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TrappedTime

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If you like/understand geometry click here

I was wondering...
Can you have 4 othogonal lines?
Then I was thinking...

Yes you can.

Think up a transparent cube. Now connect each corner with it's opposite corner to form lines. You get... 4 lines! Now, using some statements about how diagonals in squares are perpendicular, you can use that multiple times to prove all lines are perpendicular.

I don't know how to draw a diagram, so my real request is for someone to find me a picture of this :/ please...

Pike270

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Re: If you like/understand geometry click here

EDIT: ^Fail lol That is what happens when you try to do math after 12:00 midnight.

REVISED VERSION:

I hope that helps

EDIT: Personally I think this whole thing was worded wrong.

EDIT: This diagram should end all dispute in this thread.^

First of all see here:

http://www.dca.fee.unicamp.br/projects/ … gonal.html

Pick two of the planes are perpendicular. Ignore the third. Place those two planes into a square (in your mind) so that each "corner" of a plane touches one corner of the cube. While it is true that the planes are perpendicular, the line segments conecting each corner are not.

As Twipply said we live in a third dimensional universe. The 3 orthogonal lines would be the x, y and z axes. I don't know where the fourth would be.

P.S. Just wondering TrappedTime. where did you find out that you can have four orthogonal lines in a transparent cube that is made when each corner is connected to its opposite using four lines.

P.S.S. Twipply: I am just student. No REAL qualifications in mathematics .

P.S.S.S Interactive Cube: http://www.thumbleaf.com/journal/?p=79

Last edited by Pike270 (Aug 6 2011 6:36:09 pm)

Twipply

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Re: If you like/understand geometry click here

Pike270, do you have any qualifications in mathematics?   'Cus I have a feeling some of those angles you labeled as 90 degrees are not so.   EBCH and FBDH are not squares.

32OrtonEdge32dh

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From: DMV

Joined: 2015-02-15

Posts: 5,166

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Re: If you like/understand geometry click here

That's what I'd call a fail.

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Twipply

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Re: If you like/understand geometry click here

That's what I'd call a fail.

Uh huh.   I suspect the correct answer is actually no.   We do live in a 3D universe, after all.

Kuech

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Re: If you like/understand geometry click here

That is clearly a computer generated model. and anything with the universal symbol for 90º (the square) means that it is 90º (even if it doesn't look like it.) and because it is a cube, the diagonals, when they intersect. are 90º.

Twipply

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Re: If you like/understand geometry click here

That is clearly a computer generated model. and anything with the universal symbol for 90º (the square) means that it is 90º (even if it doesn't look like it.) and because it is a cube, the diagonals, when they intersect. are 90º.

Lol.

I think the angle between EC and HB is more like 70 degrees, rather than 90.

Oturan

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Re: If you like/understand geometry click here

I wish I could join to discuss this, but since it's math in english I will just fail...

32OrtonEdge32dh

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From: DMV

Joined: 2015-02-15

Posts: 5,166

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Re: If you like/understand geometry click here

That is clearly a computer generated model. and anything with the universal symbol for 90º (the square) means that it is 90º (even if it doesn't look like it.)

So if I take a piece of paper that says Wendy's and put it on the door to McDonald's, it becomes a Wendy's?   It has the universal symbol for Wendy's on it (the logo).   No, I don't think so.   Lawyered.

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Pike270

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Re: If you like/understand geometry click here

Second post updated.

treejoe4

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Re: If you like/understand geometry click here

I dont get this in the slightest

cheezpuffs

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Re: If you like/understand geometry click here

me:

thats confusing, im even a HIGH math level and i DONT get that! 1xd1

Last edited by cheezpuffs (Aug 5 2011 2:30:20 pm)

Twipply

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Re: If you like/understand geometry click here

thats confusing, im even a HIGH math level and i DONT get that! 1xd1

Look up the definitions for the long words and it becomes easy enough I think.

EDIT: ^Fail lol

It was a nice effort.
If we want proof that the lines aren't orthogonal, we can apply the dot product to two of them.
  a = EC = (1,1,1)
  b = HB = (-1,1,1)
  a.b = 1*-1 + 1*1 + 1*1 = 1
  |a| = sqrt(3)
  |b| = sqrt(3)

from
  a.b = |a||b|cos(angle)
we get
  angle = arccos( a.b/(|a||b|) ) = arccos(1/3) = 70.5 degrees, not 90 as required

Last edited by Twipply (Aug 5 2011 2:49:50 pm)

TrappedTime

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Re: If you like/understand geometry click here

Whoa calm down I don't know that advanced crap yet. I could decode it using familiar terms, but not all as one piece.

