**1**by Peter Goldsworthy

Arithmetic divides

and rules the world,

freezing the flow

in single frames,

colourising each

by numbers.

Mathematical language can heighten the imagery of a poem; mathematical structure can deepen its effect. Feast here on an international menu of poems made rich by mathematical ingredients . . . . . . . gathered by JoAnne Growney.

An Australian poet (Erica Jolly) whom I have met through this blog has helped me to learn about the great variety of poetry and related activities that are available on her continent -- and today I want to link you to the Australian Poetry Library and to offer a mathy poem by Peter Goldsworthy that I enjoyed there.

** 1 ** by Peter Goldsworthy

Arithmetic divides

and rules the world,

freezing the flow

in single frames,

colourising each

by numbers.

Arithmetic divides

and rules the world,

freezing the flow

in single frames,

colourising each

by numbers.

Here are the titles and dates of blog postings during January 2016.

For mathy poems related to a particular topic -- such as *women in math* or *black history *or **climate **or **triangle** or **circle** or **Groundhog Day** or **Valentine **or **. . . **-- enter the desired term in the **SEARCH** box in the right-hand column.

Jan 23 Not good at math . . .

Jan 21 Math Anxiety

In geometry, Napoleon's theorem (often attributed to Napoleon Bonaparte, 1769–1821) states that if equilateral triangles are constructed on the sides of any triangle, either all outward or all inward, the centers of those equilateral triangles themselves are the vertices of an equilateral triangle. In a 2015 lecture at the University of Maryland, mathematician Douglas Hofstadter (perhaps best known for *Godel, Escher, Bach: an Eternal Golden Braid* -- Basic Books, 1970) presented Napoleon’s theorem by means of a sonnet. Perhaps you will want to have pencil and paper available to draw as you read:

**Napoleon's Theorem ** by Douglas Hofstadter

Equilateral triangles three we’ll erect

Facing out on the sides of our friend ABC.

We’ll link up their centers, and when we inspect

These segments, we find tripartite symmetry.

Equilateral triangles three we’ll erect

Facing out on the sides of our friend ABC.

We’ll link up their centers, and when we inspect

These segments, we find tripartite symmetry.

Labels:
center,
centroid,
Douglas Hofstadter,
equilateral,
Napoleon's Theorem,
symmetry,
triangle

Thanks to mathemagician Colm Mulcahy who connected me with poet Lisa Dordal -- and thanks to her for permission to offer these lines, entertainingly seasoned with math words:

**Why Rabbis Need to Know **

**How to Solve Quadratic Equations **

for your logic muscles, which you’ll need

to work through those pesky J says-P says conflicts of text –-

the bumpy remains of a Torah affair.

by Lisa Dordal (with help from Laurie Samuels)

Because they are good exercise for your logic muscles, which you’ll need

to work through those pesky J says-P says conflicts of text –-

the bumpy remains of a Torah affair.

Labels:
Com Mulcahy,
equation,
factoring,
formula,
Lisa Dordal,
logic,
quadratic,
rabbi,
Torah

Mathematical historians now credit both Cardano and Tartaglia with the formula to solve cubic equations, referring to it as the
"Cardano-Tartaglia Formula." Tartaglia is known for reporting solutions of three different forms of the cubic equation in a poem (1534). Below we offer Boston poet Kellie Gutman's English translation of Tartaglia's verse, followed by the original Italian.

**When X Cubed ** by Niccolò Tartaglia (1500–1557) (Englished by Kellie Gutman)

When x cubed’s summed with m times x and then

Set equal to some number, a relation

Is found where r less s will equal n.

Now multiply these terms. This combination

rs will equal m thirds to the third;

This gives us a quadratic situation,

When x cubed’s summed with m times x and then

Set equal to some number, a relation

Is found where r less s will equal n.

Now multiply these terms. This combination

rs will equal m thirds to the third;

This gives us a quadratic situation,

Labels:
Cardano,
cubic,
equation,
Italian,
Kellie Gutman,
Mathematical Intelligencer,
solve,
Tartaglia

Connecticut poet Joan Cannon is a senior who laments her lingering anxiety over mathematics in her poem, "Humility," below. I found Cannon's poem on Senior Women Web and it is accompanied there by selections from an article by Patrick Bahls entitled "Math and Metaphor: Using Poetry to Teach Mathematics." The complete article is available here.

** Humility ** by Joan L. Cannon

Archetypes, mysteries, simple clues

that only fingers and toes, sticks and stones

and flashes of inspiration require

for universes to be disclosed ...

symbols for functions and formulae

for proof; logic so easy for some —

why am I innumerate?

