<?xml version="1.0" encoding="UTF-8"?>
<Worksheet><Version major="6" minor="0"/><View-Properties><Zoom percentage="100"/></View-Properties><Styles><Layout alignment="left" bullet="none" name="Warning"/><Layout alignment="left" bullet="none" firstindent="0.0" leftmargin="0.0" linebreak="space" name="Normal" rightmargin="0.0" spaceabove="0.0" spacebelow="0.0"/><Layout alignment="centred" bullet="none" name="Maple Plot"/><Layout alignment="centred" bullet="none" linespacing="0.5" name="Maple Output"/><Font background="[0,0,0]" family="Monospaced" foreground="[0,0,255]" name="Warning" opaque="false" readonly="true" size="12"/><Font background="[0,0,0]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" name="Text" opaque="false" size="12" underline="false"/><Font background="[0,0,0]" family="Times New Roman" foreground="[0,0,255]" name="2D Output" opaque="false" readonly="true" size="12"/><Font background="[0,0,0]" bold="true" executable="true" family="Monospaced" foreground="[255,0,0]" name="Maple Input" opaque="false" size="12"/></Styles><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">with(plots);</Text-field></Input><Output><Text-field layout="Warning" style="Warning">Warning, the name changecoords has been redefined
</Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">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</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" style="Text"> <Font size="14">Consider the following quadrilateral.</Font></Text-field><Text-field alignment="centred"><Image height="282" 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layout="Normal" style="Text"/><Text-field layout="Normal" style="Text"><Font size="14">
Let points C=(0,-1/2) and D=(0,1/2) be fixed.  The length of the segments AD and BC are fixed at length 2, and the segment AB is fixed at length 3.  Let P be the midpoint of AB, and let's say B=(a2,b2) and A=(a1,b1).   The system is free to move except for the segment CD remaining fixed, and the lengths of the other segments must stay fixed.</Font></Text-field><Text-field layout="Normal" style="Text"/><Text-field layout="Normal" style="Text"><Font size="14">Now let's move the system in the following way:  We will move the point B around the circle of radius two centered at C in the clockwise direction.  A will be move in such a way to keep the length of the segments fixed as B moves.  Our goal is to find the equation of the curve traced out by P during this motion.  To do this, we will need to first state the equations that describe the system.

First, let's note that A and B can only be located on the circles of length two centered at  D and C, respectively.  Given that B=(a2,b2) and A=(a1,b1), the equations of these circles are</Font></Text-field><Text-field layout="Normal" prompt="&gt; " style="Maple Input">f1:=(a2+1/2)^2+b2^2-4;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSNmMUc2IiwoKiQsJkkjYTJHRiUiIiIjRioiIiNGKkYsRioqJEkjYjJHRiVGLEYqISIlRio=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">f2:=(a1-1/2)^2+b1^2-4;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSNmMkc2IiwoKiQsJkkjYTFHRiUiIiIjISIiIiIjRipGLUYqKiRJI2IxR0YlRi1GKiEiJUYq</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" style="Text"><Font size="14">Next, we know the length of AB is 3, thus using the distance formula between A and B yields the equation</Font></Text-field><Text-field layout="Normal" style="Text"/><Text-field layout="Normal" prompt="&gt; " style="Maple Input">f3:=(a2-a1)^2+(b2-b1)^2-9;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSNmM0c2IiwoKiQsJkkjYTJHRiUiIiJJI2ExR0YlISIiIiIjRioqJCwmSSNiMkdGJUYqSSNiMUdGJUYsRi1GKiEiKkYq</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" style="Text"><Font size="14">Finally, we need equations describing the location of P=(x,y).  Since P is the midpoint of AB, we have that (a2-a1)/2=x-a1 and (b2-b1)/2=y-b1.  These equations give our last two equations</Font></Text-field><Text-field layout="Normal" style="Text"/><Text-field layout="Normal" prompt="&gt; " style="Maple Input">f4:=a2-a1-2*(x-a1);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSNmNEc2IiwoSSNhMkdGJSIiIkkjYTFHRiVGKEkieEdGJSEiIw==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">f5:=b2-b1-2*(y-b1);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSNmNUc2IiwoSSNiMkdGJSIiIkkjYjFHRiVGKEkieUdGJSEiIw==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" style="Text"><Font size="14">In order to find an equation for the curve  traced out by P, we need to eliminate all but the variables x and y in the above five equations.  We can do this using resultants; however, we need to be careful.  The resulting equation will contain the curve we desire, but it also may contain more than what we are looking for.  Thus, once we obtain our equation at the end of the following, we need to interpret which part of it is the curve we are looking for, and what is not.

