Tag Archives: math

Math Word of the Day: Pithon

The day before, we read that a female Burmese python weighting 98 kg and nearly 5 m was caught in Florida. She’s the largest snake ever found in that state before her death, pregnant with an amazing 122 eggs; if stretched vertically, she’d be as tall as a giraffe.

In Florida, where now lives the Viper in Chief after being ousted from the White House, who’s since preoccupied himself with terrorizing those who refuse to propagate his lasagna of lies, pythons have become pests due to irresponsible pet owners of yesteryears releasing or allowing pet pythons to escape in the wild.

With no major predators, Florida’s subtropical climate has provided serpents and snakes a conducive breeding ground for them to multiply, often outcompeting native species. Who knows? Alien vipers might eventually outnumber local pythons, if left on their own to populate the land.

Recently, some human vipers mounted a “mathematical insurrection” against textbook publishers for allegedly promoting “woke math” to K–12 students. And a rising number of foreign pythons are set to keep Florida’s annual “Python Challenge” alive—this year, the event runs from August 5–14 and is expected to lure around 500+ python hunters from 25 different states.

🐍🔢: Math with Pythons & Pithons

Like math questions on vampires and zombies, those on pythons (and pithons) are no less frightening or exciting to problem solvers. Below are two examples:

It is estimated that the female Burmese python, which was caught after Floridian researchers used a male “scout” to find her, was up to 20 years old. In human years, would she be as old as the Viper in Chief?

Python Pies or Pizzas: In 2021, the winner of the “Python Challenge” captured 223 pythons, while the longest snake was 15 feet long. Imagine if this year’s captured foreign pythons were ethically killed and exotically used to make pies or pizzas, how many pieces of either one could be made by the chefs at Mar-a-Lago for the “Florida Python Food Festival”?

© Yan Kow Cheong, June 25, 2022

What’s your definition of a pithon?

Math Word of the Day: Square

If you were given a chance to redefine a square, what would your new definition be other than it being another word for a geek, nerd, or bore? Or, a figure who refuses to do any of those immoral, illegal, or unethical things when pressured by peers: drug, booze, sex, porn, gang, scheme, graft, ….

Geometric Stereotype à la Singapour

In Chan Li Shan’s Searching for Lee Wen (2022), the author wrote:

“A well-known actress, Nancy Kwan once gave a talk at a conference of British-born Chinese. Having started in the film The World of Suzie Wong, she was talking about what it was like to be a Chinese actress working in Hollywood. Noticing Lee Wen [a deceased Singaporean artist who received the Cultural Medallion in 2005, Singapore’s highest award for the arts] at the back of the room, she said,

“Who’s that young man sitting behind? How come you’re so quiet? Where are you from?”
“I’m Lee Wen from Singapore.”
“Oh! Singapore… people there are all very square, right?”

Don’t you agree that there’s an iota of truth that people in the “fine” city don’t so much look like a square but do often behave like one? By this, I mean that they’re generally conservative, conformist, or compliant, or all three. Few would wish to be seen as an odd one in a sea of evens, because an oddball often creates waves, positively or negatively.

At work, few would step out of their invisible square to question, much less challenge, the oft-dated rules and regulations. Most hate their job, waiting for Fridays and dreading Mondays. They’ve subconsciously squared to live an uneventful or fearful life, because switching to an alternative career path looks pretty disruptive, not to say, (initially) painful.

Your choice of a meaningful life lies squarely on you. If you’re a math educator, are the math things you’re presently doing square with what you desire in future? For instance, are you waiting until you retire to write that book? Or until the kids go to college to start working on that manuscript? Whatever it is, just make sure that you don’t die with a book still inside you!

If you’ve been dubbed a square, or secretly see yourself as one, remember that squares are circles with corners, and over time, most of them do turn into a beautiful (imperfect) circle.

© Yan Kow Cheong, June 23, 2022

A right 4-gon

Math Word of the Day: Dengue-19

On April 26, 2022, after reading in the local papers that almost 5,500 dengue cases were reported in high-GDP Singapore, exceeding last year’s total, I posed and posted the following quiz:

“Covid-🇸🇬: A True or False Quiz: “In living-with-Covid Singapore, people are more afraid of contracting the dengue virus (dubbed the ‘rich man’s threat’) than the coronavirus (coined the ‘poor man’s dread’).”

