13 Math Tidbits on Friday 13

Friday 13 is one of the beloved or lucky days in the Gregorian calendar year for most recreational mathematicians and math bloggers, who can't wait to share some musings about the number 13 and Friday the thirteenth to their non-mathematical friends, fiends, and foes.

1. Triskaidekaphobia Isn't Hereditary

If you can read about the number 13, you probably don't suffer from triskaidekaphobia—the fear of the number 13… but your children and grandchildren still might.

2. Pseudoscience Triumphs Over Profit 

On a plane or in a theater, shouldn't you feel "unsafe" rather than safe because row "13" has often been intentionally mislabeled "14"?

Or, In a lift with no button number 13, would you feel "safer" that they've tried to "cheat death" by making triskaidekaphobes or paraskavedekatriaphobes (who are fearful of Friday the 13th) feel better? All in the name of profit or superstition!

3. Synesthesia AND Autism AND Math

What color and shape is the number 13? What is the taste of 13? 

© [Unknown]

This book may shed some light on the prime number 13!

4. The Closest of Two Friday the 13ths 

Can Friday the 13th occur in two successive months? It's not difficult to see that the shortest span between two consecutive Friday the 13ths is 28 days. How often do you think this event happens? Have you experienced one in your lifetime, or know of someone who rejoices in this kind of numerical (or numerological) oddity?

5. An Unsolved Arithmetic Problem

The number 13 is both a prime and a Fibonacci number. Whether there are infinitely many primes that are also Fibonacci still remains an unsolved problem.

Cracking this higher arithmetic nut may bring you some mathematical prestige or fame, as your proof graces the pages of a Number Theory publication. 

6. A Friday 13 Baby

A baby is born on Friday 13, 2013. When is the next time a baby will be born on the same day of the week in the same month, which also falls on a Friday 13? How often in a 400-year calendrical cycle does this happen?

7. A Friday 13 Survivor 

What are the odds that you will not survive on a Friday the 13th? Is the answer equivalent to finding the probability that a baby will be born on a Friday 13?

8. An Inauspicious Day 

Using the code A = 1, B = 2, C = 3, ...., show that the sum value of the phrase FRIDAY THE THIRTEENTH IS AN UNLUCKY DAY is a multiple of 13.

9. Birth and Death on a Friday 13

What are the chances that one born on a Friday 13 will also die on a Friday 13? How many thousands of folks every year experience this double whammy? 

A solution may be found from Aha! Math.

10. Bio of 13

Prepare a résumé for Number 13, showcasing some of its elementary numerical skills. For instance,

13 = 1 + 4 + 8

13 = 3⁰ + 3¹ + 3²

12 × 13 = 156 and 21 × 31 = 651

13² = 169 and 31² = 961

11. The Unluckiest and the Happiest

List 13 parallelisms between Friday 13 and December 25—what common features the most fearful (or frightful) date of the calendrical year shares with the king of the public holidays. Get creative, by connecting the unconnected!

An ideal gift for numbers lovers & creative problem solvers

 

12. Social Media 13

Defriend 13 of your Facebook friends, or unfollow 13 of your Twitter followers, who have been inactive in the last 13 months. Send them a Friday 13 alert of your mean intention to save bits and bytes on your RAM to reduce your carbon footprint.

13. Problem Posing on a Friday 13

Pose at least 13 mathematical quickies and trickies, and share them with your on-line friends and fiends.

What is the angle between the hands of a clock at 13:13?

The sum of the ages of Casey and Ian is 13 years. If Casey is 1.3 months older than Ian, how old are they?

A Happy & Blessed Friday 13!

References

Yan, K. C. (2011). CHRISTmaths: A creative problem solving math book. Singapore: MathPlus Publishing.

Yan, K. C. (2006). Aha! math. Singapore: Panpac Education.

© Yan Kow Cheong, December 13, 2013.

The Mathematics of the Cross

Amazing love! How can it be

that thou, my God, shouldst die for me?

from Thomas Campbell The Bouquet 1825

Flag of Red Cross

The cross isn't just a sacred icon or symbol for religious math educators, but it's also a geometrical shape that has borne much fruit in producing many logic and mathematics puzzles. Few recreational mathematicians, professional and amateur, wouldn't want to be challenged by these fertile dissection puzzles.

Flag of Switzerland

Let's resurrect some of these ancient cross puzzles, which have given so much intellectual satisfaction to those who have decided to take up their cross along their mathematical itinerary. Below are ten of these Christmaths puzzles, which would appeal to above-average elementary and middle-school math students and their teachers.


1. Squares in a Cross

A solid Greek cross can be formed by putting together five cubes, or from a number of squares. How many squares are there?

2. Tessellating and Dissecting Crosses

(a) Show how Greek crosses can form a tessellation.

(b) How can an infinite number of dissections from a cross tessellation produce a square?





3. A matchstick Puzzle

The cross on the left is made up of 19 matches. Move 7 of them to make a pattern consisting of four squares.




4. The Area of a Cross

A cross is made up of five congruent squares. If XY = 10 cm, what is the area of the cross?

