## Is That a Math Poem in Your Pocket?

*This is a guest post by Becky Jaffe.*

Today is National Poem in your Pocket Day, a good day to wear extra pockets.

April also just so happens to be National Poetry Month and Mathematics Awareness Month. Good gods, such abundance! In celebration of the marriage of the left and right hemispheres of the brain, I bring you a selection of poems dedicated to the fine art of mathematics – everything from the mystical to the sassy. Enjoy!

——

from *Treatise on Infinite Series* by Jacob Bernoulli

Even as the finite encloses an infinite series

And in the unlimited limits appear,

So the soul of immensity dwells in minutia

And in narrowest limits no limits inhere.

What joy to discern the minute in infinity!

The vast to perceive in the small, what divinity!

——

*Biblical PI*

A Biblical version of pi

Is recorded by some unknown guy

In “Kings,” * where he mentions

A basin’s dimensions —

Not exact, but a pretty good try.

* I Kings 7:23

——

*Sir Isaac Newton* by Paul Ritger

While studying pressures and suctions,

Sir Isaac performed some deductions,

“Fill a mug to the brim, it

Will then reach a limit,

So easily determined by fluxions.”

——

*A New Solution to an Old Problem* by Eleanor Ninestein

The Topologist’s child was quite hyper

‘Til she wore a Moebius diaper.

The mess on the inside

Was thus on the outside

And it was easy for someone to wipe her.

——

*Threes* by John Atherton

I think that I shall never c

A # lovelier than 3;

For 3 < 6 or 4,

And than 1 it’s slightly more.

All things in nature come in 3s,

Like … , trio’s, Q.E.D.s;

While $s gain more dignity

if augmented 3 x 3 —

A 3 whose slender curves are pressed

By banks, for compound interest;

Oh, would that, paying loans or rent,

My rates were only 3%!

3² expands with rapture free,

And reaches toward infinity;

3 complements each x and y,

And intimately lives with pi.

A circle’s # of °

Are best ÷ up by 3s,

But wrapped in dim obscurity

Is the square root of 3.

Atoms are split by men like me,

But only God is 1 in 3.

——

*Valentine*

You disintegrate my differential,

You dislocate my focus.

My pulse goes up like an exponential

whenever you cross my locus.

Without you, sets are null and void —

so won’t you be my cardioid?

——

*An Integral Limerick* by Betsy Devine and Joel E. Cohen

Here’s a limerick —

Which, of course, translates to:

Integral z-squared dz

from 1 to the cube root of 3

times the cosine

of three pi over 9

equals log of the cube root of ‘e’.

——

*PROF OF PROFS* By Geoffrey Brock

I was a math major—fond of all things rational.

It was the first day of my first poetry class.

The prof, with the air of a priest at Latin mass,

told us that we could “make great poetry personal,”

could own it, since poetry we memorize sings

inside us always. By way of illustration

he began reciting Shelley with real passion,

but stopped at “Ozymandias, King of Kings;

Look on my Works, ye Mighty, and despair!”—

because, with that last plosive, his top denture

popped from his mouth and bounced off an empty chair.

He blinked, then offered, as postscript to his lecture,

a promise so splendid it made me give up math:

“More thingth like that will happen in thith clath.”

——

The last poem in today’s guest post is by a mathematician who proved the Kissing Circles Theorem, which states that if four circles are all tangent to each other, then they must intersect at six distinct points. Frederick Soddy wrote up his proof in the form of a poem, published in 1936 in Nature magazine.

*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.

in Nature, June 20, 1936

——

The publication of this proof was followed six months later with an additional verse by Thorold Gosset, who generalized the case.

*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.

in Nature, January 9, 1937.

——

This was further amended by Fred Lunnon, who added a final verse:

*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.

——

These three raised the bar for presentation of mathematical proof and dialogue, throwing down the gauntlet to modern mathematicians to versify their findings. Who, dear readers, is up for the challenge?

Happy Poem in Your Pocket Day!

No new mathematical findings, but you might enjoy my poem, Imaginary Numbers Do the Trick.

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Delicious. Thanks!

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Having to teach poetry in summer school as a math teacher, I made up the following poem for myself when teaching the “5 senses” poem structure:

The 5 senses of Mathematics

Algebra looks like an unknown language

Geometry feels like a dimensional shift

Arithmetic smells like the sum of all the differences in Crayon colors

Calculus sounds like waves crashing like a sine of the times on the limit of the shore

Pi tastes like a never-ending irrational sweetness.

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Liz, I love that!

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Geoffrey Brock’s sonnet is a favorite of mine — it and several other of his poems may be found online at the Poetry Foundation website.

Here is a small (abecedarian) math poem of mine:

ABC by JoAnne Growney

Axes beget coordinates,

dutifully expressing

functions, graphs,

helpful in justifications,

keeping legendary mathematics

new or peculiarly quite rational

so that understanding’s visual

with x, y, z.

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Here’s a data science-y one (not pure maths, do forgive) — credit Cezary Podkul and Lewis Carrol:

`Twas fixed, and the slithy widths

Did gyre and gimble in the text file:

All mimsy were the headers,

And the file paths outdated.

“Beware the Fixiewock, my son!

The line endings that bite, the indentations that catch!

Beware the Footnote bird, and shun

The frumious Text-to-columns-snatch!”

He took his parsal Python in hand:

Long time the .txt foe he sought —

So rested he by the Regular Expression tree,

And stood awhile in UltraEdit.

And, as in CSVish thought he stood,

The Fixiewock, with special characters of lame,

Came whiffling through the hacky scraper,

And errbled as it came!

One, two! One, two! And through and through

The parsal script went snicker-snack!

He left it dead, and with its output

He went piping back.

“And, has thou slain the Fixiewock?

Come to my arms, my tired boy!

O frabjous day! Callooh! Callay!’

He exclamation-separated his values in his joy.

`Twas fixed, and the slithy widths

Did gyre and gimble in the text file:

All mimsy were the headers,

And the file paths outdated.

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These poem are very inspirational. Thanks for such way to show that math is in everything.

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What exactly are the hypotheses of the Four Circles Theorem? Circles with centres (4,0), (3,0), (2,0) & (1,0) and radii 4, 3, 2 & 1 meet at exactly one point.

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Maybe the hypothesis is that only two circles are permitted to pass through a point of tangency – “for a pair of lips to kiss”? So if we start with three mutually tangent circles, with no point in common to all three, then when we invert (in any arbitrary circle centered) at a point of tangency, only two of the initial three circles turn into (parallel) lines, the other circle inverts to a circle (call it C) and not a line, and it seems apparent (in the inverted picture) that given two parallel lines and the circle C tangent to them, there are only TWO (- this is part of Soddy’s claim) choices for a fourth circle (or a priori, line) to be tangent to the two parallel lines and the circle C.

In your (Jorgen Harmse) example, if we invert at the origin, then all your circles get inverted to parallel lines. If we take three of those lines, then we see that there are no honest circles (as opposed to lines) that are tangent to all three lines, and so the only way a circle in the original picture can be tangent to all three circles is if it inverts to a line parallel to the three parallel lines – and there are of course infinitely many choices for the fourth parallel line (of which your example is one), in contrast to just two in the situation in the previous paragraph.

In the poem Soddy also gives a relation between the curvature of the four circles, and presumably that equation could also be referred to as part of the kissing circles theorem, but I don’t know – I don’t work in this area, I just attend the university of wikipedia.

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this is AWESOME

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this has helped me in every way

and i like cake

i know this does not rhyme at all

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