A Tale of Two Vectors

Last November, I’d somewhat asked a similar question: “What are the odds that in Singapore the wealthy are more likely to go to hospital due to a mosquito bite rather than due to a viral infection? The delta goes for the poor; the dengue targets the rich.”

A month earlier, I’d postulated the following scenario: “In the Singapore 2021 infection contest, the dengue is no match to the delta. Even with more biting opportunities to target potential work-from-home victims, the 🦟 blamed the 🦠 for failing to meet its target.” https://lnkd.in/d5TeNdUA

In fact, way back in 2020, I’d pondered about “Singapore’s double whammy: The dengue (9,261 cases) is catching up fast to give the coronavirus (36,405 cases) some fight. Which one will win the 🇸🇬 infection contest: the mosquito 🦟 or the virus 🦠?” bit.ly/36YIzbh

Fight for Your Life

Today, in a number of war-stricken or terrorism-sponsored countries, the battle cry is: “Be a peace fighter.” In SE Asia, the rallying cry is: “Be a dengue fighter.”

© Yan Kow Cheong, June 22, 2022

Which is deadlier: Covid or Dengue?

Math Word of the Day: Covid-🇸🇬

On Monday, Singapore’s Health Minister Ong Ye Kung reported that 80,000 seniors aged 60 and above have yet to take their Covid-19 booster shots, urging them to do so as the city-state is expecting a new wave of Omicron infections in the next few months.

The minister added that the first batch of Covid-19 vaccines were engineered more for the “wild-type” virus, and now that the coronavirus has mutated into the Delta and Omicron variants, we need at least three doses of vaccines for “effective” protection—and a fourth jab (or a second booster shot) is recommended for those who’ve so far lived on this planet for at least three scores and two tens (or four scores)—aged 80 and above.

Like thousands of my fellow skeptics, when we read or hear this kind of corona update from a local politician on a Monday, our skepticism index goes up at least twenty points. It sounds more like an indecent number of WHO-approved vaccines are nearing their expiry dates, so they need to come up with some creative eleventh-hour strategies not to waste away those tens of thousands of doses.

These days, even developing countries with low vaccination rates are likely to turn down any donated near-expiry vaccines from those high-GDP hoarders. They’d reply, “Thank you very much for your [“insincere”] donation!” followed by some PC excuses not to offend the donors.

One subtle way to salvage a fraction of these surplus doses is to use some mortality statistics to scare off those who’ve yet to be jabbed or boosted.

For instance, we’re statistically being told that the probability of unvaccinated seniors aged 60 and above ending in the intensive care unit (ICU) or dying from Covid-19 is 1/25, but the figure drops to 1/100 if they’ve been doubly jabbed, or nosedives to a mere 3/1000 if they’ve been boosted.

Minister Ong emphasized that “It makes a difference whether you have taken 0, 1, 2 or 3 shots.” So, the unvaxxed would better pay heed to his life-and-death warning unless they plan to journey to the other side sooner than later.

The sombre message is: Wake up to your minister’s advice if you don’t want to have a minister at your premature wake conducting nightly services to your loved ones and friends and colleagues. The decision is yours to act if you want to prolong your stay on this planet by an extra few years or decades.

Let’s pray that the unvaccinated or unboosted lot would fear Covid-19 more than Covid-🇸🇬, while not letting themselves be paralyzed by either one.

© Yan Kow Cheong, June 20, 2022

The Fear Factor in the “Fine” City

Math Word of the Day: Inflation

Photo © 2022 Anon.

Last week, I read on Facebook that one glass of iced lemon tea at some coffeeshops is now selling at $1.80, up from $1.20. An obscene 50% rise (or ruse?). Or an outrageous 66.67% increase if they charge us $2.00 for takeaway (even before the GST or VAT kicks in next year).

For those of us who’ve already used up our S$100 government voucher in less than a week, which is meant to help us in our daily expenses as part of the Household Support Package, it looks like we won’t enjoy the next iced lemon tea until the next voucher. I wonder when the next one is coming. In late 2022 or early 2023?

Looks or feels like those in the “write” business might have chosen the “wrong” profession, including moonlighters in academia, especially if their royalties since the pandemic—and now the Ukraine-Russia war—have headed south.

For the majority of us who’re not born with a silver spoon in our mouth, I suppose it’s probably not too late to seriously consider selling or distributing slightly dearer home-made iced lemon tea, barley drink, honey tea, and chrysanthemum tea to health-conscious customers.

Pandemic or Putin? Or Both?

