Pi Day

Mar. 14th, 2024 08:03 am
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Pi Day is March 14, when the world celebrates the mathematical constant of the ratio of the circumference of a circle C to its diameter d: π = C/d. The circumference of a circle is, in turn, equal to 2πr, where r is the circle's radius. The constant is important in many scientific calculations and has long played an important role in engineering.

As a concept, pi has been in use since at least the time of the Babylonians and ancient Egypt: both approximated modern values of pi to within one percent (3.125 and 3.16, respectively). Archimedes is the attested author of the first rigorous definition of pi, which he did by way of geometry, using polygons with ever-greater numbers of sides. By 150 CE, Ptolemy had the value of pi at 3.1416, which he may have done using the Archimedean method.

The first 100 digits of pi are 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679.

Mathematicians have estimated that an approximation of pi to 39 digits will suffice for any cosmological calculation humans might attempt. At that level of precision, which mathematicians achieved in 1630, you can calculate the circumference of the observable universe with an error smaller than the diameter of a single atom of hydrogen.

As of 2023, the world record holder for the most precise calculation of pi is Jordan Ranous of StorageReview. Ranous used y-cruncher, a benchmarking program that uses the Chudnovsky algorithm for main computation, to calculate pi to a precision of one hundred trillion decimal places. The calculation and validation took a few hours shy of two months to complete, using a pair of AMD EPYC 9654 processors that drew on just under 600TB of QLC flash memory and more than 1.5 terabytes of RAM between them.

In 2022, Google Cloud Developer Advocate Emma Haruka Iwao announced that she and her team had calculated the value of pi to a precision of 100 trillion decimal places—a flex on her previous record of 31.4 trillion digits, set in 2019. "We were impressed by the achievement of Emma and the Google Cloud," Ranous wrote, "but we also wondered if we could do it faster, with a lower total cost."

Still, they had to solve one critical problem: How to create a storage volume of sufficient size to hold a text file a hundred trillion digits long. In the end, the team used a RAID 0 array, finishing their calculation in about a third of the compute time it took the team from Google Cloud. ("While RAID 0 might raise some eyebrows," Ranous wrote, "in our defense, the file server storage was carved out of a mirrored Windows Storage Spaces pool, so redundancy was available on the remote host.")

Ranous and his team also published(https://cloud.google.com/blog/products/compute/calculating-100-trillion-digits-of-pi-on-google-cloud) their y-cruncher validation file and the last 100 of those 100 trillion digits—just in case anyone wants to check their work.

So, next one is looking forward to Mole Day, which happens to be October 23.
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April is both National Poetry Month and Mathematics and Statistics Awareness Month, so a few years ago science writer Stephen Ornes dubbed it Math Poetry Month. If the words “math” and “poetry” don’t intuitively make sense to you as a pair, poet and mathematician JoAnne Growney’s blog Intersections—Poetry with Mathematic is a perfect place to start expanding your math-poetic horizons. The blog includes a broad range of poems with mathematical themes or built using mathematical rules.

Take "Geometry," by former U.S. Poet Laureate Rita Dove:

I prove a theorem and the house expands:
the windows jerk free to hover near the ceiling,
the ceiling floats away with a sigh.

Or “In Praise of Fractals” by Emily Grosholz, published in The Stars of Earth: New and Selected Poems (2017, Word Galaxy Press):

Euclid’s geometry cannot describe,
nor Apollonius’, the shape of mountains,
puddles, clouds, peninsulas or trees.
Clouds are never spheres,
nor mountains cones, nor Ponderosa pines;
bark is not smooth; and where the land and sea
so variously lie about each other
and lightly kiss, is no hyperbola.

Compared with Euclid’s elementary forms,
Nature, loosening her hair, exhibits patterns
(sweetly disarrayed, afloat, uncombed)
not simply of a higher degree n
but rather of an altogether different
level of complexity:
the number of the scales of distances
describing her is almost infinite.

Growney casts a wide net on her blog, which begins with the words: "Mathematical language can heighten the imagery of a poem; mathematical structure can deepen its effect." Some poems she features, like “Geometry," use mathematical themes or images; some are by mathematicians or math students. Growney has also gotten interested in the mathematics of poetic forms and poetic forms that employ mathematics.

Of course, sonnets and haiku are famous for employing strict counts on lines and syllables. But she is also interested in newer forms, often inspired by the constrained writing exercises of the French Oulipo group(https://poets.org/text/brief-guide-oulipo), which was founded by mathematicians and poets.

One such form is the “Fib”(https://poetrywithmathematics.blogspot.com/2010/10/fib-form-that-gathers-strength.html), a type of poem based on the Fibonacci sequence in math. The Fibonacci sequence starts 1, 1, 2, 3, 5, 8, and so on; each term (after the first two) is the sum of the two terms before it. In a Fib poem, the first line has one syllable, the second one syllable, the third two, the fourth three, and so on. Growney, a retired math professor who sometimes teaches writing workshops, says a limited form like the Fib can help beginning poets who are having trouble starting.

