## Tuesday, July 29, 2014

### Fixing something wrong

If there's something

wrong with the third

act, it's really

in the first act.

This quote from Billy Wilder, Austrian-born writer and film-director (1906-2002), reminds me of a similar observation I have made about my mathematical work -- when a reviewer notes a problem near the end, usually the fix is near the beginning. And so it goes . . .

Labels:
Billy Wilder,
first,
mathematics,
strategy,
third,
wrong

## Sunday, July 27, 2014

### Each equation is a playful catch . . .

A mathematician is probably too close to her subject matter to speak playfully about it -- and thus she, even more than others, appreciates a phrase like "each equation is a playful catch, like bees into a jar," offered by Lisa Rosenberg in the poem below. In "Introduction to Methods of Mathematical Physics," Rosenberg uses a child's anxiety about insects as a way to describe fear of mathematics and offers a smidgen of respect for "those few" who are fearless.

**Introduction to Methods of Mathematical Physics**by Lisa Rosenberg

You must develop a feeling for these symbols

that crawl across a page, for the text overrun

with scorpions. Like those books about insects

you read as a child, scared to touch the magnified photos,

Labels:
equation,
Lisa Rosenberg,
mathematical physics,
mathematics,
playful,
poem,
poetry,
symbol

## Friday, July 25, 2014

### Poems with "equation" in the title

One of the ways to explore this blog is to go to the right hand column and find the instruction,

A few moments ago I did this and entered the word "equation" and found a long list of links, many of the latter ones redundant since they are picking up archive listings of earlier postings. But the early ones can be fun to explore. Here are five of the first six items that the SEARCH BOX produced. And the first two of these links yield poems with "equation" in the title. Enjoy!

**Click here to open a SEARCH BOX for this site.**A few moments ago I did this and entered the word "equation" and found a long list of links, many of the latter ones redundant since they are picking up archive listings of earlier postings. But the early ones can be fun to explore. Here are five of the first six items that the SEARCH BOX produced. And the first two of these links yield poems with "equation" in the title. Enjoy!

Labels:
blog,
equation,
mathematics,
poetry,
search

## Saturday, July 19, 2014

### Mathematicians are not free to say . . .

The poetry of a mathematician is constrained by the definitions she knows from mathematics. Even though all but one of the prime integers is odd, she cannot use the words "prime" and "odd" as if they are interchangeable. She cannot use the words "rectangle" and "box" as synonyms. But the ways that non-math poets dare to engage with math words can be delightful to mathematical ears and eyes. For example:

**The Wasp on the Golden Section**by Katy Didden

Labels:
golden section,
Katy Didden,
mathematics,
odd,
poetry,
prime,
Stephanie Strickland

## Wednesday, July 16, 2014

### Palindromes

Palindromic numbers are not uncommon -- recently (in the July 12 posting) power-of-eleven palindromes are mentioned. Palindromic poems are more difficult to find but see, for example, the postings for October 6, 2010 and October 11, 2010.

At a recent Kensington Row Bookshop poetry reading, Hailey Leithauser revealed that all but one of the poems in her recent collection

*Swoop*(Graywolf Press, 2014) contain a palindrome.And here are a couple of my favorite palindromic phrases:

(the impossible integer)

Never

odd or

even.

odd or

even.

(the mathematician's answer when she is offered cake)

"I prefer pi."

"I prefer pi."

## Saturday, July 12, 2014

### Prove It

After observing that

1 = 1

and 1 + 3 = 4

and 1 + 3 + 5 = 9

and 1 + 3 + 5 + 7 = 16

and 1 + 3 + 5 + 7 + 9 = 25

it seems easy to conclude that, for any positive integer n, the sum of the first n odd integers is n

1 = 1

and 1 + 3 = 4

and 1 + 3 + 5 = 9

and 1 + 3 + 5 + 7 = 16

and 1 + 3 + 5 + 7 + 9 = 25

it seems easy to conclude that, for any positive integer n, the sum of the first n odd integers is n

^{2}.
Labels:
infinite,
integer,
odd,
palindrome,
poem,
power,
proof,
prove,
sum,
William Kloefkorn

## Wednesday, July 9, 2014

### Looking back . . .

I have been visiting my hometown of Indiana, Pennsylvania and not finding time to complete a new post -- and so I have looked back. On July 9, 2010 I offered a sonnet by Australian poet Jordie Albiston that begins with these lines:

might do you watch your world turn to

nought put your foot upon the path re

. . .

I invite you to go to the original post and read the rest.

**math (after)****first you get the number-rush as anyone**might do you watch your world turn to

nought put your foot upon the path re

*what cannot be said*I’ve heard before. . .

I invite you to go to the original post and read the rest.

## Sunday, July 6, 2014

### Poetry as Pure Mathematics

A recent email from Portuguese mathematician-poet F J "Francisco" Craveiro
de Carvalho brought a 40-year-old stanza to my attention. First published in the May, 1974 issue of

Whatever you add you add at your peril.

It is far better to subtract. In poetry,

Multiplication borders on madness.

Division is the mistress we agree to sleep with.

*POETRY**Magazine*, we have these enigmatic lines by William Virgil Davis. Enjoy!**The Science of Numbers: Or Poetry as Pure Mathematics**Whatever you add you add at your peril.

It is far better to subtract. In poetry,

Multiplication borders on madness.

Division is the mistress we agree to sleep with.

## Thursday, July 3, 2014

### Mathematician and Poet

Should I do it? Should I do a blog post on a novel by Brazilian poet Hilda Hilst (1930-2004) that I have begun to read but don't yet know how to understand?

Hilst's novel,

from

The cross on my brow

The facts of what I was

Of what I will be:

I was born a mathematician, a magician

I was born a poet.

Hilst's novel,

*With My Dog-Eyes*, newly translated by Adam Morris (Melville House, 2014), attracted my attention because its narrator is a mathematician and a poet. Here are the lines with which the novel begins:from

**With My Dog-Eyes**by Hilda HilstThe cross on my brow

The facts of what I was

Of what I will be:

I was born a mathematician, a magician

I was born a poet.

Labels:
Adam Morris,
Bertrand Russell,
Hilda Hilst,
magician,
mathematician,
poet

## Wednesday, July 2, 2014

### January - June, 2014 -- titles, dates of posts

Scroll
down to find titles and dates of posts in 2014. At the bottom is a links to lists of posts through 2013 and 2012 and 2011 -- and all the way back to March 2010 when this
blog was begun.

