 Ellipses

Page: 1 | 2 | 3 | 4 | 5 | 6 | 7 | View All 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... 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. It is important in this example to constrain the distance of the line from the points directly, rather than creating perpendiculars and constraining t... 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 ... 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... 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. 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... 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... Content copyright 2019 Saltire Software. All Geometric Content created by Geometry Expressions.