![]() Triangle T, point A, 0, 0, point B, 3, −1, point C, 6, 2 : Theorem : The nine-point circle of a triangle is tangent to the incircle and to each of the excircles of the triangle. ( Reference: A Survey of Geometry by Howard Eves) The following two sections demonstrate how the geometry package illustrates two theorems in Euclidean geometry. n, printtext = false, scaling = constrained, axes = none, title = Nephroid The Nephroid can be constructed by using the draw function.ĭraw seq c ‖ i, i = 1. Generates 60 points on the circle, and for each point Ai, construct a circle with center Ai that touches the line l.įor i to n do randpoint A ∥ i, c0 circle c ∥ i, A ∥ i, distance A ∥ i, l end do : ![]() n, printtext = false, scaling = constrained, axes = none, title = Limacon without an inner loop The limacon without an inner loop looks like the following:ĭraw seq c ‖ i, i = 0. n, printtext = false, scaling = constrained, axes = none, title = Limacon de monsieur PascalĬircle c0, point o, 0, 0, 2 : While i ≤ n do randpoint A ∥ i, c0 if evalf HorizontalCoord A0 − HorizontalCoord A ∥ i ≠ 0 then circle c ∥ i, A0, A ∥ i i ≔ i + 1 end if end do :ĭraw seq c ‖ i, i = 0. Generate 50 circles that envelop the constructed limacon. Two Limacon examples are provided in this section. n, printtext = false, scaling = constrained, axes = none, title = CardioidĬonstructing a Limacon de monsieur Pascal I ≔ 1 : n ≔ 50 : while i ≤ n do randpoint A ∥ i, c0 if evalf HorizontalCoord A0 − HorizontalCoord A ∥ i ≠ 0 then circle c ∥ i, A0, A ∥ i i ≔ i + 1 end if end do :ĭraw seq c ‖ i, i = 0. Generate 50 circles that envelop the constructed cardioid. ![]() Generate a random point A0 on the circle, which is the cusp of the cardioid. ( Reference: Geometry And The Liberal Arts by Dan Pedoe)Ĭircle c0, point o, 0, 0, 1 : The following sections show how to use the geometry package to construct some curves based on the method called an envelope of circles. You may want to close any other memory-intensive applications before working through this worksheet. ![]() Warning: This worksheet is computationally intensive. This worksheet demonstrates some aspects of the geometry package. ![]()
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