June 30 A recent butterfly effect

June 27 Of all geometries, feathery is best . . .

June 24 Is mathematics discovered or invented?

June 20 Three thousand, and two

June 17 Found: Elementary Calculus

June 14 Number theory is like poetry

**This link leads to a PDF file that lists searchable topics and names of poets and mathematicians presented herein.**June 30 A recent butterfly effect

June 27 Of all geometries, feathery is best . . .

June 24 Is mathematics discovered or invented?

June 20 Three thousand, and two

June 17 Found: Elementary Calculus

June 14 Number theory is like poetry

## Monday, June 30, 2014

### A recent butterfly effect

The term

Sea butterflies --

no larger than

a grain of sand,

named for the way

*butterfly effect*has entered everyday vocabulary from the mathematics of chaos theory and refers to the possibility of a major event (such as a tornado) starting from something so slight as the flutter of a butterfly wing. This sensitivity to small changes is a characteristic of chaotic systems. Recent news in*Science*magazine (9 May 2014) has drawn my attention to sea butterflies -- and the effect that ocean acidification is having on the lives of these tiny, fragile creatures -- and the environmental warning that this portends. From the details offered in*Science*, I have constructed this poem of 4x4 square-stanzas:**Warned by Sea Butterflies**by JoAnne GrowneySea butterflies --

no larger than

a grain of sand,

named for the way

Labels:
butterfly effect,
chaos,
JoAnne Growney,
mathematics,
poem,
sea butterfly,
square stanza

## Friday, June 27, 2014

### Of all geometries, feathery is best . . .

The title for this post comes from

Do not accept packages from unknown persons.

Beware non-native strangers who may be concealing

hazardous contraband "down there."

Question algebra. Dismantle thoughts traveling

the brain's baggage carousel in parabolas.

*Twinzilla*(The Word Works, 2014), by Charleston poet Barbara Hagerty. The title character of this collection is one of several poetic personalities that inhabit Hagerty's verse, and she offers a playful view of life's dualities -- sometimes versed in mathematical terminology. Here's a sample.**Twinzilla Cautions ***by Barbara G. S. HagertyDo not accept packages from unknown persons.

Beware non-native strangers who may be concealing

hazardous contraband "down there."

Question algebra. Dismantle thoughts traveling

the brain's baggage carousel in parabolas.

## Tuesday, June 24, 2014

### Is mathematics discovered or invented?

My neighbor, Glenn, is fond of asking math-folks that he meets the question "Is mathematics discovered or invented?" -- and when he asked the question of MAA lecturer William Dunham the response was one word, delivered with a smile, "Yes." The question of invention versus discovery -- which may apply to poetry or to mathematics -- is thoughtfully considered in "Notes toward a Supreme Fiction" by Wallace Stevens (1879-1955); here are a few lines from that poem.

from

He imposes orders as he thinks of them,

As the fox and the snake do. It is a brave affair.

Next he builds capitols and in their corridors,

from

**It Must Give Pleasure,****VII**by Wallace StevensHe imposes orders as he thinks of them,

As the fox and the snake do. It is a brave affair.

Next he builds capitols and in their corridors,

Labels:
discover,
invent,
mathematics,
order,
poetry,
Wallace Stevens,
William Dunham

## Friday, June 20, 2014

### Three thousand, and two

Here is a small poem richly vivid with the contrasts of opposites:

beside a stone three

thousand years old: two

red poppies of today

by Christine M. Krishnasami, India, found in

beside a stone three

thousand years old: two

red poppies of today

by Christine M. Krishnasami, India, found in

*This Same Sky: A Collection of Poems from around the World*(selected by Naomi Shihab Nye, Aladdin Paperbacks, 1996).## Tuesday, June 17, 2014

### Found: Elementary Calculus

Here is a poem by Saskatchewan poet Karen Solie.

From

Glasgow: Gibson, 1960.

Speed (like distance)

is a magnitude and has no

direction; velocity (like displacement)

has magnitude and direction.

**Found**by Karen Solie*Elementary Calculus*From

*Elementary Calculus*A. Keith and W. J. Donaldson.Glasgow: Gibson, 1960.

Speed (like distance)

is a magnitude and has no

direction; velocity (like displacement)

has magnitude and direction.

Labels:
calculus,
direction,
Karen Solie,
magnitude,
mathematics,
poem,
second,
speed,
zero

## Saturday, June 14, 2014

### Number theory is like poetry

Austrian-born Olga Taussky-Todd (1906-1995) was a noted and prolific mathematician who left her homeland for London in 1935 and moved on to California in 1945. Her best-known work was in the field of matrix theory (in England during World War II she started to use matrices to analyze vibrations of airplanes) and she also made important contributions to number theory. In the math-poetry anthology,

*Against Infinity*, I found a poem by this outstanding mathematician.
Labels:
Against Infinity,
mathematics,
mathmatician,
matrix,
number theory,
Olga Taussky-Todd,
poetry,
woman

## Wednesday, June 11, 2014

### And Now I See . . .

One of the ways we overcome our nervous shyness about our disabilities is by talking about them, and writing about them. And by encountering the poetry of Kathi Wolfe. I enjoy her work out-loud -- she is a frequent performer of her poems at local DC-area venues -- and on the page.

Kathi's "Blind Ambition" (in which she speaks of the monsters in arithmetic) is offered below; I first discovered this poem when it was posted by Split this Rock as poem of the week.

Kathi's "Blind Ambition" (in which she speaks of the monsters in arithmetic) is offered below; I first discovered this poem when it was posted by Split this Rock as poem of the week.

Labels:
addition,
arithmetic,
blind,
Kathi Wolfe,
multiplication,
poetry,
Split This Rock

## Sunday, June 8, 2014

### Impossible Things Before Breakfast

Literary works by Charles Lutwidge Dodgson (1832-1898, aka Lewis Carroll) are crammed with mentions of mathematics. One of my favorites (found here with numerous others, including "Ambition, Distraction, Uglification, Derision") is this exchange from Carroll's

"Alice laughed: "There's no use trying," she said; "one can't believe impossible things."

"I daresay you haven't had much practice," said the Queen. "When I was younger, I always did it for half an hour a day. Why, sometimes I've believed as many as six impossible things before breakfast."

*Alice in Wonderland*."Alice laughed: "There's no use trying," she said; "one can't believe impossible things."