A FB netizen commented: “Tea 1% + 1% Lemon + 1% Sugar + ALL 97% Water imply hardly anything to do with FOOD Shortage so please don’t divert the blame to Pandemic, UN or what have you NOT.”

The profit margins for selling beverages are a hundred times better than the returns or royalties earned from posing and solving math questions in school textbooks or assessment (or supplementary) titles.

Not IQ Nor EQ, But FQ

Talking about being street-smart rather than exam- or book-smart! When financial quotient (FQ) is worth more than (IQ + EQ).

Photo © 2022 Anon.

Inflation provides an oft-unseized opportunity (disguised as a problem) for mathepreneurs to generate unexpected sources of income to make up for any (potential) loss in royalty or consultancy.

© Yan Kow Cheong, June 17, 2022

Math Word of the Day: Bitcoin

The advent of cryptocurrencies like Bitcoin and Ether has provided math educators worldwide with fertile resources to indulge themselves in creative mathematical posing and solving.

Unfortunately, the negative perception that cryptocurrency or crypto is a vector for serious organized crime and money laundering has led millions of half-informed or risk-averse folks to adopt a wait-and-see attitude vis-à-vis Bitcoin transactions.

Who/What Is Satoshi Nakamoto?

Nobody knows the identity of Satoshi Nakamoto. If the name isn’t a he or she or it, could the name be a covert group of cryptographers and mathematicians?

Like the modern-day equivalent of the Bourbaki group—the collective pseudonym of a group of predominantly French mathematicians in the 1930s, who tried to axiomatize mathematics to make it more rigorous?

So far, the few suspects—digital-currency addict Nick Szabo, Japanese mathematician Shinichi Mochizuki, and Co.—all have denied being the founder of Bitcoin, except for Australian computer scientist who loudly but unprovenly claimed that he is Nakamoto.

Crypto Math

Posing fertile crypto math questions is only limited by our imagination. Thanks to Bitcoin or cryptocurrency, NFTs, and the Metaverse, I’ve toyed around with a number of crypto math questions.

Below are a sample of Bitcoin-related questions that I hope would make their way into a math booklet fit for publication in a-not-too-distant future.

  1. Bitcoins are divided into Satoshis: one hundred million Satoshis in each Bitcoin. At the current Bitcoin price, what fraction of a U.S. cent is worth the smallest fraction of a Bitcoin?
  2. In 2010, a pizza restaurant agreed to accept ten thousand Bitcoins in exchange for two large pizzas. At today’s exchange rate, how much would each pizza be worth?
  3. In September 2021, El Salvador approved Bitcoin as a secondary currency; in April 2022, Central African Republic followed suit. Which rogue or war-torn nation in Asia or the Middle East would be the first one to make Bitcoin its official currency? Or would it be “fine” city Singapore that would lead the way in becoming SE Asia’s crypto hub?
  1. Crypto Apocalypse: What are the odds that due to hyperinflation (or a possible WW3 in the aftermath of the senseless Ukraine-Russia war) people would start losing faith in Bitcoin to the point that it suffered the same fate as the Zimbabwean dollar bills?
  2. A golf resort is rumored to have been gifted with 13.257 ETH and 12.5 bitcoin from a Middle Eastern prince. How much did the shady resort receive in cash donation from their criminal donor?

Crypto Winter Is Coming!

With news of a crypto winter in the horizon, let’s hope that the mathematics of Bitcoin or cryptocurrency wouldn’t deter math educators globally from getting involved in creative mathematical thinking and problem solving.

I don’t know about you, but I’m waiting for Bitcoin to drop under $10,000 as my next buy alert. The future lies in Bitcoin—or in blockchain.

Richly yours

Continue reading Math Word of the Day: Bitcoin

Otter Math

In the aftermath of a Singapore permanent resident who was bitten 26 times by a romp of otters in 10 seconds at the Singapore Botanic Gardens, which attracted mixed reactions from both locals and foreigners, I entertained the idea how math teachers could use this once-in-a-lifetime incident to indulge in some problem posing for elementary math students.

As natural swimmers, Singapore’s smooth coated otters, once thought to be extinct, have made a comeback to the island-state. They are believed to have swum across the Straits of Johore and made their homes here. Their present “locations of choice” are: Bishan Park, the Kallang River estuary, Marina Bay, and Singapore Botanic Gardens—and the Singapore Zoo.