5. Cross into Rectangle

Using only two straight cuts, divide the cross on the right into three pieces and reassemble them to form a rectangle twice as long as it is wide.




6. Five-piece Square into Cross

Cut a square into five pieces and rearrange them to form a Greek cross, as shown below.

7. Four-piece Square into Cross

Cut a square into four pieces and rearrange them to form a Greek cross, as shown below.

8. Cross into Hollow Square

The Greek cross on the left has a square-shaped hole in the center. 
(a) Rearrange the pieces to make a square that has a hollow cross inside.
(b) Rearrange the pieces so that the resulting figure is a square that is rather smaller than the previous "hollow" one. 



9. The Cross and the Crescent 

Reassemble the seven pieces of the crescent to make the Greek cross.

10. The Rolling Disc

In the figure below, each side of the cross is 10 cm long. A small circular disc of radius 1 cm is placed at one corner. If the disc rolls along the sides of the figure and returns to the starting position, find the distance traveled by the center of the disc. 

Selected answers/solutions

1. 22 squares.
4. 100 cm².
5.













7.








8.








10. (104 + 2π) cm

Reference
Yan, K. C. (2011). CHRISTmaths: A creative problem solving math book. Singapore: MathPlus Publishing.

© Yan Kow Cheong, March 31, 2013.

Code: WR3ZTVKVUW9Z

Thank you, Math!

Journal writing in mathematics education is often perceived as a boring activity in getting students to reflect on their own mathematical thinking. Perhaps an appealing way to assess students' mastery of mathematical concepts is to encourage them to write "mathematical letters" to a buddy in the form of "thanks goodness for anything numerical or mathematical."

Let's look at a sample of these math-lite correspondences.

Dear Numbers

© mashable.com 

Thank you for being such a buddy I can always count on. You don't change because of geography or history. A while ago, you gave me an idea to blog on "Singapore Math by Numbers." Without you, the world would come to a standstill. You numbers don't just rule the world; today, you've been semi-elevated to a god—with all your metrics and analytics.

Numerically yours

Dear Calculus book

Thank you for letting me use you as a weight or support. Your thickness scares the hell out of so many otherwise intelligent mortals, especially those who have had an unpleasant experience with their high school math teachers. Besides, I use you as an inexpensive cure to help my friends and loved ones, who are suffering from insomnia—your deltas and epsilons are sufficient to hypnotize the hardcore sufferers.

Infinitesimally yours


Dear 1001

© shashindrasri.blogspot.com

You're a mirror to my numerical soul. Indeed, you provided me with so many oddities and idiosyncrasies about the Palindromic Family. In fact, I've started writing the first few chapters of "The Joy (and Pain) of Palindromic Numbers."

Palindromically yours

Dear LOGIC

Thanks for being such a reliable companion in my dealing with irrational and illogical folks. Your cold, austere character has put off many egos, who would otherwise have trampled over the rest of us.

Logically yours

An i-protractor
© 1mobile.com

Dear Protractor

I hope you won't go the way of the abacus or slide rule, because I'm seeing lesser use of you these days. Anyway, I promise to keep you as a vintage math instrument for my grandchildren.

Dear Compasses & Unmarked Ruler

Thank you for frustrating and humbling thousands of our mathematical forefathers in their futile attempts to constructing a square with the same area of a circle. To revive your popularity, I'll be conducting an enrichment math lesson on The Lost Art of the Compass.

Christmas all year-round

Dear 25

Thanks for confiding with me some of your innermost secrets, which allowed me to write some parallelisms between the king of the public holidays and the queen of the sciences. Don't worry, I'll dedicate CHRISTmaths to you on its silver edition.

Joyfully yours

Join the CHRISTmaths fan page.

Dear Boring Math Teacher

You provide jobs to half a dozen tutors, as they try to teach the most disliked subject in school in a less parrot-like manner! And your boring test of artificial questions only serves as a filter to separate the nerd from the herd—the mathematical goats from the sheep.

© business.mcmaster.ca

Dear Probability

Thanks for mocking my intuition and flawed logic. The answers to your problems have humbled the mathematical brethren, as you tease them with your counter-intuitive results.

 © tower.com

Dear FRENCH

Thank you for making me pronounce the first part of the word "factorize" to sound like the four-letter word. To test my hypothesis, I tried that trick on my French female teacher many moons ago, and the class then couldn't control themselves but burst into laughter*. 

Fact-ally yours

* Try this trick on your French-speaking friends and fans who speak English as a second or third language.

Dear Math Editor

Thank you for introducing me to so many conceptual and linguistic faux pas—I couldn't have fabricated them without your poor grammar and punctuation, and shaky grasp of some difficult mathematical concepts. Some are jaw-achingly funny. My collection of your blunders is growing, and I couldn't wait to compile them in a book for green editors. If only I knew earlier that "poor writes" could open up the doors to many freelance assignments. 

© 123opticalillusions.com

Dear Dice

Thank you for feeling so good in my hand and for showing me so many different possible outcomes. You've taught me a lot about chance and probability, and you look pretty sitting on my book shelves. That's where you'll stay. Love, Leah.