"I daresay you haven't had much practice," said the Queen. "When I was younger, I always did it for half an hour a day. Why, sometimes I've believed as many as six impossible things before breakfast."

*Alice in Wonderland*
Labels:
Charles Lutwidge Dodson,
impossible,
Lewis Carroll,
paradox

## Wednesday, June 4, 2014

### Behind the cards -- mathematics

A couple of weeks ago at an MAA math lecture by Alissa Crans on the Catalan numbers, I sat near card-trick mathematician Colm Mulcahy. And I asked him if he knew any poems about card tricks and their mathematics.

Though he at first said "no," Mulcahy turned out to have a couple of connections up his sleeve. From Matthew Wright he learned of "The Card Players" -- a colorful sonnet from Philip Larkin's 1974 collection

And Bruce Reznick reminded him of the lyrics for "The Gambler" by Kenny Rogers. The complete lyrics may be found here; I include below a stanza that offers some instruction about counting.

Though he at first said "no," Mulcahy turned out to have a couple of connections up his sleeve. From Matthew Wright he learned of "The Card Players" -- a colorful sonnet from Philip Larkin's 1974 collection

*High Windows*and available here with selections of Adriaen Brouwer's art.And Bruce Reznick reminded him of the lyrics for "The Gambler" by Kenny Rogers. The complete lyrics may be found here; I include below a stanza that offers some instruction about counting.

Labels:
Alissa Crans,
bet,
Bruce Reznick,
card,
Catalan numbers,
Colm Mulcahy,
count,
Fiorello,
Kenny Rogers,
Matthew Wright,
Philip Larkin,
poem,
poker,
politics,
Sheldon Harnick,
trick

### Jan - May, 2014 -- titles, dates of posts

Scroll
down to find titles and dates of posts in 2014. At the bottom is a links to lists of posts through 2013 and 2012 and 2011 -- and all the way back to March 2010 when this
blog was begun.

May 30 Squirrel Arithmetic

May 29 Phenomenal Woman

May 25 How many grains of sand?

May 23 Math rap

May 20 Public Image of a Mathematician

**This link leads to a PDF file that lists searchable topics and names of poets and mathematicians presented herein.**May 30 Squirrel Arithmetic

May 29 Phenomenal Woman

May 25 How many grains of sand?

May 23 Math rap

May 20 Public Image of a Mathematician

## Friday, May 30, 2014

### Squirrel Arithmetic

My maternal grandfather, James Edgar Black (1871-1931) was a western Pennsylvanian, a carpenter, and a man I never knew. But Ed, one of my cousins, found among our grandfather's long-stored things a scrapbook of collected poems and other miscellany that he recently passed on to me.

## Thursday, May 29, 2014

### Phenomenal Woman

Yesterday morning Maya Angelou (1928-1914) left us. But she has not left us alone. Her voice is with us, cheering us to be more than we were, to be all that we can become. Places to read her words and words about her include PoetryFoundation.org (scroll down past the bio for links to poems), Poets.org,

Angelou's poetry is filled with the geometry and motion of womanhood. For example:

*The Washington Post,*and Angelou's website.Angelou's poetry is filled with the geometry and motion of womanhood. For example:

Labels:
geometry,
Maya Angelou,
motion,
phenomenal,
woman

## Sunday, May 25, 2014

### How many grains of sand?

Recently one of my friends used "all the grains of sand" as an example of an infinite set "because it is impossible to count them all" and -- even as I rejected his answer -- I wondered how many of my other friends might agree with it. In the following poem, mathematician Pedro Poitevin considers a similar question as he reflects on the countability of the birds in the night sky.

A synchrony of wings across the sky

is quavering its feathered beats of flight.

Their number is too high to count -- I try

**Divertimentum Ornithologicum**by Pedro Poitevin*After Jorge Luis Borges's Argumentum Ornithologicum.*A synchrony of wings across the sky

is quavering its feathered beats of flight.

Their number is too high to count -- I try

Labels:
count,
hyperfinite,
inductive,
infinite,
Jorge Luis Borges,
less,
more,
natural number,
Pedro Poitevin

## Friday, May 23, 2014

### Math rap

Harry Baker is a Slam Champion who studies Maths at Bristol University, UK -- and his poetry sometimes features math, often having fun with the topic. His web page has a link to a rap about maths and at the JMM reading in Boston in 2012, Baker submitted this rap, 59 (a love story, now on YouTube), for presentation that evening.

## Tuesday, May 20, 2014

### Public Image of a Mathematician

From John Dawson -- a professor emeritus of mathematics at the Penn State York campus and well-known for his publications in mathematical logic, often focusing on the life and work of Kurt Godel -- a poem on a topic that this blog visits from time to time, portraits of mathematicians.

Please,

I'm not an accountant.

No,

Mine doesn't always balance either.

What do I

Well,

On good days

I prove theorems;

**Public Image**by John W. Dawson, Jr.Please,

I'm not an accountant.

No,

Mine doesn't always balance either.

What do I

*do*then?Well,

On good days

I prove theorems;

Labels:
accountant,
John Dawson,
Kurt Godel,
logic,
mathematician,
mathematics,
poem

## Friday, May 16, 2014

### Pound on poetry and mathematics

HERE at PoetryFoundation.org we find an article by Carl Sandburg (1878-1967), published in

The complete article is available here.

And, in a footnote* to the poem "In a Station of the Metro" -- found in my

*POETRY**Magazine*in 1916, in which Sandburg offers highest praise to poet Ezra Pound (1885-1972). Sandburg includes this quote from a 1910 essay by Pound that connects poetry and mathematics.
"Poetry is a sort of inspired mathematics, which gives us equations,

not for abstract figures, triangles, spheres and the like, but equations

for the human emotions. If one have a mind which inclines to magic

rather than science, one will prefer to speak of these equations

as spells or incantations; it sounds more arcane, mysterious, recondite."

The complete article is available here.

And, in a footnote* to the poem "In a Station of the Metro" -- found in my

*Norton Anthology of Modern Poetry*we find a bit more of Pound's mathematical thinking.
Labels:
abstract,
Carl Sandburg,
equation,
Ezra Pound,
figure,
mathematics,
Metro,
poetry,
sphere,
triangle

## Tuesday, May 13, 2014

### Land without a square

Here is a bit of light verse from the pen of John Updike (1932-2009).

