Ask Experts Questions for FREE Help !
Ask
    nykkyo's Avatar
    nykkyo Posts: 132, Reputation: 1
    Junior Member
     
    #1

    Jul 20, 2011, 09:47 PM
    How is a line perpendicular to a space?
    In rectagular coordintes, all dimension lines are mutually perpendicular.
    In 1D - a line is perpendiular to a point.
    In 2D - a line is perpendicular to a line.
    In 3D - a line is perpendicular to a plane. Each point on the 3D line, belongs to a plane.
    It follows that in nD, a line is perpendicular to an (n-1)D space. Again, each point on the nD line belongs to an (n-1)D space.
    Aside from the above question: How do an infinite number of dimensionless points make a line with length? That is like, adding an infinite numer of zeroes and their sum is not zero. So, does the mean sub-spaces are also dimensionless.
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
    Expert
     
    #2

    Jul 21, 2011, 05:50 AM

    To be ,more specific:

    In 2D there is a line that is perpendicular to any point on any line.

    In 3D there is a line that is perpendicular to any point on any plane. Each point on any 3D line belongs to one perpendicular plane.

    It follows that in nD there is a line that is perpendicular to any point in any (n-1)D space. Each point on the nD line belongs to one perpendicular (n-1)D space.

    As to how an infinite number of zero dimension points can ad up to have physical length - recall that the concept of a point is purely an abstract mathematical concept. It's impossible to "count" the number of infinitely small points along a line, no matter how short that line is. Similarly a line has dimension only in one direction, and is infinitely small in the perpendicular direction. Again, a purely mathemetacal concept. It follows that in nD space a line, or plane, or cube or... up through (n-1)D space has 0 dimension in the perpendicular direction in nD space.
    nykkyo's Avatar
    nykkyo Posts: 132, Reputation: 1
    Junior Member
     
    #3

    Jul 21, 2011, 05:38 PM
    Comment on ebaines's post
    If the _nD line is \bot \ to every point in _(_n_-_1_)D spcem then an arbitrary point in space (3D) that is equadistant from each axial plane, lines normal to the axial planes (3) , form a cube. In 6D, there are _6C_2= 15 axial planes. Normals to the planes form a parallelapilepiped. If the point is equadistant from all planes, it is a 6D cube. The Tetrahedon is a projection onto a plane, \bot \ to the ray to the point, and rotated so the cube shows a cube within a cube.

Not your question? Ask your question View similar questions

 

Question Tools Search this Question
Search this Question:

Advanced Search

Add your answer here.


Check out some similar questions!

We had a sewer line break into our cement crawl space, how do we get rid of the smell [ 2 Answers ]

A pipe under our house broke and sewage was draining into our cement crawl space. We had a plumber come in and fix the pipe and they also cleaned up the mess, but the smell is unbearable. Our furnace is down there, although it was not damaged by the leak, every time it turns on the whole house...

Are the lines parallel, perpendicular, or neither? [ 2 Answers ]

5x + 4y = 7 4x - 5y = 5 I think the lines are neither. Just want to double check. Thanks, Cooper

Word appears to have line break when putting in space [ 1 Answers ]

If we try to put in a space while typing, it appears to put in a line/paragraph breaks and goes to the next line. Tried to check formatting but did not see what could be causing this.

Tying 2" drain pipe to perpendicular 3" drain line under slap [ 3 Answers ]

I want to avoid a 90 degree bend under slab. However, I have to reduce from the 2" pipe that drains the WM to the 3" main drain line, and the reducing tee I find has a very small sweep. Do I need to use a reducing combination wye and is there such thing?


View more questions Search