Sarah Glaz
Estados Unidos. Poeta y matemática.
Profesora de matemáticas en la Universidad de Connecticut, se especializa en el área de matemática del álgebra conmutativa.
Tiene un interés de por vida en la poesía y sirve como editora asociada de la revista Journal of Matemáticas y las Artes. Coeditora de la antología de poesía los atractores extraños: Poemas de Amor y Matemáticas (AK Peters, 2008) y ha publicado poemas y traducciones en ambas publicaciones periódicas de matemáticas y literatura.
¿Cuál es la cosa más sabia? Número.
¿Cuál es la más hermosa? Armonía.
“Sobre el modo de vida pitagórico”
Jámblico (siglo 3 dC)
Pitágoras toca la lira
Pitágoras toca la lira
rodeado de matemáticos.
Cantamos himnos mientras el tañe
las cuerdas:
Descubrimos
la ley del cosmos:
Todo es número!
Proporciones misteriosas!
Desde la manera de vibrar las cuerdas
a las relaciones armónicas
hacen el sonido de la música
como el cielo.
Los granos sagrados brotan
en los campos cercanos.
Todos los animales son parte
de nuestra familia.
En el intervalo entre
la tierra y el firmamento
planetas en círculo y murmullos
en concierto.
Cada uno una nota
en la gran sinfonía
de la creación.
Guardamos
su secreto más íntimo.
La música se elevaba en el aire
como el humo de incienso quemado
para complacer a los dioses que nos miran
tocar y pasar.
Pythagoras plays his lyre
Pythagoras plays his lyre
surrounded by mathematicians.
We sing paeans as he strikes
the cords:
We discovered the
law of the cosmos:
All is number!
Mysterious proportions!
The way strings vibrate
to harmonic ratios
makes music sound
like heaven.
The sacred beans sprout
in the nearby elds.
All animals are part
of our family.
In the interval between
earth and the firmament
planets circle and hum
in concert.
Each One a note
in the grand symphony
of all creation.
We guard
its innermost secret.
The music wafts upward
like smoke from burnt incense
pleasing the gods who watch us
play and pass.
Sarah Glaz “Pythagoras plays his lyre” publicado en Journal of Humanistic Mathematics
http://elestablodepegaso.blogspot.com.es/
Departures in May
Big things crush, inside the brain,
like plaster of Paris on stone;
a taste of splintered metal;
terra-cotta hardness of heart's desire.
Statues motionless
at railroad depots,
proclaim imitation as life.
A white bird flies low above platforms,
sweeps above train cars;
The Orient Express of boundless motion--
preserved lanterns,
boundless upholstery,
carriages of red absorbency,
soundlessly waiting for late chances.
I had been to Paris-Roma-Venezia,
felt the grid of time
curve in space, fluid,
twined arcs convergent at infinity,
defying Euclid.
Suspended on pale May sky,
puffed-up clouds--
grave formulas,
ominous signs,
white droppings of the aged snow bird,
death white.
This poem first appeared in Ibis Review, 1995. Poet Sarah Glaz is a mathematics professor at the University of Connecticut and her webpage provides (scroll down) a wealth of links to poetry-math resources. News of Glaz's activity and her poems have appeared often in this blog; enter her name into the SEARCH box at the top of the right-hand column of this blog to find these various items.
Mathematical Modelling
Mathematical modelling may be viewed
As an organizing principle
That enables us to handle
A vast array of information
As an organizing principle
We could use the color spectrum
A vast array of information
Would become a rainbow in the sky
We could use the color spectrum
And the scaling notes spanning an octave
Would become a rainbow in the sky
Shining through the melody of rain
And the scaling notes spanning an octave
And letters gleaned from ancient alphabets
Shining through the melody of rain
Nature translated into words
And letters gleaned from ancient alphabets
That enable us to handle
Nature translated into words
May be viewed as mathematical modelling
A pantoum for the power of theorems
The power of the Invertible Matrix Theorem lies
in the connections it provides among so many important
concepts… It should be emphasized, however, that the
Invertible Matrix Theorem applies only to square matrices.
―David C. Lay, “Linear Algebra”
The power of a theorem lies
In the connections it provides
Among many important concepts
Under a certain set of assumptions
In the connections it provides
We are always able to find
Under a certain set of assumptions
Some that fell through the cracks
We are always able to find
Neglected aspects of ourselves
Some that fell through the cracks
Left unexplored by mathematics
Neglected aspects of ourselves
(The power of a theorem lies)
Left unexplored by mathematics
Among many important concepts
I am a number
1
I am tall
and
one sided
like an ostrich
Pluck
the eye
of my feather
whittle
the stick
of
remembrance
bare
of
ormamentation
Alone
2
I am fat with contentment
In the arc
of survival
we win
by a hair
Kick
the less
fortunate
down the plank
to make space
3
I am prime
and conflicted
One more or one less
The spoke in the wheel
or grease that makes it go
Increase and multiply
or divide
and divorce
4
I am Parmenides’ many
on the edge of ancient counting:
the stars in the sky
fattened sheep of pharaoh
the dappled cows of the gods grazing under the sun
and all the grains of sand
on the seashore
I am a number (II)
5
Forged in time’s fire
my golden figure
rises
open
to the past
and the future
I count my digits
All Present
yet only
half way there
6
I can be factored
into selves
from
former lives
each one
more potent
than
I
am
Unmultiplied
I disappear
7
Last prime
before
the count of time
halts
and
the great mystery
begins
8
How did it come to that
9
I have no time
10
Decem
13 January 2009
13 January 2009
12=22x3 Anuk is dying for Anuk is dying in the white of winter
11 The coldest month
10=2x5 Anuk is dying in the falling snow
9=32 The white of winter for Anuk is dying
8=23 Anuk is dying for the white of winter
7 The drift of time
6=2x3 Anuk is dying in the white of winter
5 The falling snow
4=22 Anuk is dying for Anuk is dying
3 The white of winter
2 Anuk is dying
1 .
