Combinatorics

April 25, 2007 10:53 PM

In square prism ABCD-A₁B₁C₁D₁, AB=AD=2, DC=2v3, AA₁=v3, AD ? AC, AC ? BD, and foot of perpendicular is E,
(i) Prove BD ? A₁C:
(ii) Determine the angle between the two planes A₁BD and BC₁D:
(iii) Determine the angle formed by the lines AD and BC₁ which are in different planes.

Math enthusiasts are being challenged to answer a sample question from Chinese university entrance tests.
posted by four panels (27 comments total)

double
posted by griphus at 10:55 PM on April 25, 2007

see also
posted by bhnyc at 10:58 PM on April 25, 2007

The sample lionk really should have linked to the question. You know, to the sample question.
posted by !Jim at 11:02 PM on April 25, 2007

Combinatorics? Are you.. joking? I mean, did you just pull a random mathematical category out of mid-air?
posted by TypographicalError at 11:05 PM on April 25, 2007

Exactly. Combinatorics. Jeez. Any idiot could see that.
posted by Ironmouth at 11:06 PM on April 25, 2007

This thread is useless without pictures.
posted by tracert at 11:21 PM on April 25, 2007

I went to art school to avoid math. So I'm quite happy that this thread will soon go away and stop taunting my mental weaknesses.
posted by miss lynnster at 11:22 PM on April 25, 2007

OH, it's in CHINESE, no wonder it's Greek to me!
posted by davy at 11:23 PM on April 25, 2007

That is, I'm with miss lynnster here. Please make it stop!
posted by davy at 11:24 PM on April 25, 2007

Math is hard. Let's go shopping!
posted by Opposite George at 11:36 PM on April 25, 2007

Let's go Mets?
posted by Opposite George at 11:36 PM on April 25, 2007

We're doomed.
posted by Dizzy at 11:50 PM on April 25, 2007

Me fail English Math? That's unpossible!
posted by papakwanz at 11:50 PM on April 25, 2007

Head. Hurting. Math. Evil. Please. Stop. Brain. Smoking.
posted by miss lynnster at 11:51 PM on April 25, 2007

I'll get right on solving this as soon as someone tells me what the hell a "foot of perpendicular" is. Or is this evidence that our high school mathematics is so backwards that we don't even know what this means?
posted by chrominance at 12:25 AM on April 26, 2007

Since this thread is shortly due for deletion, let me just say that I think you guys are a bunch of dicks, especially jessamyn, who looks like a very nice young Republican lady.

But, seriously. Keep this one and delete the other because I came off like a raging ignoramus in that one... or keep this one because it has an actual maths question in it.

;-)
posted by chuckdarwin at 12:33 AM on April 26, 2007

Thinking about a third dimension imposed on the Pythagorean Theorem, I'm gonna guess that the length of a space diagonal is the cube root of the sum of the cubes of the lengths of the three sides -- am I right?
posted by pax digita at 2:23 AM on April 26, 2007

Good idea, pax. Never heard that suggestion before but it makes sense.
Should try it -- measure out a few lengths in space and see if it works out on a few scales. (my math isn't good enough to know if you're right without resorting to parlour tricks aka the physical world)
posted by dreamsign at 2:35 AM on April 26, 2007

Pax digita, no.

It's the square root of the sum of the squares on all three sides - see here.
posted by plep at 2:36 AM on April 26, 2007

Oh, silly me -- it's merely another right-triangle hypotenuse, innit? This is why I like to look at math but I was a history major.
posted by pax digita at 2:39 AM on April 26, 2007

Yeah, exactly... you can generalise to any number of dimensions though.
posted by plep at 2:41 AM on April 26, 2007

Chrominance: "I'll get right on solving this as soon as someone tells me what the hell a "foot of perpendicular" is."

I suspect that might be indicating that you should use E as the origin of the coordinate system. Maybe. Whatever it means, you can get the answers they want with the rest of the information.

I think it's a slightly unfair article from the BBC. The "our students are dumb" question is described as a "diagnostic" test. In the first year of my (British) university (physics) course we did a "diagnostic" test to establish what maths we actually new. It started out with long division, and ended up with multivariable calculus, via all sorts of trigonometry. At the end of the year we all had to pass a fairly evil exam with much nastier questions than that Chinese geometry malarkey.
posted by Luddite at 3:08 AM on April 26, 2007

I have discovered a truly marvellous proof, which this <MATH> element </MATH> is too small to contain.
posted by Iosephus at 4:34 AM on April 26, 2007 [2 favorites]

I'll get right on solving this as soon as someone tells me what the hell a "foot of perpendicular" is

If you have a line L and a line M perpendicular to L, the foot of the perpendicular M is the point of intersection between M and L.
posted by leahwrenn at 5:04 AM on April 26, 2007

Um, trick question, innit?

If AD ⊥ AC, then the ABCD must look like this:

A----D
|    |
C----B

BUT AD=AB. This is impossible, unless we're not dealing with a rectangle. (AB must be > AD).

Or somehow I've labeled the spots wrong. But I can't see how I have. If we try

A----D
|    |
B----C

Now AB and AD can be the same length, but it is impossible for AD to be perpendicular to AC.

...unless I'm missing something.
posted by Deathalicious at 5:52 AM on April 26, 2007

Deathalicious..in your first diagram, keep the horizontal segments horizontal, and tilt the vertical ones 45 degrees.
posted by growli at 5:59 AM on April 26, 2007

This is impossible, unless we're not dealing with a rectangle.

We're not.
posted by signal at 6:04 AM on April 26, 2007