**ZULUS LIVE IN LAND**

**WITHOUT A SQUARE**by John Updike

*A Zulu lives in a round world. If he does not leave his reserve.*

*he can live his whole life through and never see a straight line.*

--headline and text from

*The New York Times*

In Zululand the huts are round,

The windows oval, and the rooves

Thatched parabolically. The ground

Is tilled in curvilinear grooves.

## Saturday, May 10, 2014

### Barbie (b 1959) said (c 1990) "math is hard"

On April 24 I had the pleasure of reading at the Nora School with Martin Dickinson and Michele Wolf. Back in March I had posted Dickinson's "Homage to Euclid" but mathematics is not a a focus of Wolf's work. However, her poem below about Barbie has numbers, and any mention of Barbie reminds me of the controversy over "

by Michele Wolf

My worth is most inflated when, on tiptoes, I pose

In my original box, never handled, especially if I date

Back to '59 or '60. But that is rare. I am more used

To breaking out, to being the damp flamingo

Pecking to leave the shell. I prefer moving forward.

I was an astronaut in '65, a surgeon in '73. Last year

**math is hard**" -- one of the speeches uttered by an early 90's version of this doll. (Please visit this posting from June 14, 2010 -- on "Girls and Mathematics" for additional Barbie-comments and more Barbie poetry.) Here, now, please enjoy Wolf's poem:**Barbie Slits Open Her Direct-Mail Offer to Join AARP**by Michele Wolf

My worth is most inflated when, on tiptoes, I pose

In my original box, never handled, especially if I date

Back to '59 or '60. But that is rare. I am more used

To breaking out, to being the damp flamingo

Pecking to leave the shell. I prefer moving forward.

I was an astronaut in '65, a surgeon in '73. Last year

Labels:
almost,
Barbie,
girls,
math,
mathematics,
metaphor,
Michele Wolf,
poetry

## Wednesday, May 7, 2014

### May 6, 1954

I learned about it via a news broadcast on Pittsburgh radio station KDKA and, for some reason, the event stuck firmly in my memory. I was 13 years old and on May 6, 1954 Roger Bannister ran a mile in less than 4 minutes. The integer 4 is a perfect square as was Bannister's age then -- 25. Alternatively, 13 is prime. As is 60 + 13 = 73. Yesterday marked 60 years since Bannister broke the record. I have come to love running. And playing with numbers.

I . . . never

will run out

of numbers.

I . . . never

will run out

of numbers.

Labels:
perfect square,
prime,
Roger Bannister,
running

## Sunday, May 4, 2014

### A pure mathematician (not!)

Poet Arthur Guiterman (1871-1943) was known for his humorous verse. Here is "A Pure Mathematician" -- a poem that stereotypes mathematicians in familiar, unflattering ways (from

Let Poets chant of Clouds and Things

In lonely attics!

A Nobler Lot is his, who clings

To Mathematics.

Sublime he sits, no Worldly Strife

His Bosom vexes,

Reducing all the Doubts of Life

To Y's and X's.

*The Laughing Muse*(Harper Brothers, 1915)). In contrast to Guiterman's verse that pokes fun at mathematicians, I invite you to visit this posting from 28 January 2011 to read Sherman Stein's "Mathematician" -- a poem that not only is more fair to the profession but also features a female mathematician.**A Pure Mathematician**by Arthur GuitermanLet Poets chant of Clouds and Things

In lonely attics!

A Nobler Lot is his, who clings

To Mathematics.

Sublime he sits, no Worldly Strife

His Bosom vexes,

Reducing all the Doubts of Life

To Y's and X's.

Labels:
Arthur Guiterman,
hypoetenuse,
logarithm,
mathematician,
mathematics,
portrait,
pure

### April, 2014 -- dates, titles of posts

Scroll
down to find titles and dates of posts in 2014. At the bottom is a links to lists of posts through 2013 and 2012 and 2011 -- and all the way back to March 2010 when this
blog was begun.

Apr 28 Words that warn

Apr 25 Too many selves

Apr 21 A Cento from Arcadia

Apr 20 Remembering Nina Cassian

Apr 18 Poetry of Romania - Nora School, Apr 24

Apr 15 Dimensions of a soul

Apr 12 A Vector Space Poem

**This link leads to a PDF file that lists searchable topics and names of poets and mathematicians presented herein.****Apr 30****Math, Magic, Mystery -- and so few women**Apr 28 Words that warn

Apr 25 Too many selves

Apr 21 A Cento from Arcadia

Apr 20 Remembering Nina Cassian

Apr 18 Poetry of Romania - Nora School, Apr 24

Apr 15 Dimensions of a soul

Apr 12 A Vector Space Poem

## Wednesday, April 30, 2014

### Math, Magic, Mystery -- and so few women

Today, April 30, is the final day of Mathematics Awareness Month 2014; this year's theme has been "Mathematics, Magic and Mystery" and it celebrates the 100th anniversary of the birth of one of the most interesting men of mathematics; educated as a philosopher, Martin Gardner wrote often about mathematics and sometimes about poetry. Gardner described his relationship to poetry as that of "occasional versifier" -- he is the author, for example, of:

Ï€ goes on and on

And e is just as cursed

I wonder, how does Ï€ begin

When its digits are reversed?

Ï€ goes on and on

And e is just as cursed

I wonder, how does Ï€ begin

When its digits are reversed?

## Monday, April 28, 2014

### Words that warn

Somewhere in a high school English class was a small topic that intrigues me still -- "questions that expect the answer 'yes'." A door opened. Letting me see that what we say has expectations as well as information. In graduate school math classes we considered the warning word "obviously" -- in a proof, it was likely to mean "I'm sure it's true but am not able to explain."

As I muse today about language I am wondering how

As I muse today about language I am wondering how

*words affect the population of women in mathematics, affect the numbers (too small) of women publishing mathematics. Thinking about this in the light of a wonderful time on Saturday greeting visitors to an AWM (Association for Woman in Mathematics) booth at the biennial USA Science and Engineering Festival. Temple University professor and AWM member Irina Mitrea did an amazing job planning and coordinating the AWM booth where hundreds of young people got some hands-on experience with secret codes and ciphers.***unsaid**
Labels:
AWM,
cipher,
code,
elliptical,
Harryette Mullen,
Irina Mitrea,
mathematics,
poem,
Poetry Foundation

## Friday, April 25, 2014

### Too many selves

In my childhood home, numbers were used with care and precision. There would be teasing when I would use the adverb "too" --- as if when I said "I had to walk

Alone among the superheroes,

He failed to keep his life in balance.

