## Archive for October 14, 2013

### Seven Mathematical Sins

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Lust.

Greed.

Envy.

Pride.

Sloth.

Gluttony.

Wrath.

These are the seven deadly, or mortal, or unforgivable, sins. Call them what you like, a deadly sin always has three characteristics:

- It concerns a grave matter.
- It is committed with full knowledge.
- It is committed with both deliberate and complete consent.

I’m having a good weekend. My plane landed in New Orleans on Friday afternoon, and I committed five of these sins before I arrived to my hotel. I look forward to knocking the remaining two off my list before the weekend is over. It’s pretty easy to love the Big Easy!

It’s no coincidence that there are seven deadly sins and seven castaways on Gilligan’s Island. Yep, you read that correctly. The cast of characters on *Gilligan’s Island* is isomorphic with the set of sins.

{*Gilligan’s Island* Castaways} ≅ {Seven Deadly Sins}

Can you match them up? If you don’t have access to *Nick at Nite*, you can watch the intro from the first episode of *Gilligan’s Island* on YouTube, or use this list of characters from the show:

- First Mate Gilligan
- Skipper Jonas Grumby
- Thurston Howell III
- Eunice Lovelle Wentworth Howell
- Ginger Grant
- Mary Ann Summers
- Professor Roy Hinkley

In contrast to a deadly sins is a venial, or forgivable, sin, which has the following characteristics:

- It
*does not*concern a grave matter. - It
*is not*committed with full knowledge. - It
*is not*committed with both deliberate and complete consent.

So, if you stuff yourself silly at dinner tonight with a full rack of ribs and four helpings of mashed potatoes and then willfully *choose* to have a slice of key lime pie for dessert, you would commit a deadly sin: with full knowledge and complete consent, you engaged in gluttony, which is a grave matter indeed. (Not to mention disgusting. Who pairs ribs and key lime pie? Yuck.)

On the other hand, if you *accidentally* sleep with your wife’s best friend while intoxicated, well, that would be a forgivable sin: you were too drunk to know what you were doing. (Though you may still be allowed entrance to Heaven, I recommend you keep this transgression a secret from your spouse.)

But I digress. This is a math blog. Let’s talk about mathematical sins.

**Seven Deadly Math Sins**

- Claiming that division by 0 is “impossible.”
- Omitting the middle term when expanding (
*a*+*b*)^{2}. - Using ASS as justification for a proof of triangle congruence.
- Referring to the answers in the back-of-the-book as “my good friend BOB.”
- When a student fails to understand your explanation, thinking that you can help by saying the exact same thing louder, slower and closer.
- Distributing a factor outside parentheses to only the first term within parentheses.
- Trying to break the ice with a math joke at a cocktail party, and then spending the rest of the night explaining the joke to everyone who didn’t laugh.

**Seven Venial Math Sins**

- Believing that the reciprocal of
*sine*is*co**sine*and that the reciprocal of*secant*is*co**secant*. That would be consistent with the reciprocal of*tangent*being*co**tangent*, after all. - Enunciating the
*p*in*asymptote*. - Failing to remove double-counted elements when solving problems like, “How many two-digit integers are multiples of 3 or 5?”
- Using a subtle double negative, such as, “Horatio can
**not**help**but**invert the first term when dividing fractions.” - Believing that multiplying always produces a greater result (or dividing always produces a lesser result).
- Cancelling a variable from both sides of an equation and losing a solution, such as solving 2
*x*^{2}=*x*by dividing both sides by*x*to give 2*x*= 1, and concluding*x*= 1/2. - Using a Klein bottle to hold your beer.