Archetypes, mysteries, simple clues

that only fingers and toes, sticks and stones

and flashes of inspiration require

for universes to be disclosed ...

symbols for functions and formulae

for proof; logic so easy for some —

why am I innumerate?

Labels:
conversation,
innumerate,
Joan Cannon,
logic,
math anxiety,
Patrick Bahls

Recent comments from a friend describing anxiety that seems to freeze his attempts to understand and use a new mathematical concept have caused me to recall and dig out this old poem -- and, by recalling it, to increase my understanding of my friend.

** The Math Teacher's Golf Lesson ** by JoAnne Growney

My practice swing was perfect -- slow start, easy

acceleration through the ball to finish high.

"Beautiful," he said. "It's time to hit a few."

I addressed a ball and settled down and swung --

and missed. "Concentrate," he said. I squinted

My practice swing was perfect -- slow start, easy

acceleration through the ball to finish high.

"Beautiful," he said. "It's time to hit a few."

I addressed a ball and settled down and swung --

and missed. "Concentrate," he said. I squinted

Labels:
golf,
math anxiety,
practice,
student,
teacher

For even more poetry related to the love-holiday, enter "Valentine" in the SEARCH box to the right. Enjoy!

In an earlier post I have noted how effectively mathematicians and their mathematics may be described by poets who are in the same family. This link, too, leads to portraits of mathematicians.

Poet and novelist John Updike (1932-2009) was the son of a math teacher and the selection below is a sonnet that begins in the style of a math-class word-problem linking his own age with that of his father.

from**Midpoint ** by John Updike

FATHER, as old as you when I was four,

I feel the restlessness of nearing death

But lack your manic passion to endure,

Your Stoic fortitude and Christian faith.

Remember, at the blackboard, factoring?

Poet and novelist John Updike (1932-2009) was the son of a math teacher and the selection below is a sonnet that begins in the style of a math-class word-problem linking his own age with that of his father.

from

FATHER, as old as you when I was four,

I feel the restlessness of nearing death

But lack your manic passion to endure,

Your Stoic fortitude and Christian faith.

Remember, at the blackboard, factoring?

Labels:
blackboard,
factoring,
John Updike,
midpoint,
teacher

Irish mathematician William Rowan Hamilton (1805-1865) was also a poet (see, for example, this sonnet in a prior posting (13 October 2011). Irish poet and physicist Iggy McGovern has written *A Mystic Dream of 4: A sonnet sequence based on the life of William Rowan Hamilton *(Quaternia Press, 2013).

Here is McGovern's opening sonnet.

**GEOMETRY ** by Iggy McGovern

Once, any pupil could define me best:

"points, lines, angles and figures", could amuse

The table with the Christmas cracker jest

About 'the squaw' on the hypotenuse!

The collection is prefaced by this quote from Hamilton:

"The quaternion [was] born,

as a curious offspring of a quaternion of parents,

say of geometry, algebra, metaphysics, and poetry."

Once, any pupil could define me best:

"points, lines, angles and figures", could amuse

The table with the Christmas cracker jest

About 'the squaw' on the hypotenuse!

British poet Wendy Cope frequently includes edgy humor in her poems (*s*he is, indeed, a prizewinner in *light verse*) -- and I like that. In the poem below (found at PoetryFoundation.org and originally published in *Poetry* in 2006), Cope examines arguments of whether our world is flat or round. Part 2 of the poem involves the interesting permutation pattern that is called a *pantoum* (Lines 2 and 4 of each four-line stanza are repeated (approximately) as lines 1 and 3 of the next stanza -- and the final stanza is wrapped into the first).

**Differences of Opinion ** by Wendy Cope

1 HE TELLS HER

He tells her that the earth is flat --

He knows the facts, and that is that.

In altercations fierce and long

She tries her best to prove him wrong,

But he has learned to argue well.

He calls her arguments unsound

And often asks her not to yell.

She cannot win. He stands his ground.

The planet goes on being round.

1 HE TELLS HER

He tells her that the earth is flat --

He knows the facts, and that is that.

In altercations fierce and long

She tries her best to prove him wrong,

But he has learned to argue well.

He calls her arguments unsound

And often asks her not to yell.

She cannot win. He stands his ground.

The planet goes on being round.

Labels:
flat,
light verse,
round,
sphere,
Wendy Cope,
world

Each day's email brings me a Poem-a-Day from Poets.org and today's selection by Matthew Olzmann considers the tragedies from gun-violence in our news too often these days. Numbers are "objective" -- and count those who watch and grieve as well as the guns and shooters -- or are they? Here is an excerpt from Olzmann's poem, "Letter Beginning with Two Lines by Czesław Miłosz":

. . . Did I say

I had “one” student who

opened a door and died?