We will choose to use the following sequence of equations to eliminate variables.</Font></Text-field><Text-field layout="Normal" style="Text"/><Text-field layout="Normal" prompt="&gt; " style="Maple Input">r1:=resultant(f2,f5,b1);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSNyMUc2IiwuKiRJI2ExR0YlIiIjIiIiRighIiIjISM6IiIlRioqJEkjYjJHRiVGKUYqKiZGMEYqSSJ5R0YlRiohIiUqJEYyRilGLg==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">r2:=resultant(r1,f4,a1);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSNyMkc2Iiw0IyEjOiIiJSIiIiokSSNiMkdGJSIiI0YqKiZGLEYqSSJ5R0YlRiohIiUqJEYvRi1GKUkjYTJHRiVGKiokRjJGLUYqKiZGMkYqSSJ4R0YlRipGMEY1ISIjKiRGNUYtRik=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">r3:=resultant(r2,f1,a2);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSNyM0c2IiwyKiRJInhHRiUiIiMhI2sqJkYoRilJI2IyR0YlRikiIzsqJkYsRilJInlHRiVGKUYtKiZGLCIiIkYvIiIkISNLKihGLEYxRi9GMUYoRilGMyokRi8iIiVGLSomRi9GKUYoRikiI0sqJEYoRjZGLQ==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" style="Text"><Font size="14">We now have an equation in the variables b2, x, and y.  To get another such equation, we can do the following:</Font></Text-field><Text-field layout="Normal" style="Text"/><Text-field layout="Normal" prompt="&gt; " style="Maple Input">r4:=resultant(f5,f3,b1);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSNyNEc2IiwwKiRJI2EyR0YlIiIjIiIiKiZJI2ExR0YlRipGKEYqISIjKiRGLEYpRioqJEkjYjJHRiVGKSIiJSEiKkYqKiZGMEYqSSJ5R0YlRiohIikqJEY0RilGMQ==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">r5:=resultant(r4,f4,a1);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSNyNUc2IiwwKiRJI2EyR0YlIiIjIiIlISIqIiIiKiRJI2IyR0YlRilGKiomRi5GLEkieUdGJUYsISIpKiRGMEYpRioqJkYoRixJInhHRiVGLEYxKiRGNEYpRio=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">r6:=resultant(r5,f1,a2);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSNyNkc2IixCKiZJI2IyR0YlIiIiSSJ5R0YlRikhJEciKiRGKiIiIyIjayokSSJ4R0YlRi0hJHciKiZGKEYtRipGLUYuKiZGKEYpRioiIiQhI2sqKEYoRilGKkYpRjBGLUY1KiRGKiIiJSIjOyomRipGLUYwRi0iI0sqJEYwRjhGOUYwISQjPiooRihGKUYqRilGMEYpRjUqJkYqRi1GMEYpRjsqJEYwRjRGOyomRjBGLUYoRi1GLiomRjBGKUYoRi1GLiokRihGLUY5</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" style="Text"><Font size="14">Now, to get rid of the b2 variable, we can calculate</Font></Text-field><Text-field layout="Normal" style="Text"/><Text-field layout="Normal" prompt="&gt; " style="Maple Input">r7:=resultant(r6,r3,b2);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">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</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" style="Text"><Font size="14">So res7 contains our desired curve.  To find our curve, let's factor res7 as follows:</Font></Text-field><Text-field layout="Normal" style="Text"/><Text-field layout="Normal" prompt="&gt; " style="Maple Input">factor(r7);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMsJComLDwqJEkieEc2IiIiIyIiJSokSSJ5R0YoRiohIiQqJEYnIiIkIiIpKiRGJ0YqIiM7KiZGLEYpRiciIiIhI0MqJkYsRilGJ0YpISNeKiZGLEYqRidGKSIjNiomRixGKkYnRjRGKiomRixGKUYnRioiIz4qJkYsRilGJ0YvRjIqJEYnIiInIiIqKiRGJyIiJiIjNyokRixGP0Y0RjQsMkY+RjRGMSEiJUYmRipGO0YvRjYhIihGOEYvRitGLUZERjRGNCImT2In</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" style="Text"><Font size="14">So we obtain the following two irreducible factors of res7:</Font></Text-field><Text-field layout="Normal" style="Text"/><Text-field layout="Normal" prompt="&gt; " style="Maple Input">g1:=4*x^2-3*y^4+8*x^3+16*x^4-24*y^2*x-51*y^2*x^2+11*y^4*x^2+4*y^4*x+19*y^2*x^4+16*y^2*x^3+9*x^6+12*x^5+y^6;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSNnMUc2Iiw8KiRJInhHRiUiIiMiIiUqJEkieUdGJUYqISIkKiRGKCIiJCIiKSokRihGKiIjOyomRixGKUYoIiIiISNDKiZGLEYpRihGKSEjXiomRixGKkYoRikiIzYqJkYsRipGKEY0RioqJkYsRilGKEYqIiM+KiZGLEYpRihGL0YyKiRGKCIiJyIiKiokRigiIiYiIzcqJEYsRj9GNA==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">g2:=x^6-4*x^4+4*x^2+3*y^2*x^4-7*y^2*x^2+3*y^4*x^2-3*y^4+y^6;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSNnMkc2IiwyKiRJInhHRiUiIiciIiIqJEYoIiIlISIlKiRGKCIiI0YsKiZJInlHRiVGL0YoRiwiIiQqJkYxRi9GKEYvISIoKiZGMUYsRihGL0YyKiRGMUYsISIkKiRGMUYpRio=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" style="Text"><Font size="14">We can plot these two curves as follows:</Font></Text-field><Text-field layout="Normal" style="Text"/><Text-field layout="Normal" prompt="&gt; " style="Maple Input">display({implicitplot(g1, x=-2...2, y=-2...2, scaling=constrained, numpoints=70000), implicitplot(g2, x=-2...2, y=-2...2, scaling=constrained, numpoints=70000, color=blue)});</Text-field></Input><Output><Text-field layout="Maple Plot"><Plot height="400" type="two-dimensional" width="400">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