[MWForum]Calling mathcats: geometry help please
Jeff Knope
mwforum@lists.mathcats.com
Wed, 11 Aug 2004 21:46:53 -0700
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Hi Daniel,
I haven't yet tried your first code offering. I'll tell you what I find =
(or need).
As for this, "The problem is this:
>=20
> How do you represent the line that goes through [0 0] [0 1]?
>=20
> or any vertical line for that matter?" ....
It seems to me there must be a prior test for (x1 - x2) =3D 0, since =
this calls for "division by 0" to determine slope ~ a guaranteed error. =
So these special cases (where one coordinate of the intersection is =
already known) should be dispatched with, and the procedure closed, =
before any mischief can happen.
A second problem is to find a not-too-cumbersome way to
> termine when lines do intersect, but the line segments
> between x1 and x2, and x3 and x4 do not. For example:
>=20
> [[[1 1] [5 5]]
> [[3 1] [6 5]]]
For my own purposes, I don't care if the intersection is inside or =
outside the segments. If it's the "shared point" ~ that's all I care =
about.
----- Original Message -----=20
From: "Daniel Ajoy" <dajoy@openworldlearning.org>
To: <mwforum@lists.mathcats.com>
Sent: Wednesday, August 11, 2004 8:23 PM
Subject: Re: [MWForum]Calling mathcats: geometry help please
> On 11 Aug 2004 at 17:41, Jeff Knope wrote:
>=20
> > Googling around, there appear to be a few ways to go about it. The =
most simple and direct of them
> > appears to be the algebraic solution of 2 simultaneous equations. =
Trouble is, as I examine my own
> > (weak) processes for doing that, I find I'm doing lots of visual =
scanning for opportunities to
> > algebraically reduce the expressions. It's a kind of intuitive =
process I haven't the faintest idea
> > how to reduce MW procedures.
> >=20
>=20
> There is a big problem with approaching intersections of lines
> with 2 simultaneous equations ala:
>=20
> y1 =3D a x1 + b (line 1)
>=20
> y2 =3D c x2 + d (line 2)
>=20
> (and still, textbooks don't have any admonition)
>=20
> The problem is this:
>=20
> How do you represent the line that goes through [0 0] [0 1]?
>=20
> or any vertical line for that matter?
>=20
> A second problem is to find a not-too-cumbersome way to
> termine when lines do intersect, but the line segments
> between x1 and x2, and x3 and x4 do not. For example:
>=20
> [[[1 1] [5 5]]
> [[3 1] [6 5]]]
>=20
>=20
> Daniel
> OpenWorld Learning (OWL)
> http://mia.openworldlearning.org
>=20
>=20
> _______________________________________________
> MWForum mailing list
> MWForum@lists.mathcats.com
> http://lists.mathcats.com/mailman/listinfo/mwforum
> Attachments archived at:
> http://www.mathcats.com/mwforum/attachments.html
> To unsubscribe or for administrative questions contact=20
> mailto:mwforum-admin@lists.mathcats.com
>=20
>
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<DIV><FONT face=3DArial color=3D#800000 size=3D2>Hi Daniel,</FONT></DIV>
<DIV><FONT face=3DArial color=3D#800000 size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial color=3D#800000 size=3D2>I haven't yet tried =
your first code=20
offering. I'll tell you what I find (or need).</FONT></DIV>
<DIV><FONT face=3DArial color=3D#800000 size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial color=3D#800000 size=3D2>As for this, "<FONT =
color=3D#000000>The=20
problem is this:<BR>> <BR>> How do you represent the line that =
goes=20
through [0 0] [0 1]?<BR>> <BR>> or any vertical line for that =
matter?"=20
....</FONT></FONT></DIV>
<DIV><FONT face=3DArial color=3D#800000 size=3D2><FONT=20
color=3D#000000></FONT></FONT> </DIV>
<DIV><FONT face=3DArial color=3D#800000 size=3D2>It seems to me there =
must be a prior=20
test for <STRONG>(x1 - x2) =3D 0</STRONG>, since this calls for =
"division by 0" to=20
determine slope ~ a guaranteed error. So these special cases (where one=20
coordinate of the intersection is already known) should be dispatched =
with, and=20
