Category Archives: Recreational Math

Pi Day in Singapore

Thousands of students around the world celebrate Pi Day today, but local math students in Singapore can only dream of being part of this annual mathematical event. Singapore math students, teachers, and parents don’t (and can’t) celebrate Pi Day, as long as they officially follow the British style of writing their dates (DD/MM/YY).

What makes matters worse is that this year, Pi Day falls on the first day of the one-week school break, which makes it almost impossible for hardcore math teachers, who want to buck the calendrical trend, to get their students excited about the properties and beauties of the number Pi.

Until Singapore switches to the American style of writing dates (MM/DD/YY), which may not happen, at least during my lifetime, however, this shouldn’t prevent us from evangelizing the gospel of Pi among the local student population.

Here are seven e-gifts of the holy Pi, which I started musing about 314 minutes ago on this Pi Day.

Pi Day vs. Abacus Day

  

A 14-Month Year for Singapore ONLY!

  

Where Are You in Pi?

  

Heavenly Pi

  

The Numerology (or Pseudoscience) of Pi

  

In Remembrace of the Late Singapore PM 

  

Biblical Pi vs. Mathematical Pi

   

Happy Pi Day!

© Yan Kow Cheong, March 14, 2016.

The 12 Problems of CHRISTmaths

Vintage Christmas—Just like Baby Jesus two millennia ago!
Vintage Christmas—Just like Baby Jesus two millennia ago!

Christmas is a golden and joyful opportunity for number enthusiasts and math geeks to sharpen their creative mathematical problem-solving skills.

Here are 12 CHRISTmaths cookies that may help you shake your brain a little bit in the midst of Christmas festivities.

Warning: Refrain from forwarding this post to relatives or friends living in countries, which are intolerant of Christmas and Christianity, such as Brunei, Saudi Arabia, and Somalia, as it’s haram for “infidels” to take part in any kind of Christmas celebrations. And I assume that includes reading any on-line materials deemed un-Islamic or un-Mohammedan, which might lead believers astray from the faith.

1. Unlucky Turkeys

Estimate the number of turkeys that make their way to the supermarkets every year.

2. A Xmas Candy

Mary wanted to buy a candy that costs 25 cents. A dated vending machine would take one-cent, five-cent, and ten-cent coins in any combination. How many different ways can she use the coins to pay for the candy?

Christmastize your code!
Remember to scan your Christmas item!

3. The Dimensions of a  Cross

A square of side 25 cm has four of its corners cut off to form a cross. What is the perimeter of the cross?

4. The Number of Crossings

Two lines can cross one time, three lines three times, four lines six times, and five lines ten times. If there are 25 lines, what would be the maximum number of crossings be?

5. An Eco-Xmas

If all instances of the word “CHRISTMAS” were replaced with “XMAS,” how much ink and paper (or Xmas trees) could you save every year? How much money could be channelled back to feeding the poor and the hungry during the festive season?

XMaths Tech
© T. Gauld’s You’re all just jealous of my jetpack (2013)

6. Number of Xmas Cards

In an age of Xmas e-cards and video cards, how many Christmas greetings cards are still being sent worldwide? How many trees are being saved every festive season?

7. Does Xmas! have 25 digits?

1! = 1, 2! = 1 × 2 = 2, 5! = 1 × 2 × 3 × 4 × 5 = 120—a 3-digit number, and 10! = 1 × 2 ×⋯× 10 = 3,628,800—a 7-digit number.

(a) Without a calculator, how would you verify whether the number 25! has precisely 25 digits or not.

(b) Which positive integers n (other than the trivial case n = 1) for which n! has exactly n digits?

GST with no thanks to Father Xmas
GST (or VAT) with no thanks to Father Xmas

8. Xmas Trees

Guesstimate how big a forest would 25 million Christmas trees occupy.

9. Folding papers

Fold a single piece of paper perfectly in half, from left to right. How many creases will there be after the 25th fold, when you continue folding so that all the rectangles are folded into two halves each time?

10. Pre-Xmas Tax

Imagine Singapore were to implement a pre-Christmas tax on all kinds of Christmas marketing before the first week of December. Estimate how many extra million dollars would the Income Tax department collect every festive season.