Power Man, The Human Shark--they knew

To hold their days and nights in counterpoise,

Their twin selves divided together,

As a coin bears with ease its two faces.

*too*far" I had tried to describe an unbounded distance, greater than any possible span. Now as an adult I continue to be cautious (and intrigued) with use of that word. And I am drawn to the uses of "too many" and "count" in the following poem from David Orr, poetry columnist for the*New York Times Book Review*.**The Chameleon**by David OrrAlone among the superheroes,

He failed to keep his life in balance.

Power Man, The Human Shark--they knew

To hold their days and nights in counterpoise,

Their twin selves divided together,

As a coin bears with ease its two faces.

## Monday, April 21, 2014

### A Cento from Arcadia

Last week I had the enjoyable privilege of visiting with mathematician-poet Marion Cohen's math-lit class, "Truth and Beauty" at Arcadia University -- and the class members helped me to compose a Cento (given below), a poem to which each of us contributed a line or two of poetry-with-mathematics. Participants, in addition to Dr. Cohen and me, included these students:

Theresa, Deanna, Ian, Collin, Mary, Grace, Zahra, Jen, Jenna,

Nataliya, Adeline, Quincy, Van, Alyssa, Samantha, Alexis, Austin.

Big thanks to all!

Theresa, Deanna, Ian, Collin, Mary, Grace, Zahra, Jen, Jenna,

Nataliya, Adeline, Quincy, Van, Alyssa, Samantha, Alexis, Austin.

Big thanks to all!

## Sunday, April 20, 2014

### Remembering Nina Cassian

Exiled Romanian poet Nina Cassian (1924-2014) died last week in Manhattan. Cassian was an outspoken poet whom I admired for her political views; she also was connected to mathematics -- in her subject matter and her friends. (See, for example, this posting from January 31, 2011.)

If I dress up like a peacock,

you dress like a kangaroo.

If I make myself into a triangle,

you acquire the shape of an egg.

If I were to climb on water,

you'd climb on mirrors.

All our gestures

Belong to the solar system.

"Equality" is in

**Equality**by Nina CassianIf I dress up like a peacock,

you dress like a kangaroo.

If I make myself into a triangle,

you acquire the shape of an egg.

If I were to climb on water,

you'd climb on mirrors.

All our gestures

Belong to the solar system.

"Equality" is in

*Cheerleaders for a Funeral*(Forrest Books, 1992), translated by the author and Brenda Walker.
Labels:
Brenda Walker,
equality,
mathematics,
Nina Cassian,
poetry,
Romania,
triangle

## Friday, April 18, 2014

### Poetry of Romania - Nora School, Apr 24

During several summers teaching conversational English to middle-school students in Deva, Romania, I became acquainted with the work of Romanian poets. These included: Mikhail Eminescu (1850-1889, a Romantic poet, much loved and esteemed, honored with a portrait on Romanian currency), George Bakovia (1881-1957, a Symbolist poet, and a favorite poet of Doru Radu, an English teacher in Deva with whom I worked on some translations of Bacovia into English), Nichita Stanescu (1933-1983, an important post-war poet, a Nobel Prize nominee -- and a poet who often used mathematical concepts and images in his verse).

On April 24, 2014 at the Nora School here in Silver Spring I will be reading (sharing the stage with Martin Dickinson and Michele Wolf) some poems of Romania -- reading both my own writing of my Romania experiences and some translations of work by Romanian poets. Here is a sample (translated by Gabriel Praitura and me) of a poem by Nichita Stanescu:

On April 24, 2014 at the Nora School here in Silver Spring I will be reading (sharing the stage with Martin Dickinson and Michele Wolf) some poems of Romania -- reading both my own writing of my Romania experiences and some translations of work by Romanian poets. Here is a sample (translated by Gabriel Praitura and me) of a poem by Nichita Stanescu:

## Tuesday, April 15, 2014

### Dimensions of a soul

In the poem below, Young Smith uses carefully precise terms of Euclidean geometry to create a vivid interior portrait.

The shape of her soul is a square.

She knows this to be the case

because she often feels its corners

pressing sharp against the bone

just under her shoulder blades

and across the wings of her hips.

**She Considers the Dimensions of Her Soul**by Young SmithThe shape of her soul is a square.

She knows this to be the case

because she often feels its corners

pressing sharp against the bone

just under her shoulder blades

and across the wings of her hips.

## Saturday, April 12, 2014

### A Vector Space Poem

As a Columbia undergraduate, media artist Millie Niss (1973-2009) majored in mathematics and was enrolled in a math PhD program at Brown University when she decided to make writing her full-time career. Before her untimely death in 2009 Niss was well-established in Electronic Literature. Here is a link to "Morningside Vector Space," one of the poems at Niss's website Sporkworld (at Sporkworld, click on the the E-poetry link).

Niss's electronic poem retells a story (inspired by the Oulipian Raymond Queneau's

Niss's electronic poem retells a story (inspired by the Oulipian Raymond Queneau's

*Exercises de Style*) in many different styles and following many different constraints. The computer is central to the retelling as the text varies almost smoothly along two dimensions, controlled by the position of the mouse pointer in a colored square (to the right in the screen-shot below). Behind this poetry is the mathematical concept of a two-dimensional vector space, in which each point (or text) has a coordinate with respect to each basis vector (version of the text, or dimension along which the text can change).## Thursday, April 10, 2014

### Fractal Geometry

Lee Felice Pinkas is one of the founding editors of

Father of fractals, we were foolish

to expect a light-show from you,

hoping your speech would fold upon itself

and mimic patterns too complex for Euclid.

*cellpoems --*a poetry journal distributed via text message. I found her poem,"The Fractal Geometry of Nature" in the Winter/Spring 2009 Issue (vol.14, no 1) of*Crab Orchard Review*.**The Fractal Geometry of Nature**by Lee Felice Pinkas*Most emphatically, I do not consider**the fractal point of view as a panacea. . .**--Benoit Mandelbrot (1924-2010)*

Father of fractals, we were foolish

to expect a light-show from you,

hoping your speech would fold upon itself

and mimic patterns too complex for Euclid.

Labels:
Benoit Mandelbrot,
complex,
dimension,
Euclid,
fractal,
geometry,
Lee Felice Pinkas,
pattern,
repeated,
roughness,
self-similarity,
simple,
snowflake

## Monday, April 7, 2014

### April Celebrates Poetry and Mathematics

On April 1 (the first day of National

In her comment on "Can an Equation be a Poem?"