Singaponacci Numbers and the C-Word

Mathematically or theoretically speaking, without culling, Singapore’s otters could exponentially grow as fast as Fibonacci’s rabbits, although otter sexperts think there are alternative humane ways of family planning.

An “otterman” who was furious that netizens had uttered the C-word against the cute-looking furry creature blamed them for spreading white lies or fake news about these “critically endangered animals.”

The Fear Factor

These “urban pests” seem to be better protected under the Wildlife Act than we humans against the Delta and Omicron variants. They’ve the SPCA behind them, but we’ve the POFMA* and FICA** over us to police our online behaviors.

Can you distinguish an adult otter from a baby seal?

Co-Existing with Covid and Otters

Last week, in the light of Singapore’s otter saga making the headlines overseas, I tweeted the following:

Otter Math: If the present population of 150 otters doubles every leap year, while Singapore’s annual fertility rate continues to head south, with zero immigration allowed, when would otter babies outnumber human babies? https://lnkd.in/gVfqjEZ8

Animals’ cruelty against humans: Otters bit a Singapore Botanic Gardens visitor 26 times in 10 seconds. What are the chances that such a similar incident happening again are less than the odds of someone being abducted by an alien? https://bit.ly/3oH93IO

Canals, Condos & Churches

Singaporean river otters are notorious in devouring dear ornamental fish found in condominiums and churches. If the probability of rich people disliking otters is x folds higher than that of poor folks, guesstimate x.

What are the odds that someone from a middle-income family in Singapore is more likely to cross paths with an otter family thanks to a greening Singapore, which provides an ideal milieu for otters to breed stresslessly, compared to Singaporeans, who often can’t even find a little space to do their private business?

Otter: Singapore’s Unofficial Mascot

Think of Singapore as an otter, and its frenemies-neighbors as crocodiles and monitor lizards. When threatened by its natural resources-rich, but militarily weaker, neighbors, Singapore would hit back to defend itself. Sure, they’d use low-cost warfare tactics like forest haze and arsenic-polluted rainwater to frustrate their little-red-dot neighbor—a form of asymmetric warfare to neutralize the enemy by natural and man-made means.

How not to mismanage Singapore’s otter population

Thou Shalt Not Catch an Otter! Fine: S$X

How much is the fine for someone caught capturing or trapping otters in the “fine” city of Singapore? What are the odds that a repeated offender could get jailed or/and caned for their illegal activity?

What If? Exotic Singapore Cuisine

Does otter meat taste more like chicken, beef, or pork? What if Singapore started farming otters to satisfy the desire of adventurous gourmets? Like crocodile, deer, or frog meat, could the legalized consumption of otter meat be a lucrative food business for both locals and aliens, who are looking for an exotic dish (halal, kosher & vegetarian), if there were a mismanaged otter population control in future?

An Otters Naming Contest

In the past, Singapore had the famous or notorious romp of otters called the “The Marina 10.” Now, we’ve local groups like the Zouk Family. Has the raft of otters that bit the über-unlucky British man 26 times at the Singapore Botanic Gardens been christened? If not, why about having a national contest to name them following the recent biting incident, which could have potentially led to Singapore’s first case of “death by otters”?

Otter Math for Mature Students

Let’s end with a grades 1–2 otter math question to tickle actress Sandra Bullock’s two children and their peers, who’ve been jabbed (or maybe even boosted) with a dose or two of the Singapore math vaccine to protect them against the plague of innumeracy:

After seeing an otter family of twelve devouring the fish in their condominium pond, a number of children were traumatized for weeks. Five children had recurring nightmares about the attack. There were three fewer children having nightmares than those needing counseling.
a) If two boys and a pair of twin sisters met up with a school counselor, how many children were altogether affected by the otter invasion?
b) Guesstimate how many fish were eaten up by the hungry otters in a few minutes before they made their way to the swimming pool.

Answer: (a) 13 children (b) Hint: Think about the demographics of the condo residents.

A grades 4–6 Singapore math question

Answer: 1. 8 koi fish. Can you solve the question in more than one way without algebra?

* POFMA: Protection from Online Falsehoods and Manipulation Act ** FICA: Foreign Interference (Countermeasures) Act

© Yan Kow Cheong, Dec. 16, 2021.

The Schooling Effect

Slightly more than a year before Singapore won its first gold medal at the 2016 Summer Olympics, I tweeted that “Joseph Schooling’s golds at the SEA Games looks like Barcelona or Manchester United, winning the Singapore’s S-league. #swimming” (@SingaporeLite on June 11, 2015).

