July 26, 2014

3:19 AM | Tiling using Spiral Hexaskelions
The spirals are logarithmic spirals:r(θ) = a exp(bθ), b = 0.25.The spirals are logarithmic spirals:r(θ) = a exp(bθ), b = golden ratio ~ 0.618.The spirals are Archimedean spirals.(1 < number of spiral turns < 2)The spirals are Archimedean spirals.(2 < number of spiral turns < 3)The spirals are logarithmic spirals:r(θ) = a exp(bθ), b = 0.05, 0.1, 0.15, 0.2, ..., 0.8.( Mathematical software used: GeoGebra )
2:18 AM | 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, 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 […]

July 24, 2014

6:23 PM | Spiral Starfish - a logarithmic spiral pentaskelion
A pentaskelion with five logarithmic spirals r(θ) = a*exp(b*θ),b ~ 0.30635 (same as that of the golden spiral).b = 0.25b = 0.5b = golden ratio ~ 0.618( Mathematical software used: gnuplot )

July 23, 2014

12:00 AM | Ink Molecules
Ink Molecules Suppose you were to print, in 12 point text, the numeral 1 using a common cheap ink-jet printer. How many molecules of the ink would be used? At what numerical value would the number printed approximately equal the number of ink molecules used? David Pelkey This is the kind of problem where Fermi estimation comes in handy. In Fermi estimation, we're not concerned about exact numbers. We just want, before we start doing research, to get an idea of how big the number is […]

July 20, 2014

2:20 AM | 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 […]

July 19, 2014

4:17 AM | Transcendental Darts
So I made that video about different kinds of infinity, and then had to go deeper into explaining Cantor’s diagonal proof that one infinity really can be bigger than another, and then of course needed to answer some frequently asked questions about infinite digits going to the left in a reverse-cantor, and now I’m on […]

July 16, 2014

12:45 PM | 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 […]
12:00 AM | Cannibalism
Cannibalism How long could the human race survive on only cannibalism? Quinn Shaffer There are about 500 trillion calories of human in the world. If it could be frozen or otherwise preserved, that would be enough—at least in terms of raw calories—to keep a tiny breeding population alive for millions of years. Eating nothing but meat sounds bad, nutritionally, but the lack of vegetables wouldn't necessarily kill you. People can survive on high-meat or all-meat diets, especially if […]

July 12, 2014

5:47 PM | Prove It
After observing that               1  =  1and         1 + 3  =  4and         1 + 3 + 5  =  9and         1 + 3 + 5 + 7  =  16and         1 + 3 + 5 + 7 + 9  =  25it seems easy to conclude that, for any positive integer n, the sum of the first n odd numbers […]

July 11, 2014

9:39 AM | Grid Art using Equations and Inequalities
(Monster)(Funny Face)(Monkey Face)( Mathematical software used: Graph )

July 10, 2014

1:28 AM | 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:       math (after)     first you get the number-rush as anyone     might do      you watch your world turn to     nought      […]

July 09, 2014

12:00 AM | Global Snow
Global Snow From my seven-year-old son: How many snowflakes would it take to cover the entire world in six feet of snow? (I don't know why six feet...but that's what he asked.) —Jed Scott It's been too hot where I live, so I like thinking about this question! Snow is fluffy because it has a lot of air in it. The same amount of water that makes an inch of rain would make a lot more than an inch of snow. An inch of rain is usually equal to about a foot of snow, but it depends […]

July 07, 2014

2:18 AM | 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 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 […]

July 05, 2014

2:22 PM | Flower of Golden Triangle Spirals
( Mathematical software used: Graph )
11:08 AM | Judge This Joke By Its Size, Do You?
Most everyone knows the classic 7-8-9 joke: What is 6 afraid of 7? Because 7 8 9. I recently heard a Star Wars variation: According to Yoda, why is 5 afraid of 7? Because 6 7 8. This joke isn’t funny unless you understand the syntax often used by Yoda, which involves inverting the word […]

July 04, 2014

1:59 AM | Carpool Lane Songs
These are some of the songs I invariably sing when in the carpool lane. Sometimes I fantasize about properly making an entire album of carpool lane songs and then touring the country as a carpool lane rock star, but for today I decided to settle for making rough recordings of a few. The first, the […]