For example, from “Fibonacci Poems” by Athena Kildegaard, published in Rare Momentum:

Kiss
me
again
tongue and lips
like Fibonacci's
sequence, each movement a spiral,
enfold, unfold, a working through and against, again.

Growney grew up wanting to be a writer. “I read Little Women as a girl, and maybe it was partly the name connection, but I thought that I wanted to be a writer like Jo.” She was also good at math, though, and ended up with a scholarship to study it in college. She stuck with it and earned her Ph.D. in 1970 at the University of Oklahoma. During her career as a math professor, her interest in writing continued. She took poetry classes at a nearby college when she could, discovered the math poetry anthology Against Infinity while doing a sabbatical project about mathematics and the arts, and started to see her feelings about mathematics echoed in poetry.

Mathematics and poetry, Growney says, are both “formats that can convey multiple meanings.” In mathematics, a single object or idea might take different forms. A quadratic equation, for example, can be understood in terms of its algebraic expression, perhaps y=x2+3x-7, or in terms of its graph, a parabola. Henri Poincaré, a French polymath who laid the foundations of two different fields of mathematics in the early 1900s, described mathematics as “the art of giving the same name to different things.”

Likewise, poets create layers of meaning by utilizing words and images that have multiple interpretations and associations. Both mathematicians and poets strive for economy and precision, selecting exactly the words they need to convey their meaning.

These features of mathematics and poetry can make them daunting and frustrating for students. “If a student sees only one meaning and the intent is to exploit another meaning, it seems manipulative or unfair,” says Growney. But Growney’s approach to poetry can also inform our attitude towards unfamiliar mathematics. “A rule I use for poetry is you first of all read it through once without worrying about understanding,” she says. “If there’s something you like about it, read it again. Give yourself ten readings before you say you don’t understand it.”

As a professor, she used poetry in her mathematics classes to help students to connect emotionally to mathematics, learn a little bit about the history of what they were doing in class, and think of mathematics as a shared human experience. Now that she is retired, she is still active in the math poetry world, often participating in poetry events at the annual Joint Mathematics Meetings, the largest math conference in the U.S., and the Bridges conference on mathematics and the arts(http://www.bridgesmathart.org).

From her poems is “My Dance Is Mathematics,” about Emmy Noether and women in mathematics. The poem begins with a with a poetic foreward that mathematician Hermann Weyl used to eulogize the great mathematician when she died in 1935:

Down, down, down into the darkness of the grave
Gently they go, the beautiful, the tender, the kind;
Quietly they go, the intelligent, the witty, the brave.
I know. But I do not approve. And I am not resigned.

It continues:

They called you der Noether, as if mathematics
was only for men. In 1964, nearly thirty years
past your death, I saw you in a spotlight
in a World's Fair mural, "Men of Modern Mathematics."

Colleagues praised your brilliance--but after
they had called you fat and plain, rough and loud.
Some mentioned kindness and good humor
though none, in your lifetime, admitted it was you
who led the way in axiomatic algebra.
Direct and courageous, lacking self-concern,
elegant of mind, a poet of logical ideas.

At a party when you were eight years old,
you spoke up to solve a hard math puzzle.
Fearless, you set yourself apart.

I followed you and saw you choose
between mathematics and other romance.
For women only, this exclusive standard.

I heard fathers say, "Dance with Emmy--
just once, early in the evening. Old Max
is my friend; his daughter likes to dance."

If a woman's dance is mathematics,
she dances alone.

Mothers said, "Don't tease. That strange one's heart
is kind. She helps her mother with the house
and cannot help her curious mind."

Teachers said, "She's smart but stubborn,
contentious and loud, a theory builder
not persuaded by our ideas."

Students said, "She's hard to follow, bores me."
A few stood firm and built new algebras
on her exacting formulations.

In spite of Emmy's talents,
always there were reasons
not to give her rank
or permanent employment.
She's a pacifist, a woman.
She's a woman and a Jew.
Her abstract thinking
is female and abstruse.

Today, history books proclaim that Noether
is the greatest mathematician
her sex has produced. They say she was good
for a woman.

When Growney started her math poetry blog, she thought she had about a year’s worth of material. Since then, far from dancing alone, she has made connections with poets and mathematicians around the world, finding more and more to share. Eight years and almost 900 posts later, she says, “I have more than I started with.”

For more details, please take a look to Growney’s blog at: https://poetrywithmathematics.blogspot.com
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You have 20 bottles of pills. 19 bottles have 1.0 grams pills, but one bottle has pills of weight 1.1 grams. You have been provided a weighting device to identify which bottle is the heaviest. You have to weight only once.

Solution below in first comment...
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10. Trinity, a Cray XC40 running at Los Alamos National Laboratory, has an incredible important job: replaced US nuclear test which last was conducted in September 1992. Speed: 8.1 petaflops.

9. Mira is an IBM BlueGene/Q system cranking away at the U.S. Department of Energy’s Argonne National Laboratory. System conducts scientific research in seismology, climatology, material science, transportation efficiency and computational chemistry. Speed: 8.59 petaflops.

