Five Favorites — 101Questions [5/26/12]

  • Doggie Bandana, Marshall Thompson. Marshall got me good with this one.
  • Water Power Plant, Bernard. Similar to Windmill. In both cases, I’d like to know if what we’re seeing would power a light bulb, a fridge, or a car. As in, I really want to know. No math teacherly pretense here. If you can help me answer that question, I am your eager student.
  • Snow, man, Patrick Brandt. I skipped this one initially, but Patrick’s question has been gnawing at me since I saw it. Can anyone suggest a redesign?
  • London Eye, Edwin Ulmer. I’ve been looking for just this kind of clip for a long while. Three cheers for Internet-based collaboration.
  • Shoot the Gap, LDH. Recently, I expressed a sense that posting video of GGB / GSP applets tends to miss the best parts of both. This one is different.

My own listings:

At the end of a session in Toronto just now somebody asked me how much time it takes to come up with these kinds of tasks. “More or less than when you made tasks on paper?”

“Definitely more,” I said. But, brother, can you see I’m trying to suppress some kind of goofy smile in Popcorn Picker? Same with Coffee Traveler, where I’m grinning off screen. At a certain point, I stopped coding this kind of production as “work.” No disrespect at all if that’s not your thing.

Data Dump:

Do people who upload more have higher perplexity scores? No, they don’t. I would like to see an animation of those points over time, though.

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. About the water wheel and windmill, I don’t have much experience with real-life application, but that’s my goal, so I’ll take my best shot.

    The power usage (watts) or current (amps) for any electrical appliance is printed somewhere on it. Watts is power, a measure of how much energy is used per second. If the label gives you current, you need to multiply by voltage to get the power use. Voltage for a wall outlet in a US house is 120 V, so if my fridge says it draws 3A, that means 360 W of power. This would be a maximum though, not an average over the whole day, which would depend on the room temperature and how often your teenager opens the door and complains, “There’s nothing to eat in this house!”

    For a car, I don’t know where you’d get the horsepower. There must be someplace to look that up. 1hp = 746W, but the hp rating would be a maximum. You don’t use all the horses unless you’re accelerating from 0-70mph as fast as possible like you think you’re a NASCAR driver. To figure the actual power used, hmm…you could do it based on the mass of the car, the friction between the wheels and the pavement, the drag coefficient, etc but that would be a mess. I would do it by using the gas mileage for a particular speed, and figure how much gas is used per second, and how much energy is in a gallon of gas (google). There would be some energy wasted in burning the gas, and if that’s not figured into the value you looked up, you could track that down too. However, you’d need more power to get the car moving in the first place, and I’m not sure how to figure out that part. The energy to start the engine would be provided by the battery, but I don’t know if a lab multimeter could test that; I have no idea how high the current would be. Advance Auto Parts offers free battery testing in which they attach a glorified multimeter to your battery while you start it up, so that would work.

    Okay, so now about the power source. The energy provided by water or wind will not all be converted to electrical energy, because no machine is 100% efficient, and most are far from it. So the best way to determine how much energy you’re getting is to measure output. If you don’t have a power meter, you could do this with a multimeter — measure voltage and current and multiply to get power. However that assumes you have the machine wired to transmit electricity, which the water wheel isn’t, and that you have access to the wiring, which you probably don’t in the case of the windmill.

    You could figure out the angular speed of either spinner, (rpms -> radians/sec) and calculate the rotational kinetic energy, analogous to normal kinetic energy of an object moving in a straight line. Mass is replaced with moment of inertia, and velocity is replaced with angular velocity, so that KE = 1/2 * moment of inertia * angular velocity squared. In order to figure moment of inertia, you have to have the mass of the spinner, so you probably can’t do this for the windmill.

    Once you have the kinetic energy of the spinner, that somehow gets converted into electrical energy. There must be a magnet and coil of wire involved, like the way a motor or generator works. But as I said, no machine is 100% efficient. You could find the average efficiency of the type of machine in question, and estimate based on that.

    Whew! Does this count as a woman participating in 101qs?

  2. Marshall:

    I’m guessing that’s you Dan at (63,66)?

    Yeah, though I think Statler Hilton just crept past me on the x-coordinate.

    @Kelly, thanks for walking me through it!

  3. I just realized that may not have been what you were asking for. (duh!)

    Sorry if I was too helpful. In this context I don’t know how to interact the way I usually do to get students to figure things out for themselves. And I have no idea how much you know about energy.

  4. a different eric

    May 27, 2012 - 6:32 am -

    @marshall – hilarious!! of course… I’m assuming the obvious doggie picture is a setup for kids to prove that every integer greater than 1 is a product of prime numbers?

  5. My proposed redesign of the snow man.

    Aerial view video (from roof top or something).

    Time lapse of the creation of the snow man.

    For ease sake, it may be better to stick with just one giant snowball, but that’s how I envision it.

    The more methodical you do the rolling the better (i.e. always rolling on the outside edge towards the centre).

  6. Re: snow, man – I’d quite like to see this as an area and volume of similar shapes problem.

    Timon’s scenario is fantastic, I’d have a video of a snowman built from some fraction of the entire lawn’s snow and challenge them to find the volume of a snowman built from all of the snow.

    This should negate the need for the thickness of the snow on the lawn… I think. I’ll check this in the morning.

    Then all I’ll need is for it to actually snow in the UK.

  7. mr bombastic

    May 28, 2012 - 5:09 pm -

    It would be much better if it was obvious that you intend to make the largest snowman possible.

    Maybe, in the spirit of mean spiritness, you could give a look or gesture indicating disdain for the size of the snowman in your neighbors yard.

    Or, maybe put one of those large inflatable snowman in the yard along with video of you rolling the first ball along the perimeter of your yard. Something to indicate you will use all the snow.

  8. I like Timon and Alex’s redesign of Snow, Man. I can see how the picture doesn’t exactly emphasize the question that I proposed. From a student’s perspective, many other questions would come to mind first.
    I’ll try for a redesign the next time it snows (in 8 months) (if I remember). Aerial view of yard pre-snowman, time-lapse video of me creating snowman or large ball of snow, aerial view of yard post-snowman.
    Although, I do like mr. bombastic’s idea of throwing competition into the mix. Could I show my neighbor’s snowman and their yard, and then just show my yard? Would that be enough to say ‘can I make a bigger snowman with just my snow?’

  9. Snowman redesign:

    I could see this being a video or slideshow of sorts. In the first photo: a backyard of snow and in the next the snowman made from that yard. Then a larger backyard and it’s snowman. Finally, a third backyard and stop the slideshow there. Save that snowman for the third act.

  10. Re: Marshall Thompson’s contribution, I really want to know how the question asked in this format with a more “real”-looking photo compares to the text book instance.

    What if it were a picture of an unearthly ginormous dog with a similarly ginormous bandana…

  11. Actually, all along I’ve been thinking about a chihuahua bandana.

    If somebody wants to put a bandana on their lab or German shepherd, of course they don’t measure, they just get a standard bandana, fold it in half and tie it on. But if you wanted to put a bandana on your chihuahua, that wouldn’t work — you’d have to make one the right size. You’d either have to guess, or do the math.

    And then, what if you want to make a miniature bandana that looks like a standard one, with the usual pattern? You’d have to deal with scaling. And if you want to manufacture these to sell at a pet store, how much fabric, and how much would it cost, and how much would your profit be?

    If you think this is unrealistic, you haven’t seen the way some people with tiny dogs act like they’re baby dolls.