Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

Topic: What does one call vector geometry without a coordinate system?
Replies: 32   Last Post: Sep 9, 2013 4:45 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
fom

Posts: 1,968
Registered: 12/4/12
Re: What does one call vector geometry without a coordinate system?
Posted: Aug 31, 2013 10:46 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 8/30/2013 9:25 PM, William Elliot wrote:
> On Sat, 31 Aug 2013, Sam Sung wrote:
>> On Fri, 30 Aug 2013 16:30:23 -0700 (PDT), lite.on.beta@gmail.com wrote:
>>

>>> I remember in grade school (grade 8 or 9ish) we did geometry with vectors as a tool but without any coordinate system.
>>>
>>> We often picked a random point and called it O, then proved things like if
>>> M was midpoint between two points A, B, then:
>>>
>>> OM = 1/2 * (OA + OB)
>>>
>>> A lot of stuff was proven with just points and vectors from points to
>>> other points (with the fact OX = -XO used heavily).
>>>
>>> What's the name of this geometry? I'm thinking of looking this stuff up
>>> again.

>>
>> They called it be topology...
>>

> That's wrong. It's a vector space.
>


In the kind of geometric situation described here
it is more than a vector space.

Vectors in this situation are equivalence classes
of directed line segments (magnitude and direction).
The original poster is discussing specific, labeled
directed line segments.

It would be called a Euclidean point space. The
point difference (the additional algebraic structure)
then becomes a ground for a distance function.

I posted the definition on Aug 21 2013 in the thread
"What is the modern setting for Euclidean Geometry"

Fred Jeffries found an online version of the text
from which I obtained the definition here:

<quote>

Professor Bowen has made this book available for download from
his web page:
http://www1.mengr.tamu.edu/rbowen/

Unfortunately, the download links do not appear to be working
(for me) but these do work:

http://ohkawa.cc.it-hiroshima.ac.jp/AoPS.pdf/MathTextBook/Introduction%20to%20Vectors%20and%20Tensors%20Vol%201%20%28Bowen%20314%29.pdf

http://ohkawa.cc.it-hiroshima.ac.jp/AoPS.pdf/MathTextBook/Introduction%20to%20Vectors%20and%20Tensors%20Vol%202%20%28Bowen%20246%29.pdf

The definition of Euclidean point space is from the first
chapter of volume 2.

<endquote>



Date Subject Author
8/30/13
Read What does one call vector geometry without a coordinate system?
lite.on.beta@gmail.com
8/30/13
Read Re: What does one call vector geometry without a coordinate system?
Tanu R.
8/30/13
Read Re: What does one call vector geometry without a coordinate system?
William Elliot
8/30/13
Read Re: What does one call vector geometry without a coordinate system?
Brian Q. Hutchings
8/31/13
Read Re: What does one call vector geometry without a coordinate system?
fom
8/31/13
Read Re: What does one call vector geometry without a coordinate system?
FredJeffries@gmail.com
8/31/13
Read Re: What does one call vector geometry without a coordinate system?
fom
9/1/13
Read Re: What does one call vector geometry without a coordinate system?
lite.on.beta@gmail.com
9/1/13
Read Re: What does one call vector geometry without a coordinate system?
Peter Percival
9/1/13
Read Re: What does one call vector geometry without a coordinate system?
Brian Q. Hutchings
9/3/13
Read Re: What does one call vector geometry without a coordinate system?
FredJeffries@gmail.com
9/1/13
Read Re: What does one call vector geometry without a coordinate system?
FredJeffries@gmail.com
9/2/13
Read Re: What does one call vector geometry without a coordinate system?
FredJeffries@gmail.com
9/2/13
Read Re: What does one call vector geometry without a coordinate system?
fom
9/1/13
Read Re: What does one call vector geometry without a coordinate system?
Shmuel (Seymour J.) Metz
9/1/13
Read Re: What does one call vector geometry without a coordinate system?
fom
9/2/13
Read Re: What does one call vector geometry without a coordinate system?
Shmuel (Seymour J.) Metz
9/2/13
Read Re: What does one call vector geometry without a coordinate system?
fom
9/3/13
Read Re: What does one call vector geometry without a coordinate system?
Shmuel (Seymour J.) Metz
9/3/13
Read Re: What does one call vector geometry without a coordinate system?
fom
9/4/13
Read Re: What does one call vector geometry without a coordinate system?
Shmuel (Seymour J.) Metz
9/4/13
Read Re: What does one call vector geometry without a coordinate system?
fom
9/4/13
Read Re: What does one call vector geometry without a coordinate system?
Brian Q. Hutchings
9/1/13
Read Re: What does one call vector geometry without a coordinate system?
Shmuel (Seymour J.) Metz
9/1/13
Read Re: What does one call vector geometry without a coordinate system?
Shmuel (Seymour J.) Metz
8/30/13
Read Re: What does one call vector geometry without a coordinate system?
FredJeffries@gmail.com
9/1/13
Read Re: What does one call vector geometry without a coordinate system?
JT
9/1/13
Read Re: What does one call vector geometry without a coordinate system?
Ken.Pledger@vuw.ac.nz
9/2/13
Read Re: What does one call vector geometry without a coordinate system?
lite.on.beta@gmail.com
9/2/13
Read Re: What does one call vector geometry without a coordinate system?
Ken.Pledger@vuw.ac.nz
9/3/13
Read Re: What does one call vector geometry without a coordinate system?
lite.on.beta@gmail.com
9/9/13
Read Re: What does one call vector geometry without a coordinate system?
FredJeffries@gmail.com
9/2/13
Read Re: What does one call vector geometry without a coordinate system?
Narasimham

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.