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!

## Monday, April 21, 2014

## 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.

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

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

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

**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

## 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.

Jan 31 On shoulders of giants . . .

Jan 28 Little Boxes

Jan 28 Graffiti Calculus

Jan 25 Mathematics is like . . .

**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 . . .

## 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

## Tuesday, January 28, 2014

### Little Boxes

It is hard to know what to say.

Pete Seeger died yesterday at age 94.

94 = 2 x 47. 47 is prime.

Here is a link to Pete singing "Little Boxes."

Song lyrics are poems.

Pete Seeger died yesterday at age 94.

94 = 2 x 47. 47 is prime.

Here is a link to Pete singing "Little Boxes."

Song lyrics are poems.

### Graffiti Calculus

In my dreams I am an artist -- a cartoonist, perhaps, or a graffiti artist -- so skilled with lines and curves and so clever that my art gives pleasure AND delivers a punch.

And so I am gratefully into the math-art connections provoked by a new book by Mary-Sherman Willis -- aptly titled

And so I am gratefully into the math-art connections provoked by a new book by Mary-Sherman Willis -- aptly titled

*Graffiti Calculus*(CW Books, 2013). I first met Willis in December, at Cafe Muse (where I will read next Monday, Feb 3 with Stephanie Strickland) and it was my pleasure also to hear her read again from that collection at the Joint Mathematics Meetings. These poems by Willis give us, in sixty poetic chapters, the story of a mother seeking her son by following his graffiti tags through the city. Here is a sample, sections 5 and 6:
Labels:
calculus,
continuous,
function,
graffiti,
integer,
JMM Poetry Reading,
limit,
Mary-Sherman Willis,
mathematics,
poet

## Saturday, January 25, 2014

### Mathematics is like . . .

For angling may be said to be so like the mathematics,

that it can never be fully learnt; at least not so fully,

but that there will still be more new experiments left

for the trial of other men that succeed us.

Izaak Walton (1594-1683),

*The Compleat Angler (1653-1676)*## Wednesday, January 22, 2014

### Extraneous -- and so on

Since my junior high math days, when I first heard the word "extraneous," I have loved the sound of it, the feel of my mouth when I say it, the mystery of how solving an equation can lead to extra solutions. And then learning to check found-solutions to see if they were true solutions -- a process that has been multiply useful to me far afield from mathematics.

My love for this math-word drew me quickly to the title of a poem by Alex Walsh, a high school student from Oberlin, Ohio, who presented her work at the poetry-with-math reading at JMM in Baltimore last Friday. Here are her poems "Convergence" and "The Extraneous Solution" :

My love for this math-word drew me quickly to the title of a poem by Alex Walsh, a high school student from Oberlin, Ohio, who presented her work at the poetry-with-math reading at JMM in Baltimore last Friday. Here are her poems "Convergence" and "The Extraneous Solution" :

Labels:
Alex Walsh,
convergence,
extraneous,
infinite,
JMM Poetry Reading,
math,
mathematician,
permutation,
poetry,
polynomial

## Tuesday, January 21, 2014

### Word problems

*Scarcity: Why Having Too Little Means So Much*(a

*Times*book by S. Mullainathan and E. Shafir, released last September) considers not only the facts but the

*feelings*of scarcity and finds similarities between those those with too little time and those with too little money. The authors report, further, that persons experiencing scarcity do not have the luxury of doing well in their studies -- of mathematics or poetry -- because the scarcity demands their first attention.

And . . . this connection between external environment and a student's learning brings me to a poem by Dian Sousa, a poem that gives us some things to think about.

Labels:
calculate,
Dian Sousa,
equation,
math,
problem,
scarcity,
word problem

## Sunday, January 19, 2014

### Poems and primes

Friday morning, 1-17-2014, looking north from the Baltimore Convention Center |

Labels:
Baltimore,
Ben Orlin,
Douglas Norton,
Euclid,
JMM Poetry Reading,
limerick,
math,
mathematics,
poetry,
primes

## Wednesday, January 15, 2014

### Poetry-with-math, Jan 17, Baltimore

**Please join us!**

**A Reading of Poetry with Mathematics**

Friday, January 17, 2014 4:30 - 6:30 PM

Room 308 Baltimore Convention Center

Room 308 Baltimore Convention Center

*Journal of Humanistic Mathematics*is sponsoring a poetry reading. Following participation by these poets,who have submitted work in advance, there will be an open reading in which interested audience members will be invited to share their math-related poems.

