Is it possible?

[OUDoc]

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]

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]

The angles of all triangles add to 180 degrees. 3 * 90 != 180.

[mdklatt]

The angles of all triangles add to 180 degrees.

Only in Cartesian space. :texan:

[OUDoc]

What grade is this for?
I think she's a soph or junior in HS.

And 3*90 is 270. Correct? ;)

[Ike]

if the triangle is on the surface of a sphere, absolutely.

[mdklatt]

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]

What grade is this for?

Hopefully an A!!

[sooner_born_1960]

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]

Only in Cartesian space. :texan:

You dorks and your fancy curved surfaces. ;)

[Petro-Sooner]

I love these brain teasers.

[I_SMELL_FEAR]

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]

You're the ****ing doctor. You figure it out.

[OUDoc]

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]

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]

You're the ****ing doctor. You figure it out.
One prostate exam for Dean, hold the lube...

[OUDoc]

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]

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]

You're the ****ing doctor. You finger it out.



Post reported.

[colleyvillesooner]

http://www.horrordvds.com/reviews/misc/pictures/nerds.jpg

[GottaHavePride]

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]

Cool.

[Vaevictis]

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]

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]

Can it be only straight if its linear in 2-D?

[GottaHavePride]

I didn't redefine "straight", I redefined the surface on which I put the triangle. ;)

[Vaevictis]

Define "straight".

Zero curvature is what I want to say, although I'm not sure that that is strictly correct.

[Petro-Sooner]

bingo. It can be linear in 2-D but have a curve into or out of the z direction.

[skycat]

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]

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]

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]

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. ;)

[Ike]

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]

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]

So the answer is: It depends.

[TUSooner]

So the answer is: It depends.
Go directly to law school.

:P