The Kiss Precise by Frederick Soddy
For pairs of lips to kiss maybe
Involves no trigonometry.
'Tis 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 from 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.
Published in Nature, June 20, 1936
10 comments:
The sketch and poem depict and describe Descartes' theorem
And Soddy was one interesting dude.
Everytime I turn around there's more ionic radii ... which cations can fit between which three anions in an ionic polyhedral? Why is Na seemingly interchangeable with K?
Huh?
Synova: size does matter
Alternatively, matter does size.
Nude fat woman lying face down on photocopier.
Palladian, I was thinking more Disney thoughts.
Rudolph the Red-Nosed Reindeer in the vacuum of space.
Ronald McDonald in a chocolate grinder, simplified plan view.
Rope handlers view of Macy's Thanksgiving Obama balloon. It's a bit distorted right now because it's bashing into buildings ripping out lamp posts.
2D projection of Bissage's avatar
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