**Participating poets include:**Gizem Karaali, Katharine Merow, Karen Morgan Ivy, Mary-Sherman Willis, Alex Walsh, Ted Theodosopoulos, Stephanie Strickland, Myra Sklarew, JoAnne Growney, E. Laura Golberg, Sandra DeLozier Coleman, Rosanna Iembo, and Irene Iaccarino (musician).

**Sunrise gives**

**each of us**

**a shadow.**

Labels:
2014,
Baltimore,
Gizem Karaali,
JHM,
JMM Poetry Reading,
mathematics,
poetry

## Monday, January 13, 2014

### Writing mathy poems - a student activity

On the web-page of mathematician-poet Sarah Glaz I found a link to this file of math-related poems that she prompted students to write when she visited an Arcadia University class session of "Truth and Beauty: A Course in Mathematics and Literature" taught by mathematician-poet Marion Cohen. The writing was prompted by an activity-list developed by mathematician-poet Carol Dorf. Poems by Whitney Boeckel and Olivia Lantz particularly caught my eye and, with their permission, I present them here:

## Friday, January 10, 2014

### The discipline of mathematics

This poem remembers one of my students.

Madam Professor,

let me introduce myself.

I'm Albert James,

whom you may know

by my test score

that's lower than my age.

**The Prince of Algebra**by JoAnne GrowneyMadam Professor,

let me introduce myself.

I'm Albert James,

whom you may know

by my test score

that's lower than my age.

Labels:
age,
algebra,
clock,
JoAnne Growney,
mathematics,
professor,
score,
teacher

## Tuesday, January 7, 2014

### Martin Gardner, again

This past weekend a review by Teller (magician of the Penn & Teller team) of an autobiography of Martin Gardner appeared in the

*NYTimes Book Review*. According to Teller, Gardner (1914-2010) wrote the memoir,*Undiluted Hocus-Pocus: The Autobiography of Martin Gardner*, at the age of 95 on an old electric typewriter in his single-room assisted-living apartment in Norman, Oklahoma.
Labels:
double acrostic,
magic,
Martin Gardner,
mathematical,
poem,
rhyme,
time,
Tom Hood

## Friday, January 3, 2014

### Count what counts

When I visited Iceland last month, I looked in the bookstores of Reykjavik for bilingual (Icelandic-English) poetry collections; I found none. I did, however, acquire a copy of

I would be invited

everywhere

if I needn't eat at all.

*The Sayings of the Vikings*(Gudrun Publishing, 1992), a translation by Bjorn Jonasson of*HÃ¡vamÃ¡l*-- "sayings of the high one" -- from the Poetic Edda, a collection of Old Norse poems from the Viking era and attributed to Odin. Here are several samples that involve number or measurement:**The Nature of Hospitality**I would be invited

everywhere

if I needn't eat at all.

## Thursday, January 2, 2014

### 2013 (and prior) -- titles, dates of posts

Scroll
down to find dates and titles (with links) of posts in 2013. At the bottom are links to posts through 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.**

Dec 30 Error Message Haiku

Dec 26 The angel of numbers . . .

Dec 23 Ah, you are a mathematician

Dec 20 Measuring Winter

Dec 30 Error Message Haiku

Dec 26 The angel of numbers . . .

Dec 23 Ah, you are a mathematician

Dec 20 Measuring Winter

## Monday, December 30, 2013

### Error Message Haiku

Found at Komplexify.com, a variety of (often-amusing) mathematical verses -- including a collection of Error Message Haiku. Approaching a New Year, I have been reflecting on my device-dependencies and considering resolutions about them -- and musing over some of these wistful substitutions for machine messages I dread:

A crash reduces

Your expensive computer

To a simple stone.

Chaos reigns within.

Reflect, repent, and reboot.

Order shall return.

A crash reduces

Your expensive computer

To a simple stone.

Chaos reigns within.

Reflect, repent, and reboot.

Order shall return.

