X

+

I’ve been experimenting with Apple’s new Swift language. What follows is a command-line program to compute the future value of an investment at a fixed annual rate for a given term. The code uses (a) functions as parameters (b) typealias to name a type — see typealias funcD2D = (Double) -> Double Typelias is Swift’s […]

+

2:08 AM | Fixing something wrong

If there's something wrong with the third act, it's really in the first act.This quote from Billy Wilder, Austrian-born writer and film-director (1906-2002), reminds me of a similar observation I have made about my mathematical work -- when a
[…]

+

10:30 PM | How to Play Like a Mathematician

This is a vague transcript from memory of a talk I gave at Twitter Math Camp 2014. It was a truly energising event, teacher organised peer professional development. Anyone interested in education, whether… Continue reading →

+

3:49 PM | Each equation is a playful catch . . .

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

+

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 )

Editor's Pick

+

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
[…]

+

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 )

+

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
[…]

+

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
[…]

+

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 […]

+

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
[…]

+

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
[…]

+

(Monster)(Funny Face)(Monkey Face)( Mathematical software used: Graph )

+

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
[…]

+

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
[…]

+

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
[…]

+

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 […]

+

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 […]

+

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 […]

+

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
[…]

+

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
[…]

+

(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 )

+

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
[…]

+

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 […]

+

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
[…]

+

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, […]

+

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 →

Sidebar

Filters

+

via @CERN http://t.co/9Rac42mBVh #CPviolation #CPsymmetry #matter #antimatter The CP violation is a violation of the CP-symmetry, a combination between the charge conjugation symmetry (C) and the parity symmetry (P). CP-symmetry states that the laws of physics should be the same if a particle is interchanged with its antiparticle, and then its spatial coordinates are inverted.The CP violation is discovered in 1964 by Christenson, Cronin, Fitch, and Turlay (Cronin and Fitch awarded the Nobel […]

Christenson, J., Cronin, J., Fitch, V. & Turlay, R. (1964). Evidence for the 2π Decay of the K_{2}^{0} Meson, Physical Review Letters, 13 (4) 138-140. DOI: 10.1103/PhysRevLett.13.138

Citation

+

by @ulaulaman http://t.co/Q3AODpvKAs #Godel #ontologicalproof #god #computer The ontological arguments for the existence of God was introduced for the first time by St. Anselm in 1078: God, by definition, is that for which no greater can be conceived. God exists in the understanding. If God exists in the understanding, we could imagine Him to be greater by existing in reality. Therefore, God must exist.There are a lot of phylosophies, mathematics and logicians that proposed their ontological […]

Christoph Benzmüller & Bruno Woltzenlogel Paleo (2013). Formalization, Mechanization and Automation of Gödel's Proof of God's Existence, arXiv: 1308.4526v4

Citation

+

\[(n+1)^3 - n^3 \equiv 1 \mod 6\] Claudi Alsina,, Roger Nelsen,, & Hasan Unal (2014). Proof Without Words: The Difference of Consecutive Integer Cubes Is Congruent to 1 Modulo 6 The College Mathematics Journal, 45 (2), 135-135 DOI: 10.4169/college.math.j.45.2.135 (facebook)

Claudi Alsina,, Roger Nelsen, & Hasan Unal (2014). Proof Without Words: The Difference of Consecutive Integer Cubes Is Congruent to 1 Modulo 6, The College Mathematics Journal, 45 (2) 135-135. DOI: 10.4169/college.math.j.45.2.135

Citation

+

\[(n+1)^3 - n^3 \equiv 1 \mod 6\] Claudi Alsina,, Roger Nelsen,, & Hasan Unal (2014). Proof Without Words: The Difference of Consecutive Integer Cubes Is Congruent to 1 Modulo 6 The College Mathematics Journal, 45 (2), 135-135 DOI: 10.4169/college.math.j.45.2.135 (facebook)...
Claudi Alsina,, Roger Nelsen,, & Hasan Unal. (2014) Proof Without Words: The Difference of Consecutive Integer Cubes Is Congruent to 1 Modulo 6. The College Mathematics Journal, 45(2), 135-135.
[…]

Claudi Alsina,, Roger Nelsen, & Hasan Unal (2014). Proof Without Words: The Difference of Consecutive Integer Cubes Is Congruent to 1 Modulo 6, The College Mathematics Journal, 45 (2) 135-135. DOI: 10.4169/college.math.j.45.2.135

Citation

+

La settimana scorsa, su twitter, ho diffuso alcune immagini, foto scattate dalle pagine dal volume Letture da Le Scienze: Fisica delle particelle (un indice del volume), che raccoglieva alcuni articoli usciti sulla rivista italiana (e quindi anche su Scientific American). Poiché ognuna di quelle immagini fa inevitabilmente parte della storia della fisica, mi sembra sensato proporle raccolte insieme in un unico post molto più semplicemente raggiungibile di tanti piccoli... cinguettii.
[…]

Weisskopf, V. (1968). The Three Spectroscopies, Scientific American, 218 (5) 15-29. DOI: 10.1038/scientificamerican0568-15

Barish, B. (1973). Experiments with Neutrino Beams, Scientific American, 229 (2) 30-38. DOI: 10.1038/scientificamerican0873-30

Treiman, S. (1959). The Weak Interactions, Scientific American, 200 (3) 72-84. DOI: 10.1038/scientificamerican0359-72

Cline D.B., Mann A.K. & Rubbia C. (1974). The Detection of Neutral Weak Currents, Scientific American, 231 (6) 108-119. DOI: 10.1038/scientificamerican1274-108

Glashow, S. (1975). Quarks with Color and Flavor, Scientific American, 233 (4) 38-50. DOI: 10.1038/scientificamerican1075-38

Nambu, Y. (1976). The Confinement of Quarks, Scientific American, 235 (5) 48-61. DOI: 10.1038/scientificamerican1176-48

Johnson, K. (1979). The Bag Model of Quark Confinement, Scientific American, 241 (1) 112-121. DOI: 10.1038/scientificamerican0779-112

Citation

MindAfterMath tweeted: @MindAfterMath

2014-07-31 06:57:49

freakonometrics tweeted: @freakonometrics

"The Art and Science of Data-driven Journalism" http://t.co/cO29zQB9EE ht @kdnuggets

2014-07-31 06:47:50

freakonometrics tweeted: @freakonometrics

"Our first 3 years are usually a blur and we don’t remember much before age 7. What are we hiding from ourselves?" http://t.co/boBqHIk99h

2014-07-31 06:45:38

rmathematicus tweeted: @rmathematicus

RT @abneyc: In the @BeineckeLibrary copy, Galileo himself provided another ToC to his letters. #histsci #Yale #marginaliamonday http://t.co…

2014-07-31 06:43:35

freakonometrics tweeted: @freakonometrics

"Does OKCupid need our consent?" http://t.co/gWbPdCKTPt
"We need a better quality debate about the algorithms that rule our online lives"

2014-07-31 06:39:27

freakonometrics tweeted: @freakonometrics

"Researchers in the cloud" http://t.co/O2xr3mIASg

2014-07-31 06:38:53

freakonometrics tweeted: @freakonometrics

"Open access science articles are read and cited more often than articles available only to subscribers" http://t.co/dfSKjF1nYq

2014-07-31 06:37:51

freakonometrics tweeted: @freakonometrics

"Evolution du prix et de la vente de cigarette en France depuis 2000" http://t.co/kd4puEmXYL http://t.co/x2aZjfBT2i

2014-07-31 06:33:52

X