Assignment 5: GSP Script Tools

by R. Adam Molnar

Geometer's Sketchpad and Other Tools

This assignment asks us to create a library of script tools for The Geometer's Sketchpad. This does not include all the suggestions, as I did most assignments using GeoGebra, Microsoft Excel, and Graphing Calculator. There are GeoGebra applets included in Assignments 2, 3, 4, 6, 8, and 9, plus Final Part 1. Graphing Calculator files are provided for Assignments 1, 10, and 11. Assignment 12 and Final Part 3 include Excel files, which can be viewed in Google Documents. Only assignments where GSP was mandated - 5, 7, and Final Part 2 - have GSP documents.

Through this class, I preferred free technological tools. GeoGebra and Google Documents are completely free and allow users to not only interact with constructions, but also modify them. Therefore, I worked with them when possible. Graphing Calculator provides a free viewer. While Geometer's Sketchpad does offer Java Sketchpad, enabling free Java constructions, it does not support all features. Most importantly, arcs are not supported, and the semicircle in Final Part 2 is an arc. That's a problem.

Pedagogically, I made the decision to focus on Cartesian geometry. There are several ways to approach the investigations in this class. One way would be to focus on properties in Euclidean geometry. You'll see Euclid in a few assignments, but not many. My major field, statistics, relies on coordinates and algebra, not Euclid's Elements. I went with that.

GSP Tools

All these tools were created for Geometer's Sketchpad Version 5. They have not been tested on earlier versions.

Golden Ratio: Construct a segment with two parts in the golden ratio.
Trisect a Segment: Construct an segment with divisions into three equal parts.
Equilateral Triangle: Construct an equilateral triangle, given a side.
Isoceles Triangle: Construct an isoceles triangle, given a base and altitude, assuming the base is the non-equal side.
Square: Construct a square, given a side.
Pentagon, given a radius: Construct a regular five sided pentagon, given the radius from the center to a vertex.
Pentagon, given a side: Construct a regular five sided pentagon, given a side.
Hexagon, given a side: Construct a regular six sided hexagon, given a side.
Octagon, given a side: Construct a regular eight sided octagon, given a side.

Centroid of a triangle: Centroid G is the intersection of the three medians.
Orthocenter of a triangle: Orthocenter O is the intersection of the three perpendicular lines from vertices.
Circumcenter of a triangle: Circumcenter C is equidistant from the three vertices.
Incenter of a triangle: Incenter I is the point in the interior equidistant from the three sides.
Four Centers of a triangle: Given three points, Centroid G, Orthocenter O, Circumcenter C, and Incenter I, all in one graph.
Four Centers plus Euler Line: The four "centers" Centroid G, Orthocenter O, Circumcenter C, and Incenter I, and the Euler line connecting G, O, and C.

Incircle inside a triangle: The circle centered at the incenter and tangent to all three sides.
Circumcircle around a triangle: The circle centered at the circumcenter, which intersects all three vertices.
Medial Triangle: Triangle with vertices at the intersection of the medians with the sides of a triangle.
Orthic Triangle: Triangle with vertices at the intersection of the vertex perpendiculars with the extended sides of a triangle. See Assignment 8.
Pedal Triangle: Given triangle ABC and separate point P, the triangle formed with vertices at the intersections of perpendiculars drawn from P to the sides of the triangle. See Assignment 9.

Tangent Circles: Given two circles AB and CD, plus a point P on circle AB, construct two circles through P tangent to both circle AB and circle CD. See Assignment 7.
Semicircle around a Square: Given two points that form a side, construct a square and circumscribe a semicircle around that square. See Final Part 2.