*Month and***Poetry***Awareness Month) Science writer Stephen Ornes offered a guest post at***Mathematics***The Last Word on Nothing*entitled "Can an Equation be a Poem?" and on April 2 the Ornes posting appeared again, this time in the blog*Future Tense*at Slate.com with the title "April Should Be*Mathematical Poetry*Month."In her comment on "Can an Equation be a Poem?"

*Scientific American*blogger Evelyn Lamb (*Roots of Unity*)*mentioned her math-poetry post on March 21 entitled "What T S Eliot Told Me About the Chain Rule." Lamb quotes lines from the final stanza "Little Gidding," the last of Eliot's**Four Quartets*. Here is the entire stanza with its emphasis on the mysteries of time and perspective, the circular nature of things, the difficulty of discovering a beginning.## Saturday, April 5, 2014

### Logic in limericks

In these lines, Sandra DeLozier Coleman (who participated in the math-poetry reading at the Joint Mathematics Meetings in Baltimore in January) speaks as a professor reasoning in rhyme, explaining truth-value technicalities of the logical implication, "If p then q" (or, in notation,

That

Doesn’t say very much about

For if

Then there’s really no loss

In assuming that

**p -- > q ).****The Implications of Logic**by Sandra DeLozier ColemanThat

*p --> q*is true,Doesn’t say very much about

*q*.For if

*p*should be false,Then there’s really no loss

In assuming that

*q*could be, too.
Labels:
conditional,
false,
implication,
limerick,
logic,
professor,
Sandra DeLozier Coleman,
true

## Wednesday, April 2, 2014

### Can you SEE the monument?

**Links to non-intersecting celebrations of April**

**as National Poetry Month and Mathematics Awareness Month**

Recently I revisited my copy of

*Elizabeth Bishop: The Compete Poems, 1927-1979*(FSG, 1999) and turned to "The Monument" -- a poem mathematically interesting for its geometry. Here are the opening lines; the complete text and many other Bishop poems are available online here:

from

**The Monument**by Elizabeth Bishop (1911-1979)

Now can you see the monument? It is of wood

built somewhat like a box. No. Built

like several boxes in descending sizes

one above the other.

Each is turned half-way round so that

its corners point toward the sides

of the one below and the angles alternate.

Labels:
angle,
box,
Carol Frost,
cube,
Elizabeth Bishop,
half-way,
line,
monument,
parallel,
side

### March, 2014 -- dates, titles of posts

Scroll
down to find titles and dates of posts in 2014. At the bottom is a links to lists of posts through 2013 and 2012 and 2011 -- and all the way back to March 2010 when this
blog was begun. **This link leads to a PDF file that lists searchable topics and names of poets and mathematicians presented herein.**

Mar 30

Mar 27 Women's History -- celebrate Caroline Herschel

Mar 23 Homage to Euclid

Mar 20 One geometry is not enough

Mar 16 Making something of nothing

Mar 30

**Split This Rock 2014 was great!**Mar 27 Women's History -- celebrate Caroline Herschel

Mar 23 Homage to Euclid

Mar 20 One geometry is not enough

Mar 16 Making something of nothing

## Sunday, March 30, 2014

### Split This Rock 2014 was great!

## Thursday, March 27, 2014

### Women's History -- celebrate Caroline Herschel

In the sixties when I spent a year at Bucknell University, I was a member of the "Department of Astronomy and Mathematics," a pairing of related disciplines. In past centuries, Mathematics was included in the liberal arts. In the twenty-first century often it is paired with Computer Science, and Astronomy is paired with Physics. And so it goes.

Poems by Laura Long tell of the pioneering work by astronomer Caroline Herschel -- a discoverer of eight comets, a cataloger of stars. Long describes her recent collection,

This is a work of the imagination steeped in historical siftings

and the breath between the lines.

Here is the opening poem:

Poems by Laura Long tell of the pioneering work by astronomer Caroline Herschel -- a discoverer of eight comets, a cataloger of stars. Long describes her recent collection,

*The Eye of Caroline Herschel: A Life in Poems*(Finishing Line Press, 2013), in this way:This is a work of the imagination steeped in historical siftings

and the breath between the lines.

Here is the opening poem:

Labels:
astronomy,
calculate,
Caroline Herschel,
comet,
imagination,
Laura Long,
mathematics,
star

## Sunday, March 23, 2014

### Homage to Euclid

In my preceding post (20 March 2014) Katharine Merow's poem tells of the new geometries

developed with variations of Euclid's Parallel Postulate.

Martin Dickinson's poem, on the other hand, tells of richness

*within*Euclid's geometry.**Homage to Euclid**by Martin Dickinson

What points are these,

visible to us, yet revealing something invisible—

invisible, yet real?

Labels:
apple,
circle,
Euclid,
infinity,
Innisfree,
lines,
Martin Dickinson,
math,
Nora School,
oblong,
parallelogram,
poetry,
points,
postulates,
rhomboid,
space,
sphere

## Thursday, March 20, 2014

### One geometry is not enough

Writer Katharine Merow is in the Publications Department of the Washington DC headquarters of the MAA (Mathematical Association of America) and she is one of the poets who participated in the "Reading of Poetry with Mathematics" at JMM in Baltimore last January. Here is the engaging poem Merow read at that event -- a poem that considers the 19th century development of new and "non-euclidean" geometries from variants of Euclid's fifth postulate, the so-called

*parallel postulate*:**Geometric Proliferation**by Katharine Merow
Labels:
Euclid,
geometry,
JMM Poetry Reading,
Katharine Merow,
MAA,
noneuclidean,
parallel,
postulate

## Sunday, March 16, 2014

### Making something of nothing

Was zero invented or discovered? When and how? By whom? In "The Origin of Zero" -- an article published in 2009 in in

*Scientific American*-- John Matson introduces an interesting history of zero (*something*vs.*nothing*and so on...). Recently through the Splendid Wake poetry project (**with an open-to-all meeting on Friday March 21 -- go here for details**) I have connected with Washington DC poet William Rivera who has shared with me this poem that also examines the puzzle of the somethingness of nothing.**by William Rivera***Nothing*Changes Everything
Labels:
atom,
black hole,
discover,
invent,
nothing,
recycling,
Splendid Wake,
universe,
William Rivera,
X,
zero

## Thursday, March 13, 2014

### Tomorrow is Pi Day

Tomorrow is

**and I offer no new poems but supply links to several previous posts. Poetry of***Pi Day**may be found on 23 August 2010 (an "irrational sonnet" by Jacques Bens), 6 September 2010 (featuring work by Kate Bush, Robert Morgan and Wislawa Szymborska), 10 September 2010 (mnemonics for***Ï€***, especially from Mike Keith) , 15 March, 2011,(a poem by Lana Hechtman Ayers) 27 November 2011 (a poem by Brian McCabe) and 10 March 2013 (the opening lines of a poem "3.141592 . . ." by Peter Meinke).***Ï€**## Tuesday, March 11, 2014

### Tragedy of the Commons

Thinking in syllable-squares,

recalling ecologist Garrett Hardin (1915-2003)

and his 1968 wisdom, "Tragedy of the Commons."

recalling ecologist Garrett Hardin (1915-2003)

and his 1968 wisdom, "Tragedy of the Commons."