Folding a Santa Claus
© Anonymous Folding a Santa Claus

11. A Xmas Quickie or Toughie

What is the sum of the last two digits of 1! + 2! + 3! +⋯+ 24! + 25!?

12. An Ever-Early Xmas

Show that as one celebrates more and more Christmases (or, as one gets older and wiser), Christmas seems to come earlier every year.

Xmas Möbius Strips
Christmas Möbius Strips

References

Gould T. (2013). You’re all just jealous of my jetpack. New York: Drawn & Quarterly.

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

Zettwoch, D., Huizenga, J., May, T. & Weaver, R. (2013). Amazing facts… & beyond! with Leon Beyond. Minneapolis: Uncivilized Books.

A Xmas Bonus: 25 CHRISTmaths Toughies from Singapore ?? http://tinyurl.com/q9w3ne9

 

Selected Hints & Answers

2. 12 ways. Hint: Make an organized list.

3. 100 cm. 

4. 300 crossings.

5. About 30 million gallons of ink, 500 square miles of paper, and $15 trillion could be saved.

6. Hint.

7. (b) n = 22, 23, 24.

9. 225 – 1.

11. 4.

12. Hint: Why as one gets older, time appears to fly faster.

2012-12-21 23.13.28

© Yan Kow Cheong, December 25, 2015.

 

Anything Funny about Singapore Math?

Math educators, especially stressed [often self-inflicted] local teachers in Singapore, are always on the look-out for something funny or humorous to spice up their oft-boring math lessons. At least, this is the general feeling I get when I meet up with fellow teachers, who seem to be short of fertile resources; however, most are dead serious to do whatever it takes to make their teaching lessons fun and memorable.

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© Sidney Harris Sea animals are mathematical, too!

It’s often said that local Singapore math teachers are the world’s most hardworking (and arguably the world’s “most qualified” as well)—apparently, they teach the most number of hours, as compared with their peers in other countries—but for the majority of them, their drill-and-kill lessons are boring like a piece of wood. It’s as if the part of their brain responsible for creativity and fun had long been atrophied. A large number of them look like their enthusiasm for the subject have extinguished decades ago, and teaching math until their last paycheck seems like a decent job to paying the mortgages and to pampering themselves with one or two dear overseas trips every other year with their loved ones.

Indeed, Singapore math has never been known to be interesting, fun, or creative, at least this is the canned perception of thousands of local math teachers and tutors—they just want to over-prepare their students to be exam-smart and to score well. The task of educating their students to love or appreciate the beauty and power of the subject is often relegated to outsiders (enrichment and olympiad math trainers), who supposedly have more time to enrich their students with their extra-mathematical activities.

Singapore Math via Humor

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© Sidney Harris The lost art of Roman numerals

A prisoner of war in World War II, Sidney Harris is one of the few artists who seems to have got a good grasp of math and science. While school math may not be funny, math needn’t be serious for the rest of us, who may not tell the difference between mathematical writing and mathematics writing, or between ratio and proportion. Let Sidney Harris show you why a lot of things about serious math are dead funny. Mathematicians tend to take themselves very seriously, which is itself a funny thing, but S. Harris shows us through his cartoons how these symbol-minded men and women are a funny awful lot.

Angel: “I’m beginning to understand eternity, but infinity is still beyond me.”

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© Sidney Harris There is nothing new under the mathematical sun!
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© Sidney Harris Isn’t mathematics just a man-made game?
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© Sidney Harris The world’s first “mathematical plagiarizer”
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© Sidney Harris The aftermath of Pi addiction
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© Sidney Harris Maybe we’d soon spot some bunnies running around!
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© Sidney Harris Some step just needs to be accepted on faith!
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© Sidney Harris Who says mathematicians don’t need drugs?

Mathematical humor is a serious (and dangerous) business, which few want to invest their time in, because it often requires an indecent number of man- or woman-hours to put their grey matter to work in order to produce something even half-decently original or creative. The choice is yours: mediocrity or creativity?

Humorously and irreverently yours

References
Adams, D. S. (2014). Lab math. New York: Cold Spring Harbor Laboratory Press.
Harris, S. (1970). What’s so funny about science? Los Altos, Ca.: Wm. Kaufmann, Inc.

© Yan Kow Cheong, August 20, 2015.

