2 such osculate

Each with an n + 1 fold mate

The square of the sum of all the bends

Is n times the sum of their squares.

The Kiss Precise (Further Generalized) by Fred Lunnon

How frightfully pedestrian

My predecessors were

To pose in space Euclidean

Each fraternising sphere!

Let Gauss' k squared be positive

When space becomes elliptic,

And conversely turn negative

For spaces hyperbolic:

Squared sum of bends is sum times n

Of twice k squared plus squares of bends.

*On August 15, 1936, only a few months after Soddy's poem had been published in Nature, Thorold Gosset sent a copy of the poem to Donal Coxeter on the occasion of his wedding in the Round Church in Cambridge. Gossett enclosed in his wedding congratulations, and extension of the poem to the higher dimensions*http://www.pballew.net/soddy.html **Current Music:** *The Durutti Column-Requiem for A Father*