Dear Sex

Thank you for revealing to me your intimate liaison with the most boringly taught and disliked subject in school. And for giving me enough materials to writing and getting "Mathematics And Sex" published.  Indeed, MATH is a four-letter word! 

© mathandchess.net

Dear Chess

Thank you for using me to beat those older and smarter chaps. Mentally satisfying to "humble" them! But I can't stand you when you used the same trick on me years later—when those young geeks refused to let me win or draw even one game.

Dear Calculators

Although you had atrophied my mental calculation abilities, however, you're a God-sent tool to working out those tedious and mindless computations. I'm totally dependent on you for my everyday numerical chores—from calculating the waiter's tip to finding the amount I owe to the credit card companies. On the negative side, you've upped my innumeracy index by a dozen points. On a positive note, I wished you'd upgrade yourself to becoming an instrument of desire, just like the iPad. 

Dear Amazon.com

A trick-and-tricky math book 

Thank you for showcasing our math titles on your site, but we hate that 55 percent you're charging us every time there is an order for our books. When we factor in the time we need to dispatch them, and the shipping freight, most of us are only operating at a negative profit! Plus, your payment in US dollars, and your reluctance to link with PayPal, makes authors living outside the US hesitant to promote their titles on Amazon.

Dear ZERO

© spaceadventures.com

Thanks for sharing with me how you're once marginalized by your fellow numerals, and how you're even ostracized by the Catholic Church for calling you the "infidel zero." Your forgiving spirit towards the Pope and his bishops, and your revelation to Newton and gang regarding some of your oddities and idiosyncrasies, had earned you a numerical place in the Mathematical Hall of Fame. However, your critics never cease to call you the "troublesome zero."

Dear NOTHING

Folks always mistake you for the numeral zero—both of you are like faux twins. Zero is nothing, and nothing is zero. In fact, you're anything but nothing—you're something! Philosophers and mystics curse or deify you, with their ever-convoluted arguments—they've almost elevated you to the status of an atheistic religion. 

There's almost an alphabet for your name: abyss, chasm, emptiness, hole, pit, void, nothingness, nada, naught, …, nil, nix, zilch.

books.google.com

Dear Empty Set

Thank you for causing so much confusion among school kids. Do you exist or not? Are you really a set? Are you like a club with no members? Or, a bag without items? You're like something with zero nothings.

© shop.cafepress.com 

Dear Imaginary Numbers

Once upon a time, they denied your existence, just like your rejected, dejected, and ejected cousins, the negative numbers. But today, like zero, you're having the last laugh; in fact, we often take you, guys, for granted, albeit you prefer to keep a low profile. I wished school teachers won't tell the kids that you're complex, when you're really simple to manage.

Dear May 1

This is the only date in the year, when working folks don't have to labor. A day of protests and political rallies, you remind the masses of Karl Marx's words that workers of the world must unite—that they have nothing to lose but their chains.

© eoagh.com

Dear Black Hole

It's beyond my reasoning ability to understand the math that predicted your existence. Thank God, He produces a few Hawkings among His creation every century or so to reveal your galactic existence and importance. 

 © abqjournal.com

Dear Sudoku

You give me hope that in my golden years my chances of dying from schizophrenia or dimentia are significantly reduced if I indulge myself to playing with you more often.

Dear Numerology

© geocaching.com 

From the simple idea of digital root, you manage to bluff tens of millions of numerically challenged folks into believing that they can predict their good and bad days, and that they can take control of their future from their birthdates. Indeed, a pseudo-equation of yours is: f(birthdate) = lucky/unlucky days 

Dear iPhone

Thank you for saving me the trouble of having to carry a scientific calculator around. Yes, by a mere 90-degree turn, you magically turn yourself from a four-function to a scientific calculator. I look forward to seeing you functioning as a graphing calculator in a-not-too-distant upgrade. Hope you can strike a deal with Texas or Casio, just like you did with HP.

Dear Statistics

Thank you for revealing to me all your curves and standard deviations. However, I'm still confused about your three musketeers: mean, mode, and median. Which mean do you mean? Now I understand why some folks call you "Sadistic Statistics" for torturing hundreds of thousands of students every day.

Dear 13

© sabotagetimes.com 

I know you didn't deserve that awful publicity surrounding your name, especially when those superstitious folks wickedly try to associate you with some black Friday. You're just an innocent-looking prime who had suffered so much—far worse than 666 and 4444.

Thank you for providing me with rich materials to write about, every time you fall on a Friday. We, recreational math enthusiasts, feel a bit like "numerical hypocrites," when we can't help but gossip about the numerical quirks of Friday 13.

Un-triskaidekaphobically yours

Dear Death

Thanks for being the great equalizer. You won't let the rich and the powerful, or the arrogant and the haughty, live beyond their undeservedly numbered days. Three scores and ten, or a billion odd heartbeats—that's your deadline to them, all!

It's now time to write and e-mail some math-lite letters to the rest of us to read and enjoy!

Mathematically yours

Reference
Dieterich, L. (2011). thx thx thx: thank goodness for everything. Kansas City, Missouri: Andrews McMeel Publishing, LLC. thxthxthx.com

© Yan Kow Cheong, July 24, 2012