Cross Ratio

About: private item


... do not *ANY* 4 points chosen in a continuem form a cross ratio?

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  1. cross ratio

Comments


Eiamyme says
http://www.wolframalpha.com/input/?i=cross-ratio

Mark de LA says
p.2804 OF THE TAI SHU COMMENTARY: (I don't understand why you put the not in your question?)



Mark de LA says
Perhaps P.2652 as well.

Eiamyme says
And if you want to play with it in Cinderella here is their example which you can download & run.


Seth says
seth 2014-11-17 23:21:19 17953

and even this one is a bit more accessible.

Seth says
mark:  conjectured that the fourth point defining some peculiar cross ration was infinity  (sorry i don't have access to verify that now because you made the question private)

seth: do not *ANY* 4 points chosen in a continuem form a cross ratio?

mark: I don't understand why you put the not in your question?

It seemed you were inquiring whether the 4th point of some peculiar cross ratio was infinity.   But the fourth point in a cross ration can be anyplace along the line, it is not given by the choice of the first 3 (is it?) ... or so i thought.   In other words, the fourth point could have been calculated if you had given some actual ratio ... but if you did i missed it ... so the fourth point could have been infinity, but could it not have been any other point as well?

That said, i still don't grock cross ratio ... maybe i need cross ratio for dummies.



Seth says
choy 2014-11-18 07:31:57 17953
seth 2014-11-18 07:17:15 17953
Eiamyme 2014-11-17 23:51:06 17953
And if you want to play with it in Cinderella here is their example which you can download & run.

What app does Cross-ratio.cdy need to run?  The other one ran inside java inside the browser ... but this one just asks what app to open it. 
~
~
  you can download it for free with some restriction on how much you can store in the way of stuff you can construct here.
thanks ... looks like they still have a mac app.

Eiamyme says
http://en.wikipedia.org/wiki/Projective_harmonic_conjugate a cross ratio of -1 is interesting to a lot of GW's work.


Seth says
choy 2014-11-18 08:42:45 17953
seth 2014-11-18 08:00:11 17953
mark:  conjectured that the fourth point defining some peculiar cross ration was infinity  (sorry i don't have access to verify that now because you made the question private)

seth: do not *ANY* 4 points chosen in a continuem form a cross ratio?

mark: I don't understand why you put the not in your question?

It seemed you were inquiring whether the 4th point of some peculiar cross ratio was infinity.   But the fourth point in a cross ration can be anyplace along the line, it is not given by the choice of the first 3 (is it?) ... or so i thought.   In other words, the fourth point could have been calculated if you had given some actual ratio ... but if you did i missed it ... so the fourth point could have been infinity, but could it not have been any other point as well?

That said, i still don't grock cross ratio ... maybe i need cross ratio for dummies.


Yeah ... you are asking fundamental questions which are a real far tangent to my original wallaby about time which I have not specified.  Where you found the thread was just a reminder for me. Cross ratio is constant given some kinds of projections. That is what is fascinating to me.  Normally one takes 4 points on a line & calculates the cross ratio. Otoh, one could choose a ratio given 3 points & try to find where the 4th point is.  This is a really good book if you are interested. I scanned a couple pages in 16592 & the duality thingy was inspired by the beginning of the book. I am slugging my way through it. UCLA left the geometry out of it when G & I took a course in projective geometry - all abstract algebra to avoid problems of infinity I think.
 

thanks, i rather suspected that.    Sometimes to completely grock a question one needs to know why it was asked.   In this case i asked my question above on the if chance that it would provoke you to specify your wallaby about time. 

See Also

  1. Thought [title (19804)] with 4 viewings related by tag "cross-ratio".