the procedure closed, before any mischief can happen.</FONT></DIV>
<DIV><FONT face=3DArial color=3D#800000 size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial color=3D#800000 size=3D2><FONT color=3D#000000>A =
second problem=20
is to find a not-too-cumbersome way to<BR>> termine when lines do =
intersect,=20
but the line segments<BR>> between x1 and x2, and x3 and x4 do not. =
For=20
example:<BR>> <BR>> [[[1 1] [5 5]]<BR>> [[3 1] [6=20
5]]]</FONT><BR></FONT></DIV>
<DIV><FONT face=3DArial color=3D#800000 size=3D2>For my own purposes, I =
don't care if=20
the intersection is inside or outside the segments. If it's the "shared =
point" ~=20
that's all I care about.</DIV>
<DIV><FONT color=3D#000000></FONT><BR></DIV></FONT>
<DIV><FONT face=3DArial size=3D2>----- Original Message ----- </FONT>
<DIV><FONT face=3DArial size=3D2>From: "Daniel Ajoy" <</FONT><A=20
href=3D"mailto:dajoy@openworldlearning.org"><FONT face=3DArial=20
size=3D2>dajoy@openworldlearning.org</FONT></A><FONT face=3DArial=20
size=3D2>></FONT></DIV>
<DIV><FONT face=3DArial size=3D2>To: <</FONT><A=20
href=3D"mailto:mwforum@lists.mathcats.com"><FONT face=3DArial=20
size=3D2>mwforum@lists.mathcats.com</FONT></A><FONT face=3DArial=20
size=3D2>></FONT></DIV>
<DIV><FONT face=3DArial size=3D2>Sent: Wednesday, August 11, 2004 8:23=20
PM</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>Subject: Re: [MWForum]Calling mathcats: =
geometry=20
help please</FONT></DIV></DIV>
<DIV><FONT face=3DArial><BR><FONT size=3D2></FONT></FONT></DIV><FONT =
face=3DArial=20
size=3D2>> On 11 Aug 2004 at 17:41, Jeff Knope wrote:<BR>> =
<BR>> >=20
Googling around, there appear to be a few ways to go about it. The most =
simple=20
and direct of them<BR>> > appears to be the algebraic solution of =
2=20
simultaneous equations. Trouble is, as I examine my own<BR>> > =
(weak)=20
processes for doing that, I find I'm doing lots of visual scanning for=20
opportunities to<BR>> > algebraically reduce the expressions. It's =
a kind=20
of intuitive process I haven't the faintest idea<BR>> > how to =
reduce MW=20
procedures.<BR>> > <BR>> <BR>> There is a big problem with=20
approaching intersections of lines<BR>> with 2 simultaneous equations =
ala:<BR>> <BR>> y1 =3D a x1 + b (line 1)<BR>> =
<BR>>=20
y2 =3D c x2 + d (line 2)<BR>> <BR>> (and still, =
textbooks=20
don't have any admonition)<BR>> <BR>> The problem is this:<BR>> =
<BR>> How do you represent the line that goes through [0 0] [0 =
1]?<BR>>=20
<BR>> or any vertical line for that matter?<BR>> <BR>> A second =
problem=20
is to find a not-too-cumbersome way to<BR>> termine when lines do =
intersect,=20
but the line segments<BR>> between x1 and x2, and x3 and x4 do not. =
For=20
example:<BR>> <BR>> [[[1 1] [5 5]]<BR>> [[3 1] [6 =
5]]]<BR>>=20
<BR>> <BR>> Daniel<BR>> OpenWorld Learning (OWL)<BR>> =
</FONT><A=20
href=3D"http://mia.openworldlearning.org"><FONT face=3DArial=20
size=3D2>http://mia.openworldlearning.org</FONT></A><BR><FONT =
face=3DArial=20
size=3D2>> <BR>> <BR>>=20
_______________________________________________<BR>> MWForum mailing=20
list<BR>> </FONT><A href=3D"mailto:MWForum@lists.mathcats.com"><FONT =
face=3DArial=20
size=3D2>MWForum@lists.mathcats.com</FONT></A><BR><FONT face=3DArial =
size=3D2>>=20
</FONT><A =
href=3D"http://lists.mathcats.com/mailman/listinfo/mwforum"><FONT=20
face=3DArial=20
size=3D2>http://lists.mathcats.com/mailman/listinfo/mwforum</FONT></A><BR=
><FONT=20
face=3DArial size=3D2>> Attachments archived at:<BR>> </FONT><A=20
href=3D"http://www.mathcats.com/mwforum/attachments.html"><FONT =
face=3DArial=20
size=3D2>http://www.mathcats.com/mwforum/attachments.html</FONT></A><BR><=
FONT=20
face=3DArial size=3D2>> To unsubscribe or for administrative =
questions contact=20
<BR>> </FONT><A =
href=3D"mailto:mwforum-admin@lists.mathcats.com"><FONT=20
face=3DArial =
size=3D2>mailto:mwforum-admin@lists.mathcats.com</FONT></A><BR><FONT=20
face=3DArial size=3D2>> <BR>> </FONT></BODY></HTML>
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