That’s wrong.

There were many.

The classroom of grief

. . . Did I say

I had “one” student who

opened a door and died?

That’s wrong.

There were many.

The classroom of grief

Labels:
count,
Czeslaw Milosz,
gun,
math,
Matthew Olzmann,
objective,
Poem-a-Day,
Poets.org

For one of my granddaughters who likes poems, I recently purchased *If You're Not Here, Please Raise Your Hand: Poems about School *by Kalli Dakos (Aladdin Paperbacks, 1995). It's hard to find school poems that are non-critical of math -- but this one, at least, has some rhyming fun while cooking it.

**Math is Brewing and I'm in Trouble ** by Kalli Dakos

Numbers single,

Numbers double,

Math is brewing

And I'm in trouble,

If I could mix a magic brew,

Numbers, I'd take care of you.

Numbers single,

Numbers double,

Math is brewing

And I'm in trouble,

If I could mix a magic brew,

Numbers, I'd take care of you.

Labels:
Kalli Dakos,
magic,
multiplied,
numbers,
rhyme

If you wish to easily BROWSE past postings . . .

Dec 31 Precision leads to poetry . . .

Dec 28 Can a woman learn science (or mathematics)?

Dec 24 And now welcome Christmas . . .

Dec 22 Let us not forget . . .

Dec 20 Who put the pie in Pythagoras?

Dec 18 A student writes poetry for a math class . . .

Dec 15 Generalized Pythagorean Theorem--a visual poem?

As the year ends, a quote from one of my once-favorite authors, Don DeLillo (in correspondence with David Foster Wallace -- whose *Infinite Jest* is on my to-read list), earlier offered by Jordan Ellenberg in Quomodocumque.

**Quoting DeLillo: **

Once, probably, I used to think that vagueness

was a loftier kind of poetry, truer

to the depths of consciousness, and maybe

when I started to read mathematics and science

back in the mid-70s I found an unexpected lyricism

in the necessarily precise language

that scientists tend to use.

My instinct, my superstition

is that the closer I see a thing

and the more accurately I describe it,

the better my chances of arriving

at a certain sensuality of expression.

And at the BrainyQuotes website is this quote (and many others) by DeLillo (and many others).

**HAPPY NEW YEAR! **

Once, probably, I used to think that vagueness

was a loftier kind of poetry, truer

to the depths of consciousness, and maybe

when I started to read mathematics and science

back in the mid-70s I found an unexpected lyricism

in the necessarily precise language

that scientists tend to use.

My instinct, my superstition

is that the closer I see a thing

and the more accurately I describe it,

the better my chances of arriving

at a certain sensuality of expression.

And at the BrainyQuotes website is this quote (and many others) by DeLillo (and many others).

For me, writing is a concentrated form of thinking.

It is not a new idea that women do not have scientific aptitude, that teaching them requires special accommodation. Here, in a poem by one of the greatest scientists of all time, is a description of a condescending lecture to a female student, individually and behind a curtain, followed by her mocking reply.

**Lectures to Women on Physical Science ** by James Clerk Maxwell (1831-79)

**I. ** PLACE. —*A small alcove with dark curtains. *

* The class consists of one member. *

SUBJECT.—*Thomson’s Mirror Galvanometer. *

The lamp-light falls on blackened walls,

And streams through narrow perforations,

The long beam trails o’er pasteboard scales,

With slow-decaying oscillations.

Flow, current, flow, set the quick light-spot flying,

Flow current, answer light-spot, flashing, quivering, dying.

SUBJECT.—

The lamp-light falls on blackened walls,

And streams through narrow perforations,

The long beam trails o’er pasteboard scales,

With slow-decaying oscillations.

Flow, current, flow, set the quick light-spot flying,

Flow current, answer light-spot, flashing, quivering, dying.

(a version of)

The twelfth day of Christmas.

My true love gave to me,

Twelve lords a leaping,

Eleven ladies dancing,

Ten pipers piping,

Nine drummers drumming,

Eight maids a milking,

Seven swans a swimming,

Six geese a laying,

Five golden rings,

Four colly birds,

Three French hens,

Two turtle doves,

And a partridge in a pear tree.

To learn some history of this song (and its variations), frequently sung as a cumulative marathon, see Wikipedia.

