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Topic: Random Triangle Problem
Replies: 57   Last Post: Aug 17, 1997 10:51 PM

 Messages: [ Previous | Next ]
 Bill Taylor Posts: 1,909 Registered: 12/8/04
Re: Random Triangle Problem
Posted: Aug 1, 1997 12:38 AM

tony richards <tony.richards@rl.ac.uk> writes:

>I am not a newbie.

Oh? Betcha were once!

>I have shown all my working,

And a wearisome sight much of it was.

> ...including correcting my errors.

Not all, alas. You missed the vital one.

>I have read most contributions, all with respect.

So have I, but in some cases it didn't last long.

>I have not insulted, sneered or abused anyone in this post

A saint, truly. (Mind you, some have a lot to be humble about.)

It wasn't intended to. It had other objectives.

> it may show that others understand your argument better

It may also show I get tired of treating fools kindly.

>...than you do yourself.

Many others understand things better than me. Thank heavens! Others,
sadly, only to clearly fail to understand the most basic things.
I'm exceptionally glad of the former, and their presence on sci.math;
and take every opportunity to learn from them. Not all folk do this.

>I will finish by including my final comments,

If they are truly final, it would indeed be a blessing to us all.

>An early reply stated, without proof, that the result obtained for
>three randomly chosen points 'must be' equivalent to
>triangles formed by three randomly chosen LINES.

Not me. I never used the phrase. As a refresher, here are some
relevant things I said...

>>>
Any answers to open-ended problems of this type are bound to be somewhat
subjective, or a matter of taste.
... ...
Most folk would consider a triangle formed by "3 randomly chosen points"
to be the same as one formed by "3 randomly chosen lines",
... ...
This last observation leads me to suggest that this is a "complete"
solution to the problem, and disputes of taste and subjectivity
essentially decided.
... ...
This may be considered not QUITE the original problem, in that the
re-wording has subtly altered the flavor. My view is that it IS
the same problem, and that it is a complete solution.
<<<

No doubt your extraordinary insight will find a "must be" in there.

>I do however accept that three randomly chosen LINES will give an
>obtuse triangle 75 percent of the time.

Damn decent of you!

>The reason I believe that the two processes for generating random
>triangles are not equivalent is as follows.

An excellent essay, but a disastrous conclusion.

>Given two randomly chosen points, you have defined TWO VERTECES
>but only ONE LINE, whose direction can be regarded as randomly
>selected in direction space.

Utter nonsense. You've chosen two points, and no lines. Alternatively,
you've chosen three - your one and two others perpendicular and through
the points. No wait... four - also the mid-line parallel to these.
No wait... there's another two... Oh hell, why stop at one line?

>However, as soon as the third POINT (or VERTEX) is selected,

No-one (except you) ever referred to 1st 2nd or 3rd points. This is
your big error, which many have pointed out, and which clearly you have
no intention of ever admitting. Your thought processes on this are not
so much mathematical, as magical. Give it up, and learn something.
There is nothing in the problem that refers to, or in any way suggests,
that there is, or should be, a first, second or third point chosen.
Even if there were, it is doubtful your ideas would have any cogency,
but there isn't. The problem referred to "3 random points".
Nothing is "first", except your obstinacy.

>My argument is and remains

...a prime example of how not to conduct oneself in public.

>Tony Richards 'I think, therefore I am confused'

Agreed!

>but I don't slag people off unless sorely provoked.

You have provoked us all. I chose to respond appropriately, for once.

> Proving that my reasoning is unsound

...is hardly necessary in this case.

-------------------------------------------------------------------------------
Bill Taylor W.Taylor@math.canterbury.ac.nz
-------------------------------------------------------------------------------
The Curse Of The Net: not that the same questions come up again and again, but
==================== that the same useless answers get posted again and again.
-------------------------------------------------------------------------------

Date Subject Author
7/16/97 Mike Housky
7/21/97 Bill Taylor
7/22/97 tony richards
7/24/97 Brian M. Scott
7/23/97 tony richards
7/23/97 T. Sheridan
7/24/97 Bill Taylor
7/24/97 Bill Taylor
7/25/97 Ilias Kastanas
7/23/97 Robert Hill
7/23/97 tony richards
7/27/97 Bill Taylor
7/24/97 Robert Hill
7/28/97 tony richards
7/30/97 Bill Taylor
7/30/97 tony richards
8/1/97 Bill Taylor
7/24/97 Robert Hill
7/24/97 Robert Hill
7/24/97 Robert Hill
7/25/97 Robert Hill
7/30/97 Bill Taylor
8/1/97 Charles H. Giffen
8/1/97 John Rickard
8/1/97 Chris Thompson
8/1/97 John Rickard
8/4/97 Bill Taylor
8/5/97 John Rickard
7/25/97 Charles H. Giffen
7/25/97 Charles H. Giffen
7/28/97 Hauke Reddmann
7/28/97 Robert Hill
7/28/97 Robert Hill
7/28/97 Robert Hill
7/29/97 tony richards
7/30/97 Keith Ramsay
7/30/97 tony richards
8/2/97 Keith Ramsay
7/29/97 tony richards
8/4/97 Bill Taylor
8/5/97 Charles H. Giffen
8/6/97 Terry Moore
8/7/97 Terry Moore
8/16/97 Kevin Brown
8/17/97 Kevin Brown
7/30/97 Robert Hill
7/31/97 tony richards
8/6/97 Terry Moore
7/31/97 John Rickard
7/30/97 Robert Hill
7/31/97 Robert Hill
7/31/97 Robert Hill
8/1/97 R J Morris
8/4/97 Robert Hill
8/4/97 Robert Hill
8/5/97 Charles H. Giffen
8/6/97 Robert Hill