July 03, 2014

5:19 AM | 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, 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 […]
2:44 AM | 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.   This link leads to a PDF file that lists searchable topics and names of poets and mathematicians presented herein.June 30  A recent butterfly effectJune 27  Of all geometries, feathery is best . . .June 24  Is mathematics discovered or invented?June 20  Three […]

July 02, 2014

10:34 AM | A Father’s Day Gift Worth Waiting For
Alex made a Father’s Day Book for me. Because the book didn’t make it on our trip to France, however, I didn’t receive it until this past weekend. It was worth the wait. The book was laudatory in praising my handling of routine fatherly duties: I loved when you took me to Smashburger. I appreciated […]
12:00 AM | Vanishing Water
Vanishing Water What would happen if all the bodies of water on Earth magically disappeared? —Joanna Xu As is often the case with these questions, everyone would die. The first people to notice would be swimmers and boaters, for obvious reasons. To avoid a glass half empty scenario, we'll assume the water is replaced by air. Most people swim in water which is relatively shallow, so most of them would survive the fall to the bottom, albeit with a few broken bones.[1]Those swimming in […]

July 01, 2014

10:28 AM | Double Spirals - images of nested regular polygons under conformal mappings
(n = 6, Draw type = Lines)(n = 4, Draw type = Dots)These are images of nested regular polygons (n=6 & n=4)under the Mobius transformation z -> 3(z-1)/(z+1).( Mathematical software used: Graph )

June 30, 2014

4:51 PM | A recent butterfly effect
The term 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 […]

June 29, 2014

5:36 PM | Sinusoidal Strings
Sinusoidal Strings of Pebbles (r=0.1, n=32)(r=0.15, n=42)(r=0.4, n=60)gnuplot Examples:Method 1:r = 0.1n = 32s = 2*pi/nf(t) = cos(s*floor(t/s)) + r*cos(n*(t-s*floor(t/s)))g(t) = sin(s*floor(t/s)) + r*sin(n*(t-s*floor(t/s)))theta(t) = atan2(g(t), f(t))set terminal wxt enhanced font "Arial, 10"set xtics ('-2π' -2*pi, '-π' -pi, '0' 0, 'π' pi, '2π' 2*pi)set xrange [-2*pi-0.4:2*pi+0.4]set yrange [-pi-0.2:pi+0.2]set size ratio -1set samples 10000set multiplotset parametricunset keydo for […]

June 27, 2014

8:51 PM | Of all geometries, feathery is best . . .
The title for this post comes from 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. Hagerty     Do not accept packages from […]

June 25, 2014

1:39 PM | Math in France
Driving through the French countryside using smartphone GPS for navigation is a lot like driving through rural Pennsylvania with my redneck cousin riding shotgun — there is a significant lack of sophistication, an ample amount of mispronunciation, and myriad grammatical errors. In Pennsylvania: Take that there right onto See-Quo-Eye-Ay (Sequoia) Drive. In France: At the roundabout, […]
1:02 PM | Twelve and the real life problems problem
The number 12, not the most esoteric secret of mathematics. Yet through the under appreciated power of the equals sign it can become 6+6, 3*4, 15-3, 36/3 aall before we add in unusual… Continue reading →
12:00 AM | Keyboard Power
Keyboard Power As a writer, I'm wondering what would be the cumulative energy of the hundreds of thousands of keystrokes required to write a novel. —Nicolas Dickner You probably shouldn't invest in a keyboard-based generator any time soon. People like figuring out places where we can recover "wasted" energy. Avoiding waste is a great goal, but sometimes it's hard to judge how much energy is actually moving around in a particular system. Cool-sounding ideas like the […]

June 24, 2014

11:00 PM | 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 […]
10:58 PM | Introducing eleVR
Short version: earlier this year it became clear to me that virtual reality is now the near future of everything, so I found the best people (Andrea Hawksley and Emily Eifler) and we started a project called eleVR, where we do stuff like create an open source web video player compatible with the Oculus, produce […]
6:06 PM | Proof some infinities are bigger than other infinities
A followup to How Many Kinds of Infinity Are There? that contains Cantor’s Diagonal Argument and The Fault in our Stars references. Also see Numberphile’s video about the proof with James Grime, and Minute Physics‘ short and sweet version. Nothing ever gets done if you wait for ideal circumstances. In the first infinity video, I […]
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