At this time of year in the Northern Hemisphere, many are without shelter -- and are cold. Let us think of them -- as Cecil Day-Lewis (1904-1972) does in "A Carol" below (a poem whose lines for the most part maintain an alternating 6-5 syllable count and which contains the small number *two*). **Let us remember to share our warmth.**

** A Carol ** by Cecil Day-Lewis

Oh hush thee, my baby,

Thy cradle's in pawn:

Oh hush thee, my baby,

Thy cradle's in pawn:

Irish poet and physicist Iggy McGovern
has written both humorous and serious verse. Today we have lines from him that startle and amuse -- below I present, with his permission, selections from his collection *Safe House* (Dedalus Press, 2010). Here are "Belfast Inequalities" and "Proverbs for the Computer Age":

**Belfast Inequalities ** by Iggy McGovern

*for Master Devlin*

Who put the pie in Pythagoras,

who put the bra in algebra

and who was the first to say: Let x

be that unknown quantity in sex?

the answer's in some chromosome

and not the sums you do at home

Who put the pie in Pythagoras,

who put the bra in algebra

and who was the first to say: Let x

be that unknown quantity in sex?

the answer's in some chromosome

and not the sums you do at home

Labels:
algebra,
blog,
geek,
Iggy McGovern,
inequalities,
proverbs,
Pythagoras

A recent fun experience for me has been correspondence with Melanie Simms, a poet and math student at Pennsylvania's Bloomsburg University, where I taught for a bunch of years. Melanie recently completed the course "Mathematical Thinking" -- a course that I helped to develop during my years at BU and one for which I wrote a textbook (*Mathematics in Daily Life: Making Decisions and Solving Problems*, McGraw-Hill, 1986). The course was developed to offer general quantitative skills for students majoring in fields (such as English or Art) that do not have a specific mathematics requirement. Melanie's instructor for the course, Paul Loomis, is a singer and songwriter and, with him as first reader, Melanie composed a mathematical poem involving course material. She has shared the poem with me and has given me permission to post it here.

** The Mathematics of Chance** by Melanie Simms

The gods of chance

Have left me skewed

My distribution, variable!

With ranges far, and ranges wide

My navigation's terrible!

The gods of chance

Have left me skewed

My distribution, variable!

With ranges far, and ranges wide

My navigation's terrible!

While thinking about my December 13 posting featuring work by Richard Kostelanetz -- visual poetry with numbers -- I was browsing a fascinating book by Ivan Moscovich, *The Puzzle Universe: A History of Mathematics in 315 Puzzles* (Firefly Books, 2015) and came to the following diagram*. *I offer it as a visual poem.

In addition to the squares, what other areas constructed on the sides of a right triangle may be correctly summed to give a third area of the same shape? |

Labels:
history,
Ivan Moscovich,
puzzle,
Pythagorean Theorem,
visual poetry

I have a good friend who does not care for the sorts of poetry that are written today. When I asked what he likes he cited "When I Was One-and-Twenty" by A E Housman (1859-1936) and the sonnet "Ozymandias" by Percy Bysshe Shelley (1792-1822). My own preferences in poems, on the other hand, are less certain. I like to explore, to discover what new things may be said within new forms and constraints. The following selection, "Notes on Numbers" by Richard Kostelanetz, introduces some of the ideas that this artist/writer/critic explores in his visual poetry -- with numbers -- examples of which are available through links offered at the end of this posting.

**Notes on Numbers** by Richard Kostelanetz

Labels:
arithmetic,
art,
number,
numeracy,
numeral,
numerate,
Richard Kostelanetz,
visual poetry

Since the late 1960s Toronto poet Victor Coleman has been energetically committed to innovated poetic practices. A fine introduction to this poet is offered by Alex Porco in this linked review of Coleman's recent book, *ivH: An Alphamath Serial *(Book Thug, 2010).

*i**vH: An Alphamath Serial* is a book-length poem composed in the tradition

of such precursors as Pythagoras, who taught that Number was the essence of all things;

Plato, who argued that geometry was the foundation of
all knowledge;

Labels:
4,
8,
Alex Porco,
alphamath,
concrete poetry,
Victor Coleman

"Bhaskara II (1114-1185) was an Indian mathematician and astronomer. He composed the *Siddhanta Siromani*, a treatise in four parts -- *Lilavati *(basics), *Bijaganita* (algebra), *Grahaganita *(planetary motion) and *Goladhyaya *(spheres)."

This quotation comes from an early page of a new (2015) graphic e-book entitled*The Illustrated Lilavati* -- the text is based on a 1816 John Taylor translation, edited and illustrated for lilboox by Somdip Datta and available for download on smartphones and other devices. *Lilavati *(named for the daughter of Bhaskara) was written in 1150 and was a standard textbook for arithmetic in India for many years.

