Folly of the Faithful Canine

PEDMSA?

2025-11-29T22:47:18Z

You may have seen “PEMDAS” and other mnemonics
For math, but I lack satisfaction:
Parentheses, exponents, multiplication,
Division, addition, subtraction?

You’re really supposed to subtract before adding.
Take eight minus seven plus one.
From PEMDAS, you’d think the solution was zero,
Not two as it’s properly done.

Moreover, don’t multiply ere you divide.
Of course, fractions help make the point clear,
As four over twenty times twenty is four,
Not a hundredth, which isn’t so near.

Yet mathematicians declare that M’s equal
To D and A’s equal to S.
Perform operations in left-to-right order,
And then you’ll avoid the whole mess.

To my mind, they made it less simple than needed.
Just say “P-E-D-M-S-A.”
Admittedly, that doesn’t roll off the tongue,
So perhaps it’s less catchy that way.

In any event, if you fear ambiguity,
You can rely on parens:
Whatever’s inside them gets highest priority.
Thank you for reading, my friends.

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Problematic Problem

2024-03-16T02:17:25Z

The College Board, the group that always makes the SAT,
Has rarely copped to errors in an almost century.
One infamous example came in 1982,
When zero of the options then available were true.

This item showed two circles, A and B, where B had thrice
The radius of A (the illustration was precise)
And A would roll around B, so how often, then, would A
Complete a full rotation in its circuit, would you say?

I’d like to note the text said “revolution,” not “rotation”—
Ambiguous, but not the bigger cause of consternation.
The closest given answer to the proper one was three,
But take two circles, try it for yourself, and then you’ll see.

The coin rotation paradox results in one spin more,
So A’s rotation total in the trek ‘round B is four.
Although it rolls but three times its circumference, the path
It travels on is circular, and that explains the math.

Three boys who took that SAT wrote in to tell the board
About its subtle oversight. I’m sure they left it floored.
The problem was discounted, bringing down a lot of scores
And costing takers money for correction (but of course).

Within the decades since, the board’s made many more mistakes.
I’d say its biggest issue’s not a membership of flakes:
Today most U.S. colleges say applicants need not
Take any test that’s standardized to prove what they were taught.

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The Monty Hall Problem

2023-08-20T00:26:41Z

The Monty Hall problem is named for a host
Of the game show called Let’s Make a Deal.
A player picked one of three doors, and Hall opened
Another, a goat to reveal.

The player could then choose to open that first door
Or switch to the other still shut.
One door hid Goat 2, and the other, a car
For a prize. If you go with your gut,

You might just assume the two options are equally
Likely to get you the car.
Statistician Steve Selvin asked Marilyn Mach
vos Savant if they actually are.

The magazine columnist’s answer at first
Was rejected by many a scholar.
With proofs by computers and humans, the number
Of naysayers got a lot smaller.

If Hall hadn’t already known where the car was,
The odds would be equal indeed,
But since he would start with a goat every time,
What he skipped was more apt to succeed.

This problem is called a veridical paradox,
Seeming absurd but quite true.
The Three Prisoners problem and Bertrand’s box paradox
Mirror the math of it too.

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The Luck of the Eulerish

2023-05-28T19:45:36Z

I’ve learned about a number set (a thing I do for fun)
Of 2, 3, 5, 11, 17, and 41.
They’re Euler’s “lucky” numbers, and the formula’s like so:
All positive k integers below these n’s will show
That k^2 – k + n is bound to yield a prime.
(If k were n, the value would be n^2 every time.)
You’ll notice one’s much larger than the others in the set.
It’s now my age. Here’s hoping that my luck increases yet.

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Razzle-Dazzle

2023-03-27T04:39:00Z

If you attend a carnival, beware the Razzle games,
Which go by “Cajun Bingo” and a bunch of other names.
A bettor spills eight marbles from a cup upon a board.
They land in holes with numbers to determine how it’s scored.
A grid displays which totals lead to points toward a goal
That lets you pick a prize, so no one stops at just one roll.
A throw that sums to 29 will double throwing’s price
But also means more prizes if successful, which is nice.
The trouble is, the winning sums are always high or low.
The grid’s in random order, so you likely wouldn’t know.
The chance of scoring anytime is only 2%.
A 29 is probable, and so is your lament.
Ironically, the operator often starts with lies
Pretending you got points and thus may soon attain a prize.
Take note that many prizes are expensive, like TVs,
A telling sign you can’t expect to garner them with ease.
Since folks have lost a fortune, many nations have it banned—
Which doesn’t mean you’ll never see a Razzle-Dazzle stand.

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In Its Prime

2022-12-05T05:06:57Z

You may have heard that one’s not prime.
That’s not been standard all the time.
The notion comes from ancient Greeks,
Who deemed one not a number (freaks).
Some also thought all primes were odd,
Omitting two as well (how flawed).
The Middle Ages saw at last
That one’s a number; then it passed
For prime for several centuries,
Contested seldom (Euler, please),
But after 1956,
Instructors had agreed to fix
Their lists of primes to all exclude
The number one, which now is viewed
To be a “unit.” What’s the deal?
To count it now, we would repeal
The wording of a lot of rules
Most often learned in higher schools.
The sieve of Eratosthenes,
For instance, wouldn’t work with ease.
So every prime must have two factors,
Heedless of the rule’s detractors.

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Tau and Doubt

2021-03-15T03:40:50Z

The number pi’s been championed from ancient times to now,
But many people say that we’d do better using tau,
Which equals twice the pi amount. The letter stands for “turn,”
A unit of tau radians, as I was glad to learn.
The rationale for using it: For nearly all occasions,
We multiply the pi by 2 in circle-based equations.
Circumference is noted as πd or 2πr.
Diameter gets measured less than radius by far,
And tau can surely speed us up in finding a solution
To areas of other shapes and normal distribution.
The trouble is, most formulae where tau makes sense to choose
Are ones that only certain math’maticians often use.
Most people never calculate reactance of inductors.
For areas of circles, tau is more of an obstructor.
What’s more, we know a lot of tricks for calculating pi,
From centuries of thought; with tau, they’re harder to apply.
And then, of course, to western mindsets, pi is just more fun:
We treat ourselves with pastries to enjoy a cutesy pun.

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