"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

[kitcatk8.livejournal.com]

You = The best.

[randomdreams.livejournal.com]

The math alone is pure awesomeness.

[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.

[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). ;)

[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) . . .

[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.