Labels:
computer,
error message,
haiku,
Komplexify,
memory

## Thursday, December 26, 2013

### The angel of numbers . . .

This poem by Hanns Cibulka (1920 - 2004) -- translated from the German by Ewald Osers -- is collected in the anthology,

—Rafael Alberti

*Strange Attractors: Poems of Love and Mathematics*, edited by Sarah Glaz and me (A K Peters, 2008).**Mathematics**by Hanns Cibulka (trans. Ewald Osers)*And the angel of numbers**is flying**from 1 to 2...*—Rafael Alberti

## Monday, December 23, 2013

### Ah, you are a mathematician

Thanks to Arturo Sangalli of the Writer's Union of Canada -- and fellow-participant in a recent Banff creativity conference -- who reminded me of this poem. And thanks to Bill Dunham who has spread it widely by including it in

they say with admiration

or scorn.

*The Mathematical Universe*(Wiley, 1997). These brief stanzas were written in the early 1990s when many of us kept our financial facts in checkbooks rather than online; still current, however, is the mistaken image of mathematicians as those whose task it is to keep numbers clean and orderly.**Misunderstanding**by JoAnne Growney

**Ah, you are a mathematician,**they say with admiration

or scorn.

Labels:
Arturo Sangalli,
balance,
Christmas,
digits,
JoAnne Growney,
mathematical,
mathematician,
numbers,
pi,
William Dunham

## Friday, December 20, 2013

### Measuring Winter

Thomas Campion (1567-1620) was an English composer, physician, and poet. I found this poem at poetryfoundation.org.

Now winter nights enlarge

The number of their hours;

And clouds their storms discharge

Upon the airy towers.

**Now Winter Nights Enlarge**by Thomas CampionNow winter nights enlarge

The number of their hours;

And clouds their storms discharge

Upon the airy towers.

## Tuesday, December 17, 2013

### Sieve of Eratosthenes

**The Sieve of Eratosthenes**by Robin Chapman

He was an ancient Greek

looking for primes,

those whole numbers divisible

only by 1 and themselves,

those new arrivals on the block,

fresh additions to the stock

of indivisibles spilling through

future time (for what is time

## Saturday, December 14, 2013

### Amounting to Something

From the Fall/Winter 2013 issue of

You were supposed to do that

by saving yourself up

like coins in a pig rescued

just in time sometimes

from in front of the candy counter

or the desk in the corridor

*Poet Lore*, a poem by David Wagoner about the arithmetic of expectations:

**Amounting to Something**by David WagonerYou were supposed to do that

by saving yourself up

like coins in a pig rescued

just in time sometimes

from in front of the candy counter

or the desk in the corridor

Labels:
add,
amount,
calculation,
counting,
David Wagoner,
divide,
multiply,
questions,
subtract

## Wednesday, December 11, 2013

### 13 lads of Christmas

In addition to waterfalls and geysers and the Aurora, Iceland has outstanding museums. On the morning of December 10, I visited the National Museum of Iceland in Reykjavik -- and enjoyed a careful introduction to the history of this fascinating and friendly nation. Something I missed, however, was seeing one of the 13 Yuletide Lads that are an Icelandic tradition and who visit the Museum one-by-one on the 13 days before Christmas, each wearing
traditional costume and trying to pilfer the goodies he
likes best.

## Thursday, December 5, 2013

### Iceland -- poetry, stones

British translator and editor David McDuff blogs at "Nordic Voices in Print" -- a site that he uses as "a way of making some of my translations of Nordic poetry and prose available online." Here is "stones" -- the third of a group of ten poems he has posted by Icelandic poet SjÃ³n. This one involves a few numbers and I present it here as a math-poetry token of the fascinating land I am planning to visit: a five-day Iceland vacation adventure, traveling with my Eastern Village neighbors Priscilla and Glenn.

**stones**by SjÃ³n (translated by David McDuff)
Labels:
David McDuff,
Iceland,
numbers,
poem,
Sjon,
stones,
translation

## Tuesday, December 3, 2013

### Conversational mathematics

In recent weeks I have been experimenting with poems that use mathematical terminology, wondering whether -- since there are readers who are undaunted by unknown literary references (to Dante's

*Divine Comedy*or Eliot's Prufrock, for example) -- some readers will relish a poem with unexplained mathematical connections. In this vein I have offered "Love" (posted on on November 5) and now give the following poem, "Small Powers of Eleven are Palindromes":
Labels:
Catalan,
cube,
irrational,
JoAnne Growney,
language,
mathematics,
number,
palindrome,
perfect,
poem,
power,
twin primes

### Jan - Nov, 2013 -- dates, titles of posts

Scroll
down to find titles and dates of posts in 2013. At the bottom are links to posts through 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.**

Nov 30

Nov 27 Solving equations . . .