Maximum

may not be

optimum.

## Saturday, March 8, 2014

### SHE measures the heavens . . .

Today is International Women's Day, celebrated with a charming video at google.com and here with lines from Enheduanna (2285-2250 BCE), the earliest woman known to me who was both poet and mathematician.

The true woman who possesses exceeding wisdom,

She consults a tablet of lapis lazuli,

She gives advice to all lands,

She measures off the heavens, she places the

measuring cords on the earth.

These lines (found in the preface, translated from Sumerian sources by Ake W Sjoberg and E Bergmann S J) and much more poetry-with-math are found in

The true woman who possesses exceeding wisdom,

She consults a tablet of lapis lazuli,

She gives advice to all lands,

She measures off the heavens, she places the

measuring cords on the earth.

These lines (found in the preface, translated from Sumerian sources by Ake W Sjoberg and E Bergmann S J) and much more poetry-with-math are found in

*Strange Attractors: Poems of Love and Mathematics*(AK Peters, 2008) -- a collection edited by Sarah Glaz and me.
Labels:
Enheduanna,
love,
mathematics,
measuring,
poems,
Strange Attractors,
wisdom

## Wednesday, March 5, 2014

### A poetry album by Lucille Clifton

March is Women's History Month and here, today, I celebrate by acknowledging a special woman, Lucille Clifton (1936-2010). From 1979–1985 Clifton served as Poet Laureate of Maryland. Her poetry celebrates both her African-American heritage and her womanhood. Here is "album," a poem in Clifton's spare and un-capitalized style -- and containing a few numbers to help us keep track of the times that are changing.

**album**by Lucille Clifton
Labels:
African-American,
album,
Lucille Clifton,
numbers,
poetry,
woman,
Women's History Month

## Sunday, March 2, 2014

### Sociology of Numbers

Robert Dawson is a mathematics professor at St Mary's University in Halifax, Nova Scotia -- an active mathematician who complements his research activity with mathematics education and with poetry. The following Dawson poem appeared here in 2013 -- in the

The ones you notice first are the natural numbers.

Everybody knows their names; they are the anchors,

the stars, the alphas, the reference points. And of course

the rational numbers, who hang out with them,

sit next to them in arithmetic class.

*Journal of Humanistic Mathematics*, a journal whose every issue contains some poetry-with-mathematics.**Some Contributions to the Sociology of Number**s by Robert DawsonThe ones you notice first are the natural numbers.

Everybody knows their names; they are the anchors,

the stars, the alphas, the reference points. And of course

the rational numbers, who hang out with them,

sit next to them in arithmetic class.

Labels:
denominator,
fraction,
irrational,
mathematics,
natural,
numbers,
numerator,
numerology,
poetry,
Pythagorean,
Robert Dawson

### February, 2014 -- dates, titles of posts

Scroll
down to find titles and dates of posts in January, 2014. At the bottom is a links to lists of posts through 2013 and 2012 and 2011 -- and all the way back to March 2010 when this
blog was begun. **This link leads to a PDF file that lists searchable topics and names of poets and mathematicians presented herein.**

Feb 26 Long division is difficult . . .

Feb 23 Angles in Alaska

Feb 20 Excitement of Proving a Theorem

Feb 18 Wartime recurrence

Feb 13 Mother Courage -- and speaking of opposites

Feb 26 Long division is difficult . . .

Feb 23 Angles in Alaska

Feb 20 Excitement of Proving a Theorem

Feb 18 Wartime recurrence

Feb 13 Mother Courage -- and speaking of opposites

## Wednesday, February 26, 2014

### Long division is difficult . . .

Last Monday included a visit with old friends of whom I see too little, Silver Spring artist Mark Behme -- with whom I did some art-poetry collaboration a few years back -- and Chevy Chase artist-writer-economist-activist, Kyi May Kaung. After lunch at nearby Mandalay we three walked to Mark's studio and hung out for a while, admiring and talking about his new work. When I arrived home, I dug out several poems developed from Mark's sculpture -- finding some pieces I'd not thought about for a while. Here is one of these, a mathy poem that partners with Mark's "Split Tales."

**Which Girl Am I?**by JoAnne Growney
The girl who’s not forced to divide

into the good girl and the real one

is a lucky one. I was
eleven

when I felt a crack begin.

Labels:
art,
division,
girl,
JoAnne Growney,
Kyi May Kaung,
Mark Behme,
math,
poetry,
sculpture,
split,
two

## Sunday, February 23, 2014

### Angles in Alaska

Last Thursday evening I was honored to read in Takoma Park's Third Thursday poetry series -- along with poets Judy Neri and Kathleen O'Toole -- and my reading focused on poems of my times in Alaska. The brilliant geometry of our 49th state affected me strongly and "Angles of Light" became the title poem for a chapbook I published with Finishing Line Press in 2009. Here is section 3 (of 7) from that poem.

## Thursday, February 20, 2014

### Excitement of Proving a Theorem

Wow! From first sighting, I have loved this description:

I prove a theorem and the house expands:

the windows jerk free to hover near the ceiling,

the ceiling floats away with a sigh.

These lines from "Geometry" by Rita Dove express -- as well as any string of twenty-four words I can think of -- the excitement experienced from proving a theorem.

I prove a theorem and the house expands:

the windows jerk free to hover near the ceiling,

the ceiling floats away with a sigh.

These lines from "Geometry" by Rita Dove express -- as well as any string of twenty-four words I can think of -- the excitement experienced from proving a theorem.

