Note from TK: again, if you need the link that sparked all this discussion, it's http://www.robot.se/w2/fundera.gifFrom Ken:
OK, here's the puzzle... The large shape is not a triangle. It's close, but not quite. Notice that the ratio of height to width of the red triangle is not the same as the teal triangle. Here's how the area works out:
A 13x5 triangle would have area of (13*5)/2, or 32.5
The area of the red triangle is (8*3)/2, or 12
The area of the orange piece is 7
The area of the green piece is 8
The area of the teal triangle is (5*2)/2, or 5
The sum of the areas of the pieces is 32. The top figure shows a quasi-triange with a concave upper edge, while the bottom figure shows a quasi-triangle with a convex upper edge. Add the .5 of a square delta in for each, and there's your missing square.
Well, awhile ago I said that Felicity reminded me of 90210 in the 4th year or so (once it got bad), but without the few good years to give it a little credibility. I'm glad to agree with TK that it's been better lately and I like it because it's actually pretty good, not just because I'm drawn to it like a bus crash. (ahem)From Mimi:
But I have to say, the first thought I had after Todd "no, everyone else but Felicity likes the stalker" Mulcahy lost to the laws of physics was "Wow, they don't usually show the impact of the vehicle." But my second thought was that this little gambit was eerily reminiscent of the Josh Richland death on 90210 a few years ago. You remember Josh -- the annoying intrusive reporter for the California University Condor who gets Brandon to run for Student Body VP with him, and then after getting elected gets plowed over by a truck while driving away from the peach pit. I guess it was the automotive fatality that initially sparked the comparison, but it had the same ring of annoying-person-who-will-later-be-thought-of-in-a-nice-way that I remember from that time on 90210. I don't know if this is a good or bad thing, but I'm just hoping they handle this well. We'll see tomorrow night, I guess.
The whole big figure is not really a triangle, the hypotenuse is not a straight line.From Daphne:
This can be seen from calculating the individual areas of the pieces and then the area of the big perceived triangle...
area of triangle = .5 * base * heightI think it's easier to see, that moving the pieces around can get you some extra area. In the top figure, the hypotenuse is concave but it's hard to see that we're missing .5 area. however, in the bottom figure where the whole figure's area is 33, it's easier to notice that the hypotenuse is convex.
green triangle = .5 * 5 * 2 = 5
red triangle = .5 * 8 * 3 = 12
orange shape = 7
green shape = 8
------------------------
whole figure = 32
percieved tri = .5 * 5 * 13 = 32.5
Hope that helps.
Am I the only person who's noticed that Ally is white and Greg is not? Are they ever going to address that, or are they just going to break up so that Ally can get all worked up over yet another very very bad idea??? Does she ever read Dear Abby? Married men never leave their wives!From Ben:
The problem is that the two triangles (the 3x8 and the 2x5) are not similar (i.e., not the same shape), and so the whole top image is not really a triangle at all, but some funky quadralateral. In more yucky technical terms, arctan(3/8)=20.6 degrees, but arctan(2/5)=21.8 degrees. So if you drew the diagram honestly, you'd have this very elongated triangle missing from the middle--and it's area is exactly one. So now you can tell Cristobel or whoever was confused.
Pretty cool problem, though. Took me a while to figure it out.