This e-book contains 25 illustrated problems (and solutions); here is the first:

This quotation comes from an early page of a new (2015) graphic e-book entitled

This e-book contains 25 illustrated problems (and solutions); here is the first:

Labels:
algebra,
arithmetic,
Bhaskara,
graphic novel,
India,
Lilavati,
Somdip Datta

When I began this blog in 2010, I imagined up to 100 postings -- I saw it as a way to share math-related poetry that I had written and gathered during my years of teaching. Now, as I prepare my 748th post, I am thinking about how I can organize my posts to make them findable and useful to the reader who visits and browses herein.

One thing that I have recently done is to update the blog's searchability --

If you enter a term like "**math**" into the box, the search finds most of the posts in the entire blog and is thus not very helpful -- but you might try the term "**triangle**" and you would find about 20 relevant posts; one of them (from October 13, 2010) has the title "Varieties of triangles -- by Guillevic" and is the most-visited entry herein. If you are, like me, someone who looks for math publicity and opportunities for girls, you may choose to enter "**girl**" in the search box. This search, too, will lead to about 20 postings.

Labels:
Blaise Pascal,
girl,
Guillevic,
mathematicians,
poets,
search,
triangle

For a long time I have highly valued the work of Eastern European poets -- including Wislawa Szymborska, Miroslav Holub, Nichita Stanescu, Nina Cassian -- and have been pleased to find mathematical imagery in their work. Early in November I had the privilege of attending a reading at the Goethe-Institut Washington that featured Slovenian poet Aleš Šteger -- born in 1973, winner of many awards, and described as the most translated Slovenian author of his generation. A fun event -- from which I give you one of his slightly-mathematical offerings.

** Hat ** by Aleš Šteger (trans. Brian Henry)

Who lives under the hat?

Under the hat, which are three?

Three hats.

Who lives under the hat?

Under the hat, which are three?

Three hats.

This week started with the excitement of an email message from Evelyn Lamb with a link to her *Scientific American* blog where she created a fun-to-take online poetry-math quiz based on an idea of mine (first published in 1992):

**Can **__you__ tell the difference between mathematics and
poetry?
**Here’s a link to a SCIENTIFIC AMERICAN quiz to help you
decide?**

And a couple of centuries ago there was William Wordsworth -- who also contemplated both poetry and mathematics:

And a couple of centuries ago there was William Wordsworth -- who also contemplated both poetry and mathematics:

On poetry and geometric truth

and their high privilege of lasting life,

From all internal injury exempt,

I mused; upon these chiefly: and at length,

My senses yielding to the sultry air,

Sleep seized me, and I passed into a dream.

*The Prelude*, Book 5

and their high privilege of lasting life,

From all internal injury exempt,

I mused; upon these chiefly: and at length,

My senses yielding to the sultry air,

Sleep seized me, and I passed into a dream.

William Wordsworth (1770-1850)

Labels:
Evelyn Lamb,
geometry,
mathematics,
poetry,
quiz,
Scientific American,
William Wordsworth

The following poem is by Erica Jolly -- an Australian poet and retired teacher who is working hard to have the arts and the sciences integrated in Australian schools curricula. “For too long, since the 1950s, we have witnessed serious losses across
disciplines as science and mathematics have been deliberately separated
from the arts and humanities,” Ms Jolly says.

**"What has sustainability got to do with mathematics?" ** by Erica Jolly

Does he not know or care

humankind must measure?

An exclamation attacking interdisciplinary themes in the national curriculum

by Christopher Pyne on Q & A, 28 October 2013.

Does he not know or care

humankind must measure?

Labels:
Australia,
Christopher Pyne,
Erica Jolly,
measure,
STEAM,
STEM,
sustainabilty

I do not know what

I may appear to the world;

but to myself I seem to have been

only like a boy playing on the seashore,

and diverting myself now and then

finding a smoother pebble

or a prettier shell than ordinary,

whilst the great ocean of truth

lay all undiscovered before me.

-Isaac Newton, philosopher and mathematician (1642-1727)

Today in a Facebook posting by Susanne Pumpluen

I learned of *Discov-her*,
an online journal

featuring stories about women in Science.

* * *

The following poetry offering is by Richard Smyth who has written a parody of an introduction to the mathematics of logic (specifically I invite you to enjoy this play of words and ideas:

It shall be taken as given the idea of infinition. The idea of infinition stands in direct opposition to the idea of definition.

Infinition is the act of making indefinite or unclear. That is to say, while some uses of language attempt to clarify, others attempt to obfuscate.

Make a poem.

Labels:
axiom,
definition,
Discov-her,
form,
infinition,
mathematics,
poem,
poetry,
Richard Smyth,
Spencer Brown,
Susanne Pumpluen

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