Labels:
Black History Month,
geometry,
mathematics,
Poet Laureate,
poetry,
proof,
Rita Dove,
theorem

## Tuesday, February 18, 2014

### Wartime recurrence

In mathematics, it is not unusual to define an entity using a recurrence relation.

For example, in defining powers of a positive integer:

The 2nd power of 7 may be defined as 7 x 7

the 3rd power of 7 may be defined as 7 times 7

and the 4th power is 7 times 7

and, in general, for any positive integer n, 7

Several weeks ago I attended a reading of fine poetry here in Silver Spring at the Nora School -- a reading that featured DC-area poets Judith Bowles, Luther Jett, and David McAleavey. I was delighted to hear in "Recessional" -- one of the poems presented that evening by Jett -- the mathematical pattern of recurrence, building stepwise with a potentially infinite number of steps (as with the powers of 7, above) into a powerful poem. I include it below:

For example, in defining powers of a positive integer:

The 2nd power of 7 may be defined as 7 x 7

^{1};the 3rd power of 7 may be defined as 7 times 7

^{2},and the 4th power is 7 times 7

^{3},and, in general, for any positive integer n, 7

^{n+1 }= 7 x 7^{n}.Several weeks ago I attended a reading of fine poetry here in Silver Spring at the Nora School -- a reading that featured DC-area poets Judith Bowles, Luther Jett, and David McAleavey. I was delighted to hear in "Recessional" -- one of the poems presented that evening by Jett -- the mathematical pattern of recurrence, building stepwise with a potentially infinite number of steps (as with the powers of 7, above) into a powerful poem. I include it below:

Labels:
Beltway,
Luther Jett,
Nora School,
poetry reading,
recurrence

## Thursday, February 13, 2014

### Mother Courage -- and speaking of opposites

Bertolt Brecht (1898-1956) was a poet, but I have not found mathematics in his poems. Still, I want to note here a fantastic performance of his play,

And here, with a nod to the mathematical bent of this blog, is a quote from Brecht's

*Mother Courage and her Childre*n, starring Kathleen Turner and a talented ensemble at Washington,DC's Arena Stage. Invited by my neighbors, Mitzi and Pati, I joined them yesterday for a riveting performance. Here is a link to "How Fortunate the Man with None," a Brecht poem heartily sung as "Solomon's Song" in the current musical production.And here, with a nod to the mathematical bent of this blog, is a quote from Brecht's

*Mother Courage*that involves counting; also, it is one of many examples of a strategy that Brecht uses often and well -- encouraging an idea by speaking of its opposite.
Labels:
Bertolt Brecht,
counting,
Mother Courage,
opposite,
peace,
poet,
war,
word play

## Monday, February 10, 2014

### To love, in perfect syllables

While looking for Valentine verse with a math connection, I opened my copy of

*The Complete Illustrated Works of Lewis Carroll*(Chancellor Press, 1982). And found this one in which Carroll (a pen name for English mathematician Charles Lutwidge Dodson (1832-1898)) uses the word*one*twice and the word*half*twice and has counted sounds so that in each line the number of syllables is either*a cube of an integer*or is*perfect*.**Lesson in Latin**by Lewis Carroll (May 1888)
Labels:
Charles Lutwidge Dodson,
count,
cube,
half,
Lewis Carroll,
love,
mathematician,
mathematics,
one,
Pablo Neruda,
perfect,
Valentine

## Friday, February 7, 2014

### Love and Mathematics -- Please be my Valentine!

Poet extraordinaire Maxine Kumin (1925-2014) died yesterday.

Late in 2007, AKPeters released *Strange Attractors: Poems of Love and Mathematics*, edited by Sarah Glaz and me. Recently at a Howard County Math Festival I met a young man who browsed my copy of this anthology and found it the perfect Valentine. And so might you. Below I include a sample from the collection -- a love sonnet by Jean de Sponde (1557-1595), translated from the French by David Slavitt.

Several previous postings have offered love poems of mathematics and mathematicians;

these include 9 February 2013, 12 February 2012, 12 February 2011, 10 November 2011,

## Wednesday, February 5, 2014

### Six Million

Sometimes numbers become labels for particular events. When I was growing up, all of us knew

While mentioning this poem of witness and remembering, I want also to remind you of the very special

*1492*as a label for the discovery of America. And*1941*recognized Pearl Harbor. The following selection from a poem by Israeli poet Yehuda Amichai (1924-2000) reminds us of the awful importance of*6 million*.While mentioning this poem of witness and remembering, I want also to remind you of the very special

**Split This Rock Poetry Festival: Poems of Provocation & Witness**, to held in Washington, DC, March 27-30, 2014. (Early-bird registration ends on Valentine's Day, February 14th at midnight.) Hope to see you there.## Sunday, February 2, 2014

### Forecasting snow and poetry

**Snowbound**

is that other world

in which no schedules sit

and no ambitions flare

to interrupt the bluest sky

and whitest field

and coldest air

### January, 2014 -- dates, titles of posts

Scroll
down to find titles and dates of posts in January, 2014. At the bottom is a links to lists of posts through 2013 and 2012 and 2011 -- and all the way back to March 2010 when this
blog was begun. **This link leads to a PDF file that lists searchable topics and names of poets and mathematicians presented herein.**

Jan 31 On shoulders of giants . . .

Jan 28 Little Boxes

Jan 28 Graffiti Calculus

Jan 25 Mathematics is like . . .

Jan 31 On shoulders of giants . . .

Jan 28 Little Boxes

Jan 28 Graffiti Calculus

Jan 25 Mathematics is like . . .

## Friday, January 31, 2014

### On shoulders of giants . . .

Washington, DC is a city rich with both poetry and mathematics. Last Tuesday evening I attended a Mathematical Association of America (MAA) lecture by author and math historian William Dunham (whom I knew when he taught for a bunch of years at Pennsylvania's Muhlenberg College, in Eastern Pennsylvania, not so far from my employer, Bloomsburg University). Dunham spoke of insights gained by many hours reading the correspondence of British mathematician and scientist, Sir Isaac Newton (1642-1727). The discoverer of "gravity," and, moreover, both a genius and a disagreeable man. Still, Newton was a man who gave a nod to his predecessors, "If I have seen further it is by standing on ye sholders of Giants."

Labels:
David Arns,
fluxions,
gravity,
MAA,
mathematician,
poem,
Principia,
Sir Isaac Newton,
William Dunham

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