## A Conversation for Curved Space and the Fate of the Universe

### dimensional problem

Marjin, After a long time of procrastination back lurking Started conversation Nov 26, 2004

I see a problem with the fifth postulate as stated here.

The first four seem to be independent of the number of dimensions we are talking about. The fifth, as it is stated here, requires a two dimensional space.

This is easily shown by starting with two meeting lines and a connecting line in two dimensions. Now 'disconnect' the meetingpoint and raise one of the lines a bit in the third dimension. The angles will stay practically the same, but the lines now cross without meeting each other.

### dimensional problem

Gnomon - time to move on Posted Nov 26, 2004

Euclid probably did state it in terms of 2 dimensions. I'll have to look it up to see. I'd say the ambiguity lies in my paraphrasing of it.

### dimensional problem

Gnomon - time to move on Posted Nov 26, 2004

No, it was implicit in Euclid's definition that he was talking about lines that were all in the one plane. So as you say, it was two dimensions only.

### dimensional problem

flyingtwinkle Posted Nov 28, 2004

meeting point of two lines is two dimensional and on raising one of the lines is on the third dimension

### dimensional problem

Marjin, After a long time of procrastination back lurking Posted Nov 28, 2004

Flyingtwinkle, I deliberately moved it to the third dimension to show the problem in the way the postulate is stated.

I wonder if there is a way to formulate this postulate so it also will be independent of the number of dimensions. I can think of a few that need terms like 'distance' or 'right angle', but I am not sure you can derive these from the first four postulates.

### dimensional problem

flyingtwinkle Posted Nov 29, 2004

hi archangel nice to know we agree on some points like the third dimension a straight line is also an angle of 180 degrees so it is also two dimensional

a straight line is also an angle of 360 degrees so it is also three dimensional

a staight line if split lengthwise become two parrallel lines

### dimensional problem

Doug_the_Cat_Lover Posted Oct 23, 2005

Just so you know, two lines that are not on the same plane are

called "skew" lines; they do not intersect AND they aren't parralel.

### dimensional problem

Doug_the_Cat_Lover Posted Oct 23, 2005

On a similiar not, the two lines perpindicular to another line

with a weird parralel relationship can exist; however, the two lines are skew, not parralel.

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### dimensional problem

- 1: Marjin, After a long time of procrastination back lurking (Nov 26, 2004)
- 2: Gnomon - time to move on (Nov 26, 2004)
- 3: Gnomon - time to move on (Nov 26, 2004)
- 4: flyingtwinkle (Nov 28, 2004)
- 5: Marjin, After a long time of procrastination back lurking (Nov 28, 2004)
- 6: flyingtwinkle (Nov 29, 2004)
- 7: Doug_the_Cat_Lover (Oct 23, 2005)
- 8: Doug_the_Cat_Lover (Oct 23, 2005)
- 9: Doug_the_Cat_Lover (Oct 23, 2005)

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