Hello, reader! If you intend to post a link to this blog on Twitter, be aware that for utterly mysterious reasons, Twitter thinks this blog is spam, and will prevent you from linking to it. Here's a workaround: change the .com in the address to .ca. I call it the "Maple Leaf Loophole." And thanks for sharing!

Saturday, June 2, 2012

Criticism + Ennui

I have been going through my far-flung poorly-organized digital files and attempting to bring some order to the chaos (it's basically hopeless but was prompted by Project "scan all the paper so you don't have to move it to Argentina.") And for SOME reason I saved a pdf of a Mathematics Teacher article based on the problem below. Evidently I thought it was worth saving in July of 2008. Now I don't know which it makes me want to do more: scream, hide, or sigh really loud. It makes me sad for my profession. We are never going to figure this out. He wants to keep his lines of sight perpendicular? Excuse me? What? We can't do any better than that?

1. Maybe you could rethink this as "the guy" (e.g. Neo, Bourne, Ethan Hunt or whoever...) seeking a escape route, pointing with two guns at two bad guys at the same time. We don't have many choices, I think. That's kind of awful.

2. I'm not sure that constant perpendicular implies semi-circle is a compelling or great thing to explore anyway? But if we decided it was, we'd just have to do better than this.

3. Hmm, how about wanting to broadcast (or listen) to two land-based stations, but the broadcast array/receiver has a 90-degree limit? Then, because the signal strength decreases with distance, you desire to keep the angle at 90-degrees rather than move further away?

(probably too much background for the problem, but maybe it will help someone else figure out the right set-up)

4. Here's another interpretation. If a square picture frame is resting on two nails, what are the possible positions for the bottom corner? I made a GeoGebra applet that demonstrates this.

5. Commenters, are we staying on point here? I'm not at all sure Kate's looking for a better "constant perpendicular" task. I think she just wants to state that, despite the (alleged) fact that "this problem conforms to the recommendations of the NCTM," it stinks.

Hi! I will have to approve this before it shows up. Cuz yo those spammers are crafty like ice is cold.