Nov 24 Algebra cadabra

Nov 20 A poet (math-daughter) speaks of math's beauty

Nov 18 Counting responses

Nov 16 Inequality of Compromise

Nov 30

**Last year's prediction**Nov 27 Solving equations . . .

Nov 24 Algebra cadabra

Nov 20 A poet (math-daughter) speaks of math's beauty

Nov 18 Counting responses

Nov 16 Inequality of Compromise

## Saturday, November 30, 2013

### Last year's prediction

This poem by Halifax mathematician and poet, Robert Dawson, appeared in

As you may know, at this years’ Winter Solstice

the 12-baktun Long Count will overflow.

*LabLit*in December 2012 (just in time to offer gentle mocking of predicted disaster)! Enjoy!**Survivor's Guide to the Baktun-13 Bug**by Robert DawsonAs you may know, at this years’ Winter Solstice

the 12-baktun Long Count will overflow.

Labels:
baktun,
calendar,
count,
mathematics,
overflow,
poetry,
Robert Dawson

## Wednesday, November 27, 2013

### Solving equations . . .

*collection*of poetry-with-mathematics that I came to was

*Against Infinity: An Anthology of Contemporary Mathematical Poetry*(Primary Press, 1979), collected and edited by Ernest Robson and Jet Wimp. This volume introduced me to poems I could use with my math students and one of my long-term favorites is "Algebra" by Linda Pastan who has, in turn, become one of my favorite poets.

Labels:
Against Infinity,
algebra,
equal,
equations,
Linda Pastan,
math,
poetry,
solving,
Thanksgiving,
unknown,
X,
y

## Sunday, November 24, 2013

### Algebra cadabra

It was my good fortune to meet Colette Inez back in the early 1990s when she was poet-in-residence at Bucknell University. Then, as now, I was collecting poems-with-mathematics, and I have long loved this poem that weaves figuring into forests.

We heard swifts feeding in air,

sparrows ruffling dusty feathers,

a tapping on stones, mud, snow, pulp

when rain came down, the hiss of fire.

Counting bird eggs in a dome of twigs,

we heard trees fall and learned

to name them on a page for school.

**Forest Children**by Colette InezWe heard swifts feeding in air,

sparrows ruffling dusty feathers,

a tapping on stones, mud, snow, pulp

when rain came down, the hiss of fire.

Counting bird eggs in a dome of twigs,

we heard trees fall and learned

to name them on a page for school.

## Wednesday, November 20, 2013

### A poet (math-daughter) speaks of math's beauty

I met Minnesota poet Roseann Lloyd when we served together on an AWP (Associated Writing Programs) conference panel on translation several years ago. There I was considering, as I so often am, the translation of mathematics into representations that poets understand. Roseann 's father was a mathematics professor and she learned early that "mathematics is its own beauty." And she has permitted me to offer you this poem.

Once Daddy enthralled his students at SMS --

handsome in his navy blue suit and dusty hands,

chalk clicking out equations lickety-split.

A third-grader, I waited for him every day

in the cool marble hall. Listened to the rhythm

of the chalk on the board. Even then I knew

that pure math is an art equal to music, second

only to poetry in the realm of beauty.

**HOW MY DADDY CHANGED WHEN HE GAVE UP TEACHING COLLEGE FOR SELLING INSURANCE**by Roseann LloydOnce Daddy enthralled his students at SMS --

handsome in his navy blue suit and dusty hands,

chalk clicking out equations lickety-split.

A third-grader, I waited for him every day

in the cool marble hall. Listened to the rhythm

of the chalk on the board. Even then I knew

that pure math is an art equal to music, second

only to poetry in the realm of beauty.

Labels:
beauty,
equation,
math,
mathematics,
poet,
poetry,
prime,
Roseann Lloyd,
translation

## Monday, November 18, 2013

### Counting responses

At the Poetry Foundation website, poet Audre Lorde (1934-1992) is described thus:

and her creative talent to confronting and addressing

the injustices of racism, sexism, and homophobia.

Here is a counting poem by this fine, bold poet:

A self-styled "black, lesbian, mother, warrior, poet,"

writer
Audre Lorde dedicated both her life and her creative talent to confronting and addressing

the injustices of racism, sexism, and homophobia.

