01/17/2003 Entry: "Rolling Back Math"

In one of my regular channels on IRC the subject of Sam's Club comes up, they're having some anniversary and are distributing some propaganda out to the masses. I have a very low quality fax of a page from that flyer, it contains a fun fact that I repeat here:

"Over the past year, 10,182,853 hot dogs have been sold at the SAM'S CLUB Café. If laid end to end, these hot dogs would stretch from the moon and back over 13 times. Laid end to end, they would go around the world 254.5 times."

It just so happens that I discovered the 'units' command today, a program that converts between units of measure. I'm part of a very small percentage of people who would enjoy playing with such a program. Upon seeing these facts, I immediately thought to plug them into 'units' and calculate the one unknown: how long is a SAM'S CLUB hot dog?

Units has a unit called 'moondist' already programmed into it, this is the "mean earth-moon distance." As the fun fact states, this chain of hot dogs goes to the moon and back over 13 times, so this is over 13 * 2 * moondist.

bash-2.05a$ units -v "13 * 2 * moondist" miles
        13 * 2 * moondist = 6210232.2 miles

So the chain of hot dogs is 6,210,232.2 miles long. To figure the length of each hot dog, we simply divide this number by their quantity:

bash-2.05a$ units -v "13 * 2 * moondist / 10182853" miles
        13 * 2 * moondist / 10182853 = 0.60987154 miles

Ah, interesting! Now we know why Paula Puckett thinks these hot dogs are so great. These very affordable hot dogs are over a half mile long.

We can double check this figure with the corroborating world encirclement number. Units also has a unit called 'earthradius.' To calculate the circumference we have to remember that c = 2 * Pi * r. The hot dog chain is 254.5 times Earth's circumference.

bash-2.05a$ units -v "254.5 * 2 * pi * earthradius" miles
        254.5 * 2 * pi * earthradius = 6330659.5 miles

6,330,659.5 miles is relatively close to the first result, and if you consider their moon figure is "over 13 times," that can account for the difference.

bash-2.05a$ units -v "254.5 * 2 * pi * earthradius / 10182853" miles
        254.5 * 2 * pi * earthradius / 10182853 = 0.62169802 miles

That's a big hot dog.

So what are the real fun facts, anyway? I have no idea how long the hot dogs are at SAM'S CLUB, but I would bet they aren't much longer than 10 inches. A little more fun with 'units'...

bash-2.05a$ units -v "10182853 * 10 inches / moondist"
        Definition: 0.0067285241

Ah, that's a shame. Those hot dogs only go over 6/1000ths the way to the moon. Hardly seems worth mentioning, really.

bash-2.05a$ units -v "10182853 * 10 inches / 2 * pi * earthradius"
        Definition: 0.064609017

65/1000ths the way around the world. This is 1,607 miles. That might get you to and from SAM'S CLUB 254.5 times, if there's one nearby.

One final question is, how many hot dogs would they really have to sell in order to stretch a chain of hot dogs as far as they claim?

bash-2.05a$ units -v "254.5 * 2 * pi * earthradius / 10 inches"
        Definition: 4.0111059e+10

A lot. Forty billion. Eat up, America.