The Enigmatic Number e
It ambushed Napier at Gartness,
like a swashbuckling pirate
leaping from the base.
He felt its power, but never realized its nature.
e's first appearance in disguise—a tabular array
of values of ln, was logged in an appendix
to Napier's posthumous publication.
Oughtred, inventor of the circular slide rule,
still ignorant of e's true role,
performed the calculations.
A hundred thirteen years the hit and run goes on.
There and not there—elusive e,
escape artist and trickster,
weaves in and out of minds and computations:
Saint-Vincent caught a glimpse of it under rectangular hyperbolas;
Huygens mistook its rising trace for logarithmic curve;
Nicolaus Mercator described its log as natural
without accounting for its base;
Jacob Bernoulli, compounding interest continuously,
came close, yet failed to recognize its face;
and Leibniz grasped it hiding in the maze of calculus,
natural basis for comprehending change—but
misidentified as b.
The name was first recorded in a letter
Euler sent Goldbach in November 1731:
"e denontat hic numerum, cujus logarithmus hyperbolicus est=1."
Since a was taken, and Euler
was partial to vowels,
e rushed to make a claim—the next in line.
We sometimes call e Euler's Number: he knew
e in its infancy as 2.718281828459045235.
On Wednesday, 6th of May, 2009,
e revealed itself to Kondo and Pagliarulo,
digit by digit, to 200,000,000,000 decimal places.
It found a new digital game to play.
In retrospect, following Euler's naming,
e lifted its black mask and showed its limit:
e=limn→∞(1+1n)ne=limn→∞(1+1n)n
Bernoulli's compounded interest for an investment of one.
Its reciprocal gave Bernoulli many trials,
from gambling at the slot machines to deranged parties
where nameless gentlemen check hats with butlers at the door,
and when they leave, e's reciprocal hands each a stranger's hat.
In gratitude to Euler, e showed a serious side,
infinite sum representation:
e=∑n=0∞1n!=10!+11!+12!+13!+⋯e=∑n=0∞1n!=10!+11!+12!+13!+⋯
For Euler's eyes alone, e fanned the peacock tail of
e−12e−12's continued fraction expansion,
displaying patterns that confirmed
its own irrationality.
A century passed till e—through Hermite's pen,
was proved to be a transcendental number.
But to this day it teases us with
speculations about ee.
e's abstract beauty casts a glow on Euler's Identity:
eiπ + 1 = 0,
the elegant, mysterious equation,
where waltzing arm in arm with i and π,
e flirts with complex numbers and roots of unity.
We meet e nowadays in functional high places
of Calculus, Differential Equations, Probability, Number Theory,
and other ancient realms:
y = ex
e is the base of the unique exponential function
whose derivative is equal to itself.
The more things change the more they stay the same.
e gathers gravitas as solid under integration,
∫exdx=ex+c∫exdx=ex+c
a constant c is the mere difference;
and often e makes guest appearances in Taylor series expansions.
And now and then e stars in published poetry—
honors and administrative duties multiply with age.
Sarah Glaz (University of Connecticut), "The Enigmatic Number [i]e:[/i] A History in Verse and Its Uses in the Mathematics Classroom - The Annotated Poem," Convergence (November 2010), DOI:10.4169/loci003482
Calculus
I tell my students the story of Newton versus Leibniz,
the war of symbols, lasting five generations,
between The Continent and British Isles,
involving deeply hurt sensibilities,
and grievous blows to national pride;
on such weighty issues as publication priority
and working systems of logical notation:
whether the derivative must be denoted by a "prime,"
an apostrophe atop the right hand corner of a function,
evaluated by Newton's fluxions method, Δy/Δx;
or by a formal quotient of differentials dy/dx,
intimating future possibilities,
terminology that guides the mind.
The genius of both men lies in grasping simplicity
out of the swirl of ideas guarded by Chaos,
becoming channels, through which her light poured clarity
on the relation binding slope of tangent line
to area of planar region lying below a curve,
The Fundamental Theorem of Calculus,
basis of modern mathematics, claims nothing more.
While Leibniz―suave, debonair, philosopher and politician,
published his proof to jubilant cheers of continental followers,
the Isles seethed unnerved,
they knew of Newton's secret files,
locked in deep secret drawers—
for fear of theft and stranger paranoid delusions,
hiding an earlier version of the same result.
The battle escalated to public accusation,
charges of blatant plagiarism,
excommunication from The Royal Math. Society,
a few blackened eyes,
(no duels);
and raged for long after both men were buried,
splitting Isles from Continent, barring unified progress,
till black bile drained and turbulent spirits becalmed.
Calculus―Latin for small stones,
primitive means of calculation; evolving to abaci;
later to principles of enumeration advanced by widespread use
of the Hindu-Arabic numeral system employed to this day,
as practiced by algebristas―barbers and bone setters in Medieval Spain;
before Calculus came the Σ (sigma) notion―
sums of infinite yet countable series;
and culminating in addition of uncountable many dimensionless line segments―
the integral integral―snake,
first to thirst for knowledge, at any price.
That abstract concepts, applicable―at start,
merely to the unseen unsensed objects: orbits of distant stars,
could generate intense earthly passions,
is inconceivable today;
when Mathematics is considered a dry discipline,
depleted of life sap, devoid of emotion,
alive only in convoluted brain cells of weird scientific minds.
.
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