Re: A New Scientist article verified with Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg107271] Re: A New Scientist article verified with Mathematica
• From: sigismond kmiecik <sigismond.kmiecik at wanadoo.fr>
• Date: Sun, 7 Feb 2010 06:14:31 -0500 (EST)
• References: <hkj907\$dt7\$1@smc.vnet.net>

```sigismond kmiecik a =E9crit :
> Hello to everybody
>
> In  the last Xmas issue of the New Scientist magazine there is on page
> 40 a small article about the continuity principle applied to
> intersecting circles.
> I used Mathematica to confirm its conclusions but some questions remain
>
> These circles are represented by
>
> Show[{Graphics[{Red, Circle[{0, 0}, 2]}], Graphics[Circle[{2, 0}, 2]],
>     Graphics[{Red, Dashed, Circle[{5, 0}, 2]}]}, AxesOrigin -> {0, 0},
>   PlotRange -> {{-3, 8}, {-3, 3}}, Axes -> True ]
>
> The intersection coordinates of the red (non-dashed) and black circle is
> found by:
>
> Solve [{ x^2 + y^2 - 4 == 0, (x - 2)^2 + y^2  - 4  == 0 }, {x, y}
> ]
>
> And there is indeed an imaginary intersection of the red and red-dashed
> circle even if they are not touching -  as found by:
>
> Solve [{ x^2 + y^2 - 4 == 0, (x - 5)^2 + y^2  - 4  == 0 }, {x, y}
> ]
>
> My questions are:
> - Is there a way to draw  with Mathematica these three circles using
> their cartesian equations and not the Circle graphics primitive
92 ?
> - How can I transform the list of rules solutions to the last equation
> above  in order to represent them on the complex plane  (I thought about
> a ListPlot [{Re[],Im[]}=85  but I know not  enough of Mathematica to
> obtain that)
> - And last is there a Mathematica notebook on the web dealing with the
> intersection of  planes with cones?
>
> Thanks
>
> Sigismond Kmiecik
>
Hi
THe two Solve expressions that I copied/pasted from a Mathematica
notebook to Thunderbird
became corrupted after being  added to the forum. What precautions must
I take in order to
avoid that ?
Thanks
Sigismond Kmiecik

```

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