----

I cam across thinking about having 4 perpendicular lines quite some time ago really. It was like an emaculate conception.
Although we do live in 3 dimensions, we can still have 4 orthogonal directions. They're similar, I'll admit, but they go in different directions.
(Although on two squares...)

But my main point is that if you have enough squares within the cube you can prove that all 4 line segments are in fact perpendicular to one another.

----

So pike, are you saying there can't be 4 orthogonal lines? I didn't quite get your main message.
The cubes and stuff were fine, though.

EDIT: Thanks for the pics!!

Last edited by TrappedTime (Aug 6 2011 7:43:04 am)

musuki

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Re: If you like/understand geometry click here

But my main point is that if you have enough squares within the cube you can prove that all 4 line segments are in fact perpendicular to one another.

What do you mean?

TrappedTime

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Re: If you like/understand geometry click here

In squares, all diagonals are perpendicular.
So if you have 4 slanted squares(Or more if needed) within the cube, you've proven all line segements to be perpendicular.

Last edited by TrappedTime (Aug 6 2011 8:09:42 am)

Kuech

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Re: If you like/understand geometry click here

That is clearly a computer generated model. and anything with the universal symbol for 90º (the square) means that it is 90º (even if it doesn't look like it.)

So if I take a piece of paper that says Wendy's and put it on the door to McDonald's, it becomes a Wendy's?   It has the universal symbol for Wendy's on it (the logo).   No, I don't think so.   Lawyered.

Hm, how old are you again?

anyway, I was in an IB Math Class, and my teacher did a lesson on angles. He said: "Whenever you see an angle with a square, it means it is 90º. Even if it doesn't look like it." (This is a rough outline of what he said)

Again, this is Geometry, not Fast Food Chains. So what you just said had nothing to do with what I said. :/

TrappedTime

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Re: If you like/understand geometry click here

Yes but using the laws of sulligism or however you spell it, any statement can be proven to be true.

musuki

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Re: If you like/understand geometry click here

In squares, all diagonals are perpendicular.
So if you have 4 slanted squares(Or more if needed) within the cube, you've proven all line segements to be perpendicular.

I still don't know what you mean. If you imagine 3 (mutually orthogonal) coordinate axes, where does the fourth one go?

Yes but using the laws of sulligism or however you spell it, any statement can be proven to be true.

'Syllogism'? you've lost me here anyway

TrappedTime

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Re: If you like/understand geometry click here

Yeah syllogism. Either that or the other one that states trues properties for transitive effects.

a= michael has $30
b= toy costs $30
c= michael can buy toy

a=b=c
if michael has $30 then he can buy the ctoy

Twipply

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Re: If you like/understand geometry click here

3 orthogonal lines is maximum.   Twipply has spoken.

TrappedTime

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Re: If you like/understand geometry click here

Incorrect, I have proven there can be 4. 4 is maximum, no more.
You're not thinking straight.

EDIT: We really need someone to make a model and post a vid on youtube.

Last edited by TrappedTime (Aug 6 2011 8:49:48 am)

Twipply

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Re: If you like/understand geometry click here

Incorrect, I have proven there can be 4. 4 is maximum, no more.
You're not thinking straight.

Feel free to give us a diagram of your 4 orthogonal lines so I can have many lulz.

TrappedTime

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Re: If you like/understand geometry click here

Umm... the stuff above me, duh.
How do you think we got to discuss this stuff? the diagrams above.

Go take a look and come back crying, LOL.
(jk)

Twipply

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Re: If you like/understand geometry click here

Umm... the stuff above me, duh.
How do you think we got to discuss this stuff? the diagrams above.

Go take a look and come back crying, LOL.
(jk)

Didn't I already show that the lines in the above diagrams weren't orthogonal?   I hope you read my post with all the numbers in it.

anyway, I was in an IB Math Class, and my teacher did a lesson on angles. He said: "Whenever you see an angle with a square, it means it is 90º. Even if it doesn't look like it." (This is a rough outline of what he said)

That was likely because the diagrams in tests are known to be correct, otherwise the question would be flawed and misleading.   The diagrams above are not so correct.

Last edited by Twipply (Aug 6 2011 8:57:31 am)