View Full Version : Is it possible?
OUDoc
10/13/2006, 10:47 AM
To have a "triangle with only 90 degree angles"? My nurse's daughter had this as an extra credit question. I don't know if that's the full question, or if it is worded exactly that way. I was told only 3 people have gotten it right in 22 years, for what that's worth.
mdklatt
10/13/2006, 10:51 AM
To have a "triangle with only 90 degree angles"? My nurse's daughter had this as an extra credit question. I don't know if that's the full question, or if it is worded exactly that way. I was told only 3 people have gotten it right in 22 years, for what that's worth.
What grade is this for?
SoonerInKCMO
10/13/2006, 10:52 AM
The angles of all triangles add to 180 degrees. 3 * 90 != 180.
mdklatt
10/13/2006, 10:53 AM
The angles of all triangles add to 180 degrees.
Only in Cartesian space. :texan:
OUDoc
10/13/2006, 10:54 AM
What grade is this for?
I think she's a soph or junior in HS.
And 3*90 is 270. Correct? ;)
if the triangle is on the surface of a sphere, absolutely.
mdklatt
10/13/2006, 10:56 AM
I think she's a soph or junior in HS.
If only 3 people have gotten the right answer, then the obvious answer (no) is obviously incorrect. And the reason it's incorrect is that the angles of a spherical triangle do not have to sum to 180 degrees (or pi radians, if you prefer). But that's not something you'd expect somebody in a HS geometry class to know.
Was this a yes/no question? Because the smart money would be to assume it was a trick question and choose the "wrong" answer.
Mjcpr
10/13/2006, 10:59 AM
What grade is this for?
Hopefully an A!!
sooner_born_1960
10/13/2006, 11:05 AM
If you use something like google sketchUp to draw three lines; one vertical, one horizontal, and one for depth, then rotate the image, the 2 dimensional view is of a triangle.
SoonerInKCMO
10/13/2006, 11:17 AM
Only in Cartesian space. :texan:
You dorks and your fancy curved surfaces. ;)
Petro-Sooner
10/13/2006, 11:20 AM
I love these brain teasers.
I_SMELL_FEAR
10/13/2006, 11:27 AM
I think she's a soph or junior in HS.
And 3*90 is 270. Correct? ;)
not if you put ! before the =
The angles of all triangles add to 180 degrees. 3 * 90 != 180.
C&CDean
10/13/2006, 11:28 AM
You're the ****ing doctor. You figure it out.
OUDoc
10/13/2006, 11:30 AM
not if you put ! before the =
I think it's obvious my math skills have deteriorated since Calc III in 1988. :O
I used to be good at math. :(
BeetDigger
10/13/2006, 11:35 AM
I think it's obvious my math skills have deteriorated since Calc III in 1988. :O
I used to be good at meth. :(
:eek:
OUDoc
10/13/2006, 11:38 AM
You're the ****ing doctor. You figure it out.
One prostate exam for Dean, hold the lube...
OUDoc
10/13/2006, 11:43 AM
If you use something like google sketchUp to draw three lines; one vertical, one horizontal, and one for depth, then rotate the image, the 2 dimensional view is of a triangle.
I thought about the 3-D thing, but is it really a triangle if the last side doesn't meet (at least in 3-D space)?
sooner_born_1960
10/13/2006, 11:56 AM
I thought about the 3-D thing, but is it really a triangle if the last side doesn't meet (at least in 3-D space)?
It would depend on how the question was worded. As you admited you weren't sure of the actual wording, I offed one way of "viewing" a triange without drawing a triangle.
BeetDigger
10/13/2006, 11:58 AM
You're the ****ing doctor. You finger it out.
Post reported.
colleyvillesooner
10/13/2006, 12:02 PM
http://www.horrordvds.com/reviews/misc/pictures/nerds.jpg
GottaHavePride
10/13/2006, 03:14 PM
I thought about the 3-D thing, but is it really a triangle if the last side doesn't meet (at least in 3-D space)?
Think about a globe. Put one corner of the triangle at the north pole and make that a 90-degree angle. The two sides curve down the globe and both will intersect the equator at a 90-degree angle. Make the equator the third side. You now have a triangle with three 90-degree angles. The only catch is you're no longer on a Cartesian plane, you're on a spherical surface.
Petro-Sooner
10/13/2006, 03:22 PM
Cool.
Vaevictis
10/13/2006, 03:45 PM
So basically, the answer is "Yes", if you're willing to relax the requirement that a triangle's line segments be straight.
(ie, if you're willing to change the definition of a triangle, then sure, you can have a triangle with the sum of angles be anything you want.)
mdklatt
10/13/2006, 03:54 PM
So basically, the answer is "Yes", if you're willing to relax the requirement that a triangle's line segments be straight.
Define "straight".
Petro-Sooner
10/13/2006, 03:58 PM
Can it be only straight if its linear in 2-D?
GottaHavePride
10/13/2006, 04:03 PM
I didn't redefine "straight", I redefined the surface on which I put the triangle. ;)
Vaevictis
10/13/2006, 04:04 PM
Define "straight".
Zero curvature is what I want to say, although I'm not sure that that is strictly correct.
Petro-Sooner
10/13/2006, 04:08 PM
bingo. It can be linear in 2-D but have a curve into or out of the z direction.
skycat
10/13/2006, 04:09 PM
The key to it being a triangle is that it is a two dimensional object with three sides. The surface of a ball is just as two dimensional as the surface of a square box. There's nothing wrong with GHP's definition. It's just not what we normally think of.
GottaHavePride
10/13/2006, 04:14 PM
Heh. Plus, I'm used to these kinds of questions. Too damn many math classes for me. I gave up on the math degree when I realized I could no longer visualize abstract n-dimensional sets being transformed through r-dimensional space. At that point it was time for me to hang up the TI-92, take the music degree and run.
Vaevictis
10/13/2006, 04:18 PM
Well, the definition of triangle I always worked on required that the lines be straight. Triangles like what you're talking to were referred to as "non-planar triangles", which are what you get when you take the triangle definition and relax the straight line requirement ;)
GottaHavePride
10/13/2006, 04:22 PM
OK, so our answer for Doc is that unless the question specifically says "can you have a triangle with three 90-degree angles in Cartesian space" the answer is yes. ;)
Well, the definition of triangle I always worked on required that the lines be straight. Triangles like what you're talking to were referred to as "non-planar triangles", which are what you get when you take the triangle definition and relax the straight line requirement ;)
actually, it's not relaxing the straight line requirement. It's just a different definition of a plane.
If a straight line is defined as the shortest path between 2 points, then if your space is confined to be on the surface of a sphere, the straight line requirement still holds.
Another way of putting this is: what does a plane look like in a curved space?
OUinFLA
10/13/2006, 05:03 PM
Another way of putting this is: what does a plane look like in a curved space?
Here's one from 1TC's back yard.
http://www.shopnbu.com/classic-pedal-planes-retro-ride-on-toys/red-baron-pedal-plane-classic-ride-on-toy.jpg
Stoop Dawg
10/13/2006, 05:18 PM
So the answer is: It depends.
TUSooner
10/13/2006, 06:45 PM
So the answer is: It depends.
Go directly to law school.
:P
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