Check out an inexpensive (but risky) way to make a Singapore math lesson less boring: The Use of Humor in Mathematics. The author would be glad to visit local schools and tuition centers to conduct in-service three-hour math courses for fellow primary and secondary math teachers, who long to bring some humor to their everyday mathematical classrooms—as part of their annual 100 hours professional upgrading. Please use his e-mail coordinates on the Contact page.

Number Patterns on Social Media

If you had been on Facebook for some time, it’s very likely that you would have come across a certain type of numbers puzzles streaming your feed. Clearly, they’re not quite the typical numerical puzzles that often appear in school math books; rather, they’re closer to the types of questions posed in aptitude or IQ tests. One such number puzzle is the following.

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Unlike in textbooks that often present these logic puzzles in an uninteresting way, by seeing these colorful number puzzles on Facebook or Pinterest, and being hinted that only a small percent of the problem solvers apparently managed to get the correct answer, this entices readers to give it a try to see how well they’ll fare vis-à-vis their oft-mathematically challenged Facebook friends. Here’s another such number puzzle.

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Arguably, these numbers-and-words puzzles have a certain charm to it, because they often require just simple logic to solving them, unlike similar brainteasers that may require some knowledge of elementary or middle-school math. What about the following Facebook numerical puzzle?

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What is 1 + 1?

What do you make of this one?

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If these on-line numbers puzzles indirectly help promote logic and number sense among math-anxious social-media addicts; and along the way, provide them with some fun and entertainment, let’s have more of them in cyberspace!

Let me leave you with half a dozen of these numerical puzzles, stolen from my Facebook feed. Note that these types of brain-unfriendly math or logic questions may have more than one mathematically or logically valid answer, depending on the rule or formula you use—they serve as numerical catalysts for promoting creative thinking in mathematics.

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Happy Creative Problem Solving!

© Yan Kow Cheong, June 12, 2014.

Some Fun with Stewart Francis’s Puns

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www.cafepress.com

In my formative years, I don’t recall any elementary school teachers sharing some mathematical puns with us. I suppose that the arithmetic of yesteryear was often taught in the most uninteresting way by many who probably didn’t look forward to teaching it to a bunch of noisy kids.

Recently, while reading Stewart Francis’s Pun direction: Over 500 of his greatest gags…and four crap ones!,  I came across a number of numerical puns that might even be appreciated by some nerdy seven-year-olds. Stewart Francis is considered to be the best Canadian comedian from Southern Ontario. Here are two dozen odd math-related puns I’ve stolen from his punny book. Hope you enjoy them!

The number of twins being born has doubled.

They also stole my calculator,
which doesn’t add up.

Four out of ten people are used in surveys. Six are not.

Crime in lifts is on the rise.

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“QED Gravestone Small Poster” www.cafepress.com

I recently overcame my fear of calculators
It was a twelve-step progra
m.

Women are attracted to foreign men. I’ve heard that at least uno, dos, tres times.

All seventeen of my doctors say I have an addictive personality.

There’s a slim chance my sister’s anorexic.

Truthfully, we met at a chess match, where she made the first move.

Is my wife dissatisfied with my body? A tiny part of me says yes.

I read that ten out of two people are dyslexic.

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From: wherethepunis.com

They now have a website for stutterers, it’s
wwwdotwwwdotwwwdotwwwdotdotdot.

I have mixed race parents, my father prefers the 100 metres.

I’m the youngest of three, my parents are both older.

Clichés are a dime a dozen.

I’m an underachiever 24-6.

I used to recycle calendars.
Those were the days.

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www.cafepress.com

I’ve learned two things in life.
The second, is to never cut corners.

‘Any man who lives his life in accordance to a book is a fool.’
Luke 317

I can say ‘No one likes a show off’ in forty-three languages.

I was once late because of
high-fiving a centipede.

Of the twenty-seven
students in my maths class,
I was the only one who failed.
What are the odds of that, one
in a million?

I’ve met some cynical people
in my twenty-eight years.

I was good at history.
Wait a minute, no, no I wasn’t.

I was terrible at school. I failed
maths so many times, I can’t even
count.

Reference
Francis, S. (2913). Pun direction: Over 500 of his greatest gags…and four crap ones! London: Headline Publishing Group.

© Yan Kow Cheong, March 19, 2014.

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