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Contents 1. Compass & Straightedge 2. Triangle: Points & Lines 3. Economical Constructions 4. 3D Workshop 5. Wire Puzzles 6. Quadratic Functions 7. Conics and Other Curves 8. Linkages 
Conics and Other Remarkable CurvesIn this part of our collection we present models of several wellknown curves and their constructions. Conics are the curves obtained by cutting a cone with a plane. Depending on the position of the plane such a curve can be an ellipse, a hyperbola, or a parabola. Alternatively, these curves can be defined in terms of the distances from a point on a curve to two fixed points or, for parabola, to a point and a line. It is the latter definition that we use in the constructions of these curves. Also, we explore the behavior of light rays after reflection in a conicshaped mirror. Another kind of curve we consider is a cardioid. This curve is formed by light rays reflected in a circle or in a totally different way, by rolling one circle around another one. Ellipse
ActivityConstruct an ellipse given its two foci and a segment equal to the sum of distances to them from any of its points. Take a point on the given segment. Draw two circles centered at the foci whose radii are equal to the two parts into which this point divides the segment. Construct the intersection points of the circles and the locus of each of these two points. Together, the two curves thus obtained form an ellipse. Optical Property of an Ellipse
Hyperbola
ActivityConstruct a hyperbola given its two foci and a segment equal to the difference of distances to them from any of its points. Take a point P on the extension of the given segment beyond any of its endpoints. Draw two circles centered at the foci whose radii are equal to the distances from P to the endpoints. Construct the intersection points of the circles and the locus of each of these two points. Each of these loci will consist of two branches, halves of the branches of the hyperbola. Together they form the entire curve. Optical Property of HyperbolaA ray of light issued from a hyperbola's focus reflects off the hyperbola as if it was issued from the other focus.
Parabola
ActivityConstruct a parabola given its focus and directrix. To construct a parabola, take a point P on the directrix, draw the line perpendicular to the directrix at P and the perpendicular bisector to FP (where F is the focus). Then the desired parabola is the locus of the intersection point of the two perpendiculars. Optical Property of Parabola
Cardioid
ActivityConstruct the cardioid as the locus of a point on a circle that rolls without slipping around a fixed circle of the same radius. Cardioid as a Caustic Curve

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