"Pennies" for your thoughts...

[gement]

I saw this picture of a penny pyramid in Wired, with the caption, "Call Mexico now for just pennies."


My first thought was, "I wonder if that's enough pennies to buy the G3 it's advertising."

The volume of a regular pyramid is base * height / 3. My source for this screencap was PCWorld, November 2009, http://www.scribd.com/doc/21560824/pc, the back cover (page 103). If you zoom in, you can see details like the count of one stack, which I determined from a print copy of Wired, November 2009 (page 53).

Base: I approximated the base by counting the stacks of coins along one bottom edge (I counted 26, so 24-28 for margin of error), squaring that, and then multiplying by the number of coin edges I could see in the corner bottom stack (17).

$97.92 to $114.92. That's just the base. Yeesh.

The stacks don't seem to be of uniform height, but they're pretty close, so at this point I start treating each "step" as height 1 and assuming that's 17 pennies high throughout. The pyramid as it stands is 12 units high with a truncated top approximately 8 stacks wide. (It's 9 at the top, but it's also two stacks of the same width and I can see a hollow in there, so to calculate uniform slope, I'm saying 8.)

Time for fun with rise over run! (Dad, I blame you for the fact that I even thought that horrible rhyme, and you're free to use it.) I'll do the math twice, once for a width of 24 and once for a width of 28. (I'm solving for h, the height of the missing bit of pyramid.) 12/(24-8)=h/8 -> h=6 -> H=18. 12/(28-8)=h/8 -> h=4.8 -> H=16.8.

So the full pyramid has a square base of W=24, H=18, or W=28, H=16.8. That's $587.52 (tall and narrow) to $746.37 (short and broad). I still need to truncate it.

The subtracted pyramid is w=8, h=6 or h=4.8. Subtract $21.76 from the tall or $17.41 from the short.

Final total:

This pyramid, if presumed to be made of solid pennies, would cost $565.76 to $728.96 to build. This, ladies, gentlemen, and small furry creatures from Alpha Centauri, is a $650 pile of pennies.

And it's an ad bragging that a smartphone will make it cheaper to call Mexico. The irony is making it a little hard to breathe in here.

Comments

[sistawendy.livejournal.com]

They must not be counting the cost of the phone itself, just the international long distance plan. You simply have to buy a smartphone anyway, right?

[gement.livejournal.com]

Also, assuming these are the (lighter) pennies minted since 1982, at 2.5g each, $650 is 162.5 kg = 358 lbs.

... I wonder what my friendly local T-Mobile retailer would make of me trying to buy a phone with more than twice my own weight in copper-plated zinc.

[danibearess.livejournal.com]

.
You are such a sweet geek.

Thanx for the card

Dani

[gement.livejournal.com]

Very welcome! I had to use subtle guile and lie in wait for your mailing address. ;)

[kitcatk8.livejournal.com]

You = The best.

[randomdreams.livejournal.com]

The math alone is pure awesomeness.

[gement.livejournal.com]

I'm thrilled you think so! You were one of the people that I hoped would check my work. I'm antsy about the boundary conditions, as discrete math was never my strong point. I'm not sure what an off-by-one error would do here, either in terms of total volume (am I rounding all the way to the inside or the outside of the steps?) or the truncation (did I accidentally count one step too often or too few?).

Then there are those pesky ramps...

[maribou]

Your math is adorable, as is your enthusiasm for self-generated geometry problems. But I would suggest that the pyramid is most likely (based on my knowledge of advertising types) to be either hollow or built around a styrofoam base. There's no frackin' way they built a solid pyramid entirely out of pennies. The geek who thought've it might've wanted to, but no wai his bosses would've let him.

[gement.livejournal.com]

Well, yes, I know. It makes me sad. But the impression of what they're selling is an image of a pyramid of pennies, so I took it as an exercise on what advertising makes people think. ETA: Honestly, I hadn't presumed it was built in real life, rather than taking some reference shots of stacks of pennies and then computer generated.

You can blame the self-generated geometry problems on my dad, who teaches high school math and just about jumps up and down when these things present themselves.

[maribou]

Heh. So apparently you're even more of a visual cynic than I am, but more cheerful about finding interesting places to go from there:).

[hollyking.livejournal.com]

Ah, the kind of math I deal with every day. Although I'm more concerned about the weight of a random selection of coins that naturally fall into a conic shape in an armored bin.

For fun, an uncirculated penny weighs 2.5 grams so 56,576 pennies would weigh 141.44 Kg (311.82 lbs) and 72,896 pennies would weigh 182.24 Kg (401.77 lbs). ;)

[gement.livejournal.com]

HA! What kinds of armored bins do you concern yourself with? Do you have pre-measured constants to avoid having to do all the statistics, or are you in charge of generating those pre-measured constants?

Re: weights, see my other comment. GMTA.

[hollyking.livejournal.com]

I work for Coinstar as a software engineer. So the bins are the ones in the machines you see in grocery stores. The goal is to predict when the bins going to be full so a collection can be scheduled.

[ilmarinen.livejournal.com]

As a complete aside, I once carried $1,000 bags of quarters (as I recall). It was heavy, but not outrageously so. I should try to look that up (weight) . . .

[gement.livejournal.com]

5.67 g (if minted since 1965) * 4000 = 22.68kg = 50.001 pounds. Apparently the new quarter weight was designed SPECIFICALLY to make round (decimal) numbers of quarters weigh in exact pounds. Fascinating!

Re: Inspired (infinite loop?!)

[gement.livejournal.com]

I less than three you!

[annissamazing]

The former VP of HR for my company took a vacation to Mexico and decided she should be able to use her company-provided iPhone while she was down there. I called AT&T and added an international calling plan to her line. The customer service rep failed to mention that we also needed to add an international data plan on top of her unlimited data plan and we ended up with over $700 in data charges. This ad seems pretty honest to me.

[gement.livejournal.com]

Yowza! I think Neil Gaiman actually blogged about the same thing happening to him, and his service didn't even offer an international option. Data plans are bizarre money sinks.

[gement.livejournal.com]

Hooray! Glad you enjoyed it.