From 4-Year Games to 4D Gambling

On August 13, 2016, within an hour of Joseph Schooling’s historic feat for winning Singapore its first gold at the Rio Olympics, punters in Singapore were lining up outside betting outlets islandwide to leverage on his Olympic record-breaking time of 50.39sec in the Men’s 100m butterfly. Who says that medalists’ record times can’t numerologically be used to divine the next winning lottery numbers?

A Grade 9 Singapore Math Question: “How many possible 4D numbers (with and without repetitions) could punters choose from Joseph Isaac Schooling’s winning time of 50.39 seconds?”

The Olympicology of Schooling

Following the mania among superstitious punters to strike it big, I coined Olympiocology to poke fun at their irrational or paranormal behaviors.

On the same day, I also tweeted: “How can Singapore experience the Schooling Effect in the aftermath of winning its first gold medal?” with a link that opens up the DIY e-card below.

August 13: Singapore’s “Schooling Day”

Sports Awards First, Military Service Second

Three days later, @Zero_Math, I texted: “Military rules are man-made—not cast in stone. How many Joseph Schooling’s and Fandi Ahmad’s does Singapore have?,” accompanied by the following e-card:

Should gold medalists be exempted from military service?

A Tale of Two Promoters: Vandal & Victor

On August 16, 2016, I also tweeted tongue-in-cheek another DIY e-card, comparing the notorious Michael Fey (the American teenager who was caned for vandalism in Singapore) and the glorious Joseph Schooling (whom some “bigoted” locals or Trump “patriots” claimed not to be a “true-blue Singaporean”).

When a cane brings more attention to Singapore than a coin.

Mathletes & Olympians: Mental v. Physical

Which is harder for most countries to produce: a gold medalist at the International Mathematical Olympiad (IMO) or at the Olympic Games?

Although differentiating mathletes and olympians might look like comparing apples with oranges, however, for a number of developed countries, it appears that the chances of their athletes bringing in an Olympic gold medal home are higher than the odds of their IMO mathletes being a gold medalist, if some of their representatives aren’t foreign-born, or if they were to rely solely on their limited pool of local talents.

Below is another e-card I produced in the aftermath of Singapore’s first ever-win of a gold medal at the Olympics.

Which Singapore values more: Olympic or IMO gold medalists?

A Guesstimation Question: In a number of highly competitive events at the Olympic Games, where victory is determined by mini-seconds or centimeters, and if winning a gold medal is arguably “60% skill, 40% luck,” or “50% talent, 50% luck,” guesstimate what percentage of gold medalists make it by pure luck rather than by sheer skill.

Count on Me, Singapore!

Can Singapore still count on Joseph Schooling for more medals? Would he prove his critics or detractors wrong in making his country proud again? What are the chances that he’d “make Singapore great(er) again”?

Let’s wish him all the best in the next phase of his swimming career! Let no one take away what he did to make Singapore and Singaporeans proud.

2016: Singapore & Schooling: 🏊 🇸🇬 🥇

2020: Singapore & (Kimberly Lim and Cecilia Low): ⛵️ 🇸🇬 [🏅?]

Bibliography & References

Commentary: Singapore sports must learn lessons from Schooling’s decline
https://www.todayonline.com/node/12067716

President Halimah, govt leaders speak up against ‘negative, hurtful’ comments on Joseph Schooling’s Olympics performance
https://www.todayonline.com/node/12062406

‘It’s hard to swallow’: Joseph Schooling disappointed by butterfly performance at Olympics, vows to fight harder
https://www.todayonline.com/node/12056111

Golden ticket 5039 sold out after Schooling’s win http://www.todayonline.com/node/2318881

© Yan Kow Cheong, July 31, 2021.

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.

20140421-203849.jpg
© 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

20140421-203921.jpg
© 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.”

20140421-203941.jpg© Sidney Harris There is nothing new under the mathematical sun!

20140421-204019.jpg
© Sidney Harris Isn’t mathematics just a man-made game?

20140421-204119.jpg© Sidney Harris The world’s first “mathematical plagiarizer”
20140421-204146.jpg© Sidney Harris The aftermath of Pi addiction
20140421-204413.jpg© Sidney Harris Maybe we’d soon spot some bunnies running around!
20140421-204454.jpg© Sidney Harris Some step just needs to be accepted on faith!
20140421-204714.jpg© 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.