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 > 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 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
- Follow-Ups:
- Re: Re: A New Scientist article verified with Mathematica
- From: DrMajorBob <btreat1@austin.rr.com>
- Re: Re: A New Scientist article verified with Mathematica