Math Maps The Island of Utopia

Under the category of “Somebody Had To Figure It Out,” Dr. Andrew Simoson of King University (Bristol, Tennessee) used calculus to determine the shape of the island of Utopia in the 500-year-old book by Sir Thomas More based on the description of island given in the book’s introduction.

News article: https://www.insidescience.org/news/math-maps-island-thomas-mores-utopia

Paper by Dr. Simoson: http://archive.bridgesmathart.org/2016/bridges2016-65.html

This Is Why There Are So Many Ties In Swimming

From the excellent article “This Is Why There Are So Many Ties In Swimming“, ties in swimming are allowed by the sport’s governing body because of the inevitability of roundoff error.

In 1972, Sweden’s Gunnar Larsson beat American Tim McKee in the 400m individual medley by 0.002 seconds. That finish led the governing body to eliminate timing by a significant digit. But why?

In a 50 meter Olympic pool, at the current men’s world record 50m pace, a thousandth-of-a-second constitutes 2.39 millimeters of travel. FINA pool dimension regulations allow a tolerance of 3 centimeters in each lane, more than ten times that amount. Could you time swimmers to a thousandth-of-a-second? Sure, but you couldn’t guarantee the winning swimmer didn’t have a thousandth-of-a-second-shorter course to swim. (Attempting to construct a concrete pool to any tighter a tolerance is nearly impossible; the effective length of a pool can change depending on the ambient temperature, the water temperature, and even whether or not there are people in the pool itself.)

Proportion in Grammar

ProportionInGrammarSource: https://www.facebook.com/analyticalgrammar/photos/a.167941616890.130074.131324516890/10153609226726891/?type=3

Report Cards for Famous Mathematicians

From Math With Bad Drawings:

20151201070935_00008

 

Additionally, my favorites from the comments:

Evariste Galois gets an A+ in math and gets a D in behavior. Evariste is a very creative mathematician with potential for greatness. But he needs to get along better with others. Getting into fights is not the way to succeed.

Gödel is excellent at logic but his work is often incomplete.

I am missing Heisenberg’s report card here. “Werner refuses to give an exact answer and seems to be proud of his uncertainty.”

Benoit Mandelbrot C+, great at drawing designs but keeps going on and on and on about perimeters. Next time he should work on calculating areas as his answers were always zero…

 

Look at my tan line

look-at-my-tan-line-me-irl-2629801Source: https://onsizzle.com/i/look-at-my-tan-line-me-irl-653242

Fibonacci convention

Fibonacci

Source: https://www.facebook.com/Mathhappiness/photos/a.170688796611683.1073741829.101136273566936/321994341481127/?type=3&theater

Another Poorly Written Word Problem: Index

I’m doing something that I should have done a long time ago: collecting a series of posts into one single post. The following links comprised my series poorly written word problem, taken directly from textbooks and other materials from textbook publishers.

Part 1: Addition and estimation.

Part 2: Estimation and rounding.

Part 3: Probability.

Part 4: Subtraction and estimation.

Part 5: Algebra and inequality.

Part 6: Domain and range of a function.

Part 7: Algebra and inequality.

Part 8: Algebra and inequality.

Part 9: Geometric series.

 

 

Predicate Logic and Popular Culture: Index

I’m doing something that I should have done a long time ago: collecting a series of posts into one single post. The following links comprised my series on using examples from popular culture to illustrate principles of predicate logic. My experiences teaching these ideas to my discrete mathematics students led to my recent publication (John Quintanilla, “Name That Tune: Teaching Predicate Logic with Popular Culture,” MAA Focus, Vol. 36, No. 4, pp. 27-28, August/September 2016).

Unlike other series that I’ve made, this series didn’t have a natural chronological order. So I’ll list these by concept illustrated from popular logic.

green lineLogical and \land:

  • Part 1: “You Belong To Me,” by Taylor Swift
  • Part 21: “Do You Hear What I Hear,” covered by Whitney Houston
  • Part 31: The Godfather (1972)
  • Part 45: The Blues Brothers (1980)
  • Part 53: “What Does The Fox Say,” by Ylvis
  • Part 54: “Billie Jean,” by Michael Jackson

Logical or \lor:

  • Part 1: Shawshank Redemption (1994)

Logical negation \lnot:

  • Part 1: Richard Nixon
  • Part 32: “Satisfaction!”, by the Rolling Stones
  • Part 39: “We Are Never Ever Getting Back Together,” by Taylor Swift

Logical implication \Rightarrow:

  • Part 1: Field of Dreams (1989), and also “Roam,” by the B-52s
  • Part 2: “Word Crimes,” by Weird Al Yankovic
  • Part 7: “I’ll Be There For You,” by The Rembrandts (Theme Song from Friends)
  • Part 43: “Kiss,” by Prince
  • Part 50: “I’m Still A Guy,” by Brad Paisley
  • Part 76: “You’re Never Fully Dressed Without A Smile,” from Annie.

For all \forall:

  • Part 3: Casablanca (1942)
  • Part 4: A Streetcar Named Desire (1951)
  • Part 34: “California Girls,” by The Beach Boys
  • Part 37: Fellowship of the Ring, by J. R. R. Tolkien
  • Part 49: “Buy Me A Boat,” by Chris Janson
  • Part 57: “Let It Go,” by Idina Menzel and from Frozen (2013)
  • Part 65: “Stars and Stripes Forever,” by John Philip Sousa.
  • Part 68: “Love Yourself,” by Justin Bieber.
  • Part 69: “I Will Always Love You,” by Whitney Houston.
  • Part 74: “Faithfully,” by Journey.
  • Part 79: “We’re Not Gonna Take It Anymore,” by Twisted Sister.
  • Part 87: “Hungry Heart,” by Bruce Springsteen.