8. The K computer is installed at the Riken Advanced Institute for Computational Science in Kobe, Japan. It could perform advanced climate research, disaster prevention and medical research. Speed: 10.5 petaflops.

7. Oakforest-PACS is a Fujitsu PRIMERGY system operated by Japan’s Joint Center for Advanced High Performance Computing. It’s installed in the Information Technology Center at the University of Tokyo’s Kashiwa Campus, though its number crunching superpowers also benefit the University of Tsukuba. Speed: 13.5 petaflops.

6. Cori, Cray XC40 is named for Gerty Cori, the first woman to win a Nobel Prize in Physiology or Medicine—and the first American woman to win a Nobel Prize in science. Cori the supercomputer does its best as the centerpiece of a new Big Data Center , a collaboration between the U.S. National Energy Research Scientific Computing Center, Intel and five Intel Parallel Computing Centers. Speed: 14 petaflops.

5. Sequoia, the IBM BlueGene/Q supercomputer, installed at the U.S. Department of Energy’s Lawrence Livermore National Laboratory. It’s tapped to quantify uncertainties “in numerical simulations of nuclear weapons performance” and perform “advanced weapons science calculations". Speed: 17.1 petaflops.

4. Titan, the Cray XK7 megamachine installed at the U.S. Department of Energy’s Oak Ridge National Laboratory. A University of California, Santa Cruz, research team is on the case, using Titan’s massive compute powers to generate “nearly a trillion-cell simulation of an entire galaxy, which would be the largest simulation of a galaxy ever. Speed: 17.5 petaflops.

3. Piz Daint is a mountain in the Swiss Alps whose name translates roughly to “inner peak.” It’s also the name of the supercomputer, installed in Switzerland, at the Swiss National Supercomputing Centre. Climate scientists in Bern recently tapped Piz Daint to help them understand the causes of Europe’s destructive summer storms. Speed: 19.5 petaflops.

2. Tianhe-2, or as it’s known in English, Milky Way-2, which was developed by China’s National University of Defense Technology and is deployed at the National Supercomputer Center in Guangzho, China. In April 2015, the U.S. government rejected Intel’s application for an export license that would have increased the power of Tianhe-2’s CPUs and coprocessor boards due to concerns about the supercomputer being used for “nuclear explosive activities.” Speed: 33.8 petaflops.

1. Sunway TaihuLight lives at the National Supercomputing Center in Wuxi, China, where its 10 million+ CPU cores have created the biggest, most detailed simulation of the universe. The simulation covers millions of years in the universe’s history, with the goal of helping scientists uncover new discoveries. And it’s “just a warm-up exercise,” says an author of the simulation study. Reportedly China is building “an even larger computer that will be capable of performing over ten times as many calculations as TaihuLight. Speed: 93 petaflops.

$2.56

May. 26th, 2017 09:02 am
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"If you think you're a really good programmer... read (Knuth's) Art of Computer Programming ... You should definitely send me a résumé if you can read the whole thing," read a quote from Bill Gates on the cover of the third edition of the first volume.

In the world of Silicon Valley, there are few books held in higher esteem than "Art of Computer Programming" a multivolume set by Stanford professor emeritus Donald Knuth.

When the first volume of "The Art of Computer Programming" came out in 1962, it was the first book to take a deep look into the math and science of programming. Knuth has made this his life's work, and has said that it'll be a seven-volume set before it's done. The most recent piece of the book was released in December 2015.

And despite its long publishing history, Knuth keeps "The Art of Computer Programming" up to date by enlisting his many fans. If you spot any kind of error in his books, you might get one of his famous "Knuth reward checks," a bounty in the amount of $2.56, or what he calls "one hexadecimal dollar." Those checks are a valuable prize for anyone who wants to prove that they know what they're talking about.
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The British mathematician and computer scientist was born on June 23, 1912 - one hundred years ago.

Alan Turing is most famous for his work at Bletchley Park, England , during World War II. His algorithms were critical to breaking German codes, and for his involvement in the construction of computers(called bombes) that helped automate the decryption process. His name is synonymous with the Enigma, the German navy's fiendishly complicated code machine.

Turing is also known for his work on what we call the Turing Machine, a theoretical device that he envisioned could solve any computer algorithm that could be described on paper tape. However, sometimes the Turing Machine would halt and present a solution. Sometimes it would not halt and would keep running forever, meaning the problem could not be solved.

And of course, there is the Turing Test, his thought experiment that said that if a computer could trick a human into thinking that he or she was conversing with another human, then the computer could be said to be thinking. Through the Turing Test and other works, Alan Turing is one of the fathers of artificial intelligence(AI).

Sadly, the homosexual Turing was a victim of that era's intense prejudice. After being forced to endure chemical castration as the alternative to imprisonment for violating Britain's decency laws, the brilliant mathematician committed suicide at age of 41.
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This year we will experience 4 unusual dates:
 
1/1/11,
1/11/11,
11/1/11, and
11/11/11
 
Now figure this out:  Take the last 2 digits of the year you were born, plus the age you will be this year, and it will equal 111!

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