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A New Scientist article verified with Mathematica

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  • Subject: [mg107238] A New Scientist article verified with Mathematica
  • From: sigismond kmiecik <sigismond.kmiecik at>
  • Date: Sat, 6 Feb 2010 03:25:10 -0500 (EST)

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
to be answered.

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 =91primitive=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?


Sigismond Kmiecik

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