Ellipses

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We’ll examine a specific case. Let’s assume our triangle has vertices on the axes and on the line X+Y=10. We assume that two of the sides pass throu...
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To create a triangle with constant perimeter k, we set one leg equal to a, and then solve for the other side length. The envelop is a circle.
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It is important in this example to constrain the distance of the line from the points directly, rather than creating perpendiculars and constraining t...
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Salmon states that the radius of curvature of any conic is equal to the cube of the normal divided by the semi-parameter. We create this quantity in ...
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We generate the evolute, as the envelope of the normals. Point at parametric location t on the evolute is the center of curvature of the point at par...
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If we drop a perpendicular from the normal to the focal radius, then drop a perpendicular back onto the normal this is the center of curvature.
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We dilate an ellipse by factor k about its center. We observe that the segments of a chord of the outer ellipse cut off by the inner ellipse are equa...
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If we examine the two tangents to an inner conic which pass through a point on the outer conic, we see that each makes the same angle with the outer c...
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