2 comments on “CNET has some TV viewing size/distance recommendations.”

CNET has some TV viewing size/distance recommendations.

Feels like there’s a similarity (and a lot of other stuff) type problem in here.

Artifact

From CNET:

 In a perfect videophile world, you’d want to sit no closer than 1.5 times the screen’s diagonal measurement, and no farther than twice that measurement to the TV. For example, for a 50-inch TV, you’d sit between 75 and 100 inches (6.25 and 8.3 feet) from the screen. Many people are more comfortable sitting farther back than that, but of course the farther away you sit from a TV, the less immersive feeling it provides.

I’m wondering if you could pair this with Tim’s TV 3 Act problem. Perhaps even Brian’s Holiday Shopping problem. There’s honestly a lot of stuff going on here from CNET: proportion, distance, maybe even a system of equations or linear programming problem (what with the upper and lower bounds suggested above, then toss in cost constraints).

Update (6/12/17): CNET has apparently redirected the original article to a generic TV buying guide, so the above text is no longer viable. However, here’s something from The Home Cinema Guide.

A good rule of thumb is that the ideal viewing distance for a flat screen HDTV is between 1.5 and 3 times the diagonal size of the screen – and we can use this to calculate both approaches.

Still, the work for the rest of this article reflects CNET’s original viewing recommendations.

Guiding Questions

  • How big a TV should I buy based on the above guidelines and my particular living room?
  • Could we develop a mathematical model to illustrate these guidelines? With, like, variables and stuff?
  • Alternatively, how could I set up my living room in order to fit the kind of TV I purchased?

Suggested Activities

  • Have students develop a model (or “rules” to follow) to express the above recommendation mathematically. (This one’s partially answered below)
  • Students could optimize viewing experience given a floorplan and a TV.
  • A Consumer Reports-ish type TV buying guide? We’re veering here…

Attempted Solution

So the initial model for the constraints listed by CNET aren’t terribly complex.

Constraint 1) “you’d want to sit no closer than 1.5 times the screen’s diagonal measurement”

Constraint 2) “no farther than twice that measurement to the TV”

So lower bound: d>1.5x ; upper bound: d<2x ; and there you have it.

Surely we could ramp up the complexity of the problem with some of the above floorplanning activities and additional cost constraints. How would you modify this situation to serve our mathematical purpose here?

5 comments on “More math food blogging: I may need some help from my Southern friends.”

More math food blogging: I may need some help from my Southern friends.

I think I may have an eating problem. Or just a eating mathematically problem. Here’s my problem today.

Delicious, delicious pigs-in-a-blanket (from pillsbury.com):

Pigs-in-a-blanket, for the uninitiated, are little hot dog/sausage type things warmly embraced by crescent rolls dough. In fact, that’s the ingredient list:

  • Little sausages.
  • A can of crescent rolls dough.

Cooking instructions: Wrap those little buggers up and toss them into an oven until you can’t stand it any longer.

At least, that’s how I’ve always made them. Maybe I could get super-ambitious and make my own dough but that sounds a lot of work for breakfast (side note: yes, this is a breakfast food).

Here’s the problem. How am I supposed to cut this triangular piece of dough to ensure proper sausage coverage?

Like this, this, or this? Or none of the above?

I can’t seem to get congruent triangles out of this thing. So I end up with mismatched pigs-in-blankets. Some have too much dough, some have too little. Many don’t wrap properly.

Awful. Just awful.

Like I said, I can’t get the triangles to come out congruent.

Not only are the triangles not congruent, they’re not similar at all. They’re not even the same type of triangle. So I need advice on a few levels.

How can I cut the initial right triangle dough in order to get:

    • The most congruent-like triangles?
    • The most similar-like triangles?
    • Obtain congruent and similar triangles that make for easy sausage-wrapping?

Here’s what I start with.

I want to end with those perfectly covered pigs-in-blankets above. How to I get from start to finish? Please let me know in the comments or tweet me a picture of the proper triangle-slicing orientation.