For all and implication:

  • Part 8 and Part 9: “What Makes You Beautiful,” by One Direction
  • Part 13: “Safety Dance,” by Men Without Hats
  • Part 16: The Fellowship of the Ring, by J. R. R. Tolkien
  • Part 24 : “The Chipmunk Song,” by The Chipmunks
  • Part 55: The Quiet Man (1952)
  • Part 62: “All My Exes Live In Texas,” by George Strait.
  • Part 70: “Wannabe,” by the Spice Girls.
  • Part 72: “You Shook Me All Night Long,” by AC/DC.
  • Part 81: “Ascot Gavotte,” from My Fair Lady
  • Part 82: “Sharp Dressed Man,” by ZZ Top.
  • Part 86: “I Could Have Danced All Night,” from My Fair Lady.

There exists \exists:

  • Part 10: “Unanswered Prayers,” by Garth Brooks
  • Part 15: “Stand by Your Man,” by Tammy Wynette (also from The Blues Brothers)
  • Part 36: Hamlet, by William Shakespeare
  • Part 57: “Let It Go,” by Idina Menzel and from Frozen (2013)

Existence and uniqueness:

  • Part 14: “Girls Just Want To Have Fun,” by Cyndi Lauper
  • Part 20: “All I Want for Christmas Is You,” by Mariah Carey
  • Part 23: “All I Want for Christmas Is My Two Front Teeth,” covered by The Chipmunks
  • Part 29: “You’re The One That I Want,” from Grease
  • Part 30: “Only You,” by The Platters
  • Part 35: “Hound Dog,” by Elvis Presley
  • Part 73: “Dust In The Wind,” by Kansas.
  • Part 75: “Happy Together,” by The Turtles.
  • Part 77: “All She Wants To Do Is Dance,” by Don Henley.
  • Part 90: “All You Need Is Love,” by The Beatles.

DeMorgan’s Laws:

  • Part 5: “Never Gonna Give You Up,” by Rick Astley
  • Part 28: “We’re Breaking Free,” from High School Musical (2006)

Simple nested predicates:

  • Part 6: “Everybody Loves Somebody Sometime,” by Dean Martin
  • Part 25: “Every Valley Shall Be Exalted,” from Handel’s Messiah
  • Part 33: “Heartache Tonight,” by The Eagles
  • Part 38: “Everybody Needs Somebody To Love,” by Wilson Pickett and covered in The Blues Brothers (1980)
  • Part 46: “Mean,” by Taylor Swift
  • Part 56: “Turn! Turn! Turn!” by The Byrds
  • Part 63: P. T. Barnum.
  • Part 64: Abraham Lincoln.
  • Part 66: “Somewhere,” from West Side Story.
  • Part 71: “Hold On,” by Wilson Philips.
  • Part 80: Liverpool FC.
  • Part 84: “If You Leave,” by OMD.

Maximum or minimum of a function:

  • Part 12: “For the First Time in Forever,” by Kristen Bell and Idina Menzel and from Frozen (2013)
  • Part 19: “Tennessee Christmas,” by Amy Grant
  • Part 22: “The Most Wonderful Time of the Year,” by Andy Williams
  • Part 48: “I Got The Boy,” by Jana Kramer
  • Part 60: “I Loved Her First,” by Heartland
  • Part 92: “Anything You Can Do,” from Annie Get Your Gun.

Somewhat complicated examples:

  • Part 11 : “Friends in Low Places,” by Garth Brooks
  • Part 27 : “There is a Castle on a Cloud,” from Les Miserables
  • Part 41: Winston Churchill
  • Part 44: Casablanca (1942)
  • Part 51: “Everybody Wants to Rule the World,” by Tears For Fears
  • Part 58: “Fifteen,” by Taylor Swift
  • Part 59: “We Are Never Ever Getting Back Together,” by Taylor Swift
  • Part 61: “Style,” by Taylor Swift
  • Part 67: “When I Think Of You,” by Janet Jackson.
  • Part 78: “Nothing’s Gonna Stop Us Now,” by Starship.
  • Part 89: “No One Is Alone,” from Into The Woods.

Fairly complicated examples:

  • Part 17 : Richard Nixon
  • Part 47: “Homegrown,” by Zac Brown Band
  • Part 52: “If Ever You’re In My Arms Again,” by Peabo Bryson
  • Part 83: “Something Good,” from The Sound of Music.
  • Part 85: “Joy To The World,” by Three Dog Night.
  • Part 88: “Like A Rolling Stone,” by Bob Dylan.
  • Part 91: “Into the Fire,” from The Scarlet Pimpernel.

Really complicated examples:

  • Part 18: “Sleigh Ride,” covered by Pentatonix
  • Part 26: “All the Gold in California,” by the Gatlin Brothers
  • Part 40: “One of These Things Is Not Like the Others,” from Sesame Street
  • Part 42: “Take It Easy,” by The Eagles

Sine of madness

sine of madness

Abbott and Costello and subtraction

For more on Abbott and Costello and mathematics, here’s the classic routine “Two Tens for a Five.” (On my first job as a teenager, my boss successfully pulled this joke on me using two dimes and a nickel.)