Here is a counting poem by this fine, bold poet:

Labels:
Audre Lorde,
counting,
injustice,
poem,
questions

## Saturday, November 16, 2013

### Inequality of Compromise

This past week I attended a wonderfully stimulating BIRS (Banff International Research Station) Conference -- a gathering of creative writers in mathematics and the sciences -- and, as I told colleagues at Banff of early days in my long-term interest in the poetry of mathematics, I recalled the fine collection

*Against Infinity: An Anthology of Contemporary Mathematical Poetry*(Primary Press, 1979), collected and edited by Ernest Robson and Jet Wimp. Today I pulled it from my shelves and again turned its pages. "Compromise" by Missouri mathematician Charles S. Allen caught my eye. Here it is:
Labels:
Against Infinity,
anthology,
Charles Allen,
compromise,
inequality,
mathematics,
poetry

## Monday, November 11, 2013

### The minute in infinity

*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!

*Translated from the Latin by Helen M. Walker*

Found in the anthology,

*Strange Attractors: Poems of Love and Mathematics*(A K Peters, 2008), edited by Sarah Glaz and me. A complete table of

*Contents*for this collection may be found here.

## Thursday, November 7, 2013

### Like advanced math?

One thing leads to another . .. . poet Amy Eisner connected me to mathematician Jordan Ellenberg who knew of

There was a pattern to the way the mythical beasts

flew over the dreary town, but we were too dreary

to understand it. The psychologist, too, was in touch

with extraterrestrials, but she had to stand on the spire

of a church and wear 3-D glasses to see them.

*Easy Math*(Sarabande Books, 2013) by Lauren Shapiro -- and Lauren gave me permission to post her "Bent Syllogism."**Bent Syllogism**by Lauren ShapiroThere was a pattern to the way the mythical beasts

flew over the dreary town, but we were too dreary

to understand it. The psychologist, too, was in touch

with extraterrestrials, but she had to stand on the spire

of a church and wear 3-D glasses to see them.

## Tuesday, November 5, 2013

### Love mathematics!

In the stanzas below, I have some fun with math terminology. Hope you'll enjoy it too.

Love algebra! Through variable numbers

of factored afternoons and prime evenings,

party in and out of your circle of associates,

identify your identity, meet your inverse.

**Love!**by JoAnne GrowneyLove algebra! Through variable numbers

of factored afternoons and prime evenings,

party in and out of your circle of associates,

identify your identity, meet your inverse.

Labels:
arithmetic,
calculus,
chaos,
identity,
imaginary,
Integral,
inverse,
Mobius band,
pi,
prime,
rational,
real,
symmetries,
tangent

## Sunday, November 3, 2013

### Neruda speaks of numeration

The collection, Late and Posthumous Poems, 1968-1974 (Grove Press, 1988) by Chilean Nobelist Pablo Neruda (1904-1973) offers to readers a collection of Neruda's later work, ably translated by Ben Belitt. Here is a poem that explores the vast world opened by the invention of numeration.

A hand made the number.

It joined one little stone

to another, one thunderclap

to another,

one fallen eagle

to another, one

arrowhead to another,

and then with the patience of granite

the hand

made a double incision, two wounds,

and two grooves: and a

number was born.

**28325674549**by Pablo NerudaA hand made the number.

It joined one little stone

to another, one thunderclap

to another,

one fallen eagle

to another, one

arrowhead to another,

and then with the patience of granite

the hand

made a double incision, two wounds,

and two grooves: and a

number was born.

Labels:
counting,
number,
numeral,
numeration,
Pablo Neruda,
poem

### Jan - Oct, 2013 -- dates, titles of posts

Scroll
down to find titles and dates of posts in 2013. At the bottom are links to posts through 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.**

Oct 31 On poetry and geometric truth . . .

Oct 29 From order to chaos -- a sonnet

Oct 26 Two cultures

Oct 22 Two-line poems -- Landays -- from Afghanistan

Oct 21 Topology for poets

Oct 18 Mathematics of love . . .

Oct 31 On poetry and geometric truth . . .

Oct 29 From order to chaos -- a sonnet

Oct 26 Two cultures

Oct 22 Two-line poems -- Landays -- from Afghanistan

Oct 21 Topology for poets

Oct 18 Mathematics of love . . .

## Thursday, October 31, 2013

### On poetry and geometric truth . . .

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.

William Wordsworth (1770-1850)

from

*The Prelude,*Book 5

Labels:
geometric,
poetry,
truth,
William Wordsworth

## Tuesday, October 29, 2013

### From order to chaos -- a sonnet

**Fractals**by Diana Der-Hovanessian

*Euclid alone has looked on beauty bare*

--Edna St. Vincent Millay

Euclid alone began to formulate

the relation of circle, plane and sphere

in equations making it quite clear

that symmetry is what we celebrate.

Labels:
Benoit Mandelbrot,
chaos,
Diana Der-Hovanessian,
Euclid,
fractal,
symmetry,
turbulence

## Saturday, October 26, 2013

### Two cultures

The opening poem of

much money in poetry:

and none vice-versa.

The first part stays true

if we replace poetry

by mathematics.

*Uneasy Relations*by mathematician-poet Michael Bartholomew-Biggs is concerned with similarities and differences between mathematical and poetic cultures -- a topic of immense interest also to me and one that I too try to address in my verse. I wonder -- HOW can I show non-mathematicians that good mathematics is poetry??!! And, moreover, how can I (mostly a mathematician) write (as advocated by Wallace Stevens and agreed with by other poets) of things rather than (as mathematics wants) of ideas. OR, may one make poetry of ideas?**Two Cultures**by Michael Bartholomew-Biggs**Graves claimed there isn't**

much money in poetry:

and none vice-versa.

The first part stays true

if we replace poetry

by mathematics.

## Tuesday, October 22, 2013

### Two-line poems -- Landays -- from Afghanistan

**Celebrate Activist Poetry -- At Nov. 1 Event**

**BE THERE on November 1, 2013 at the Goethe-Intitut in Washington DC**when poet and journalist

**Eliza Griswold**is honored with the

**Split this Rock Freedom Plow Award**(register here for this important event)

**for Poetry and Activism**for her work collecting and introducing the folk poems of Afghan women to America. The June issue of

*Poetry Magazine*is entirely dedicated to

*-- two-line poems by Afghan women that capture dark, funny, and revealing moments that few outsiders ever witness. (Edited and introduced by Griswold, the poems are magnificently supplemented by photographs by Seamus Murphy.)*

**landays**Here are three landays from Griswold's

*Poetry*collection, each selected for inclusion here because it includes at least one number:

Labels:
Afghan,
Eliza Griswold,
Freedom Plow Award,
landay,
number,
poem,
Poetry Foundation,
Split This Rock

## Monday, October 21, 2013

### Topology for poets

The title of this posting ("Topology for Poets") comes from Maryland Poet Amy Eisner's poem "Lure" (offered below) -- a poem that plays with math concepts. (In mathematics, "topology" is a variant of geometry in two shapes are "equivalent" if one could be obtained from the other by stretching or bending.)

It was my pleasure to meet Amy when she read in the Takoma Park Third Thursday Poetry Series earlier this year. I like her work. Enjoy!

My friend is crocheting a fishing line. This is not a gift and keeps no one warm.

This is withdrawing. Persisting in a flaw. Forfending.

She knows there’s something perverse in it. Like growing a mold garden.

Fishing does involve a hook, a line, and a net. But not like this.

It was my pleasure to meet Amy when she read in the Takoma Park Third Thursday Poetry Series earlier this year. I like her work. Enjoy!

**Lure**by Amy Eisner**1.**My friend is crocheting a fishing line. This is not a gift and keeps no one warm.

This is withdrawing. Persisting in a flaw. Forfending.

She knows there’s something perverse in it. Like growing a mold garden.

Fishing does involve a hook, a line, and a net. But not like this.

Labels:
Amy Eisner,
infinite series,
line,
mathematics,
net,
poem,
Takoma Park,
topology

## Friday, October 18, 2013

### Mathematics of love . . .

"Mathematics of Love" is the title poem of a collection by John Edwin Cohen (1941-2012), published in 2011 by Anaphora Literary Press and presented here with press permission. Cohen has used mathematics playfully and does what a mathematician never dares to do, use a mathematical term with other than its precise meaning. Still, perhaps, even math folks may enjoy this application of geometric shape and poetic license!

**Mathematics of Love**by John Edwin Cohen**1.**

**Engine of joy****arithmetic and sincere****holding the hemisphere****and geometry of****youth**
Labels:
algebras,
circle,
geometry,
hypotenuse,
John Edwin Cohen,
mathematician,
mathematics,
tangent,
zeroes

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