Title: Making Script Tools for gsp.
Problem Statement: In order to do investigations in gsp it is often a good idea to make a script of tools that are used often. These tools will be more efficient and save time in later gsp investigations.
Problem Setup: I am going to provide my reader with instructions on how to make a script tool in gsp and then I will provide several script tools that I think will be useful to them in the future.
Investigation/Exploration of the Problem:
To make a script tool in gsp one must complete the following steps:
1.) Select everything that is on the gsp sketch
2.) Go to Create New tool, this is under the last arrow on the toolbox.
3.) Name the new tool.
4.) This allows the new tool to be used with only this particular gsp sketch if one wishes to have it as a permanent tool of gsp in one's home computer, one must save it in the hard drive in the Application Folder under tools.
Click HERE to view a gsp file with all the script tools below displayed on it. Individual tools for each script are listed and described below. Each new script tool is in bold print so you can see it. The steps for the construction follow the bold print.
centroid of a triangle
1.) First, begin by constructing three points.
2.) Then connect those three points by constructing segments, one has now obtained a triangle.
3.) Construct the midpoints of these three segments.
4.) Then, construct the three medians of a triangle, the segment from the vertex to the midpoint of the opposite side.
5.) Construct the intersection of two of these medians.
6.) Where medians intersect is the centroid.
I constructed two centroid tools. The first one shows the median and the tool is named Centroid. The second hides the median and is named centroid with a lower case c.
Click HERE to view the centroid script tool.
orthocenter of a triangle
1.) First, begin by constructing a triangle, as done for the construction of the centroid.
2.) Construct the three altitudes of the triangle. The altitudes of a triangle are the perpendicular segments from the vertex to the line of the opposite side.
3.) Construct the intersection of two of the altitudes.
4.) Hide the perpendicular lines and you have the orthocenter.
Click HERE to view the orthocenter script tool.
circumcenter of a triangle
1.) Construct a triangle
2.) Construct midpoints of the segments
3.) Construct perpendicular bisectors of the triangle, which are the lines perpendicular to the sides of a triangle through the midpoints of the side. Construct this by first selecting the midpoint and the side of the triangle and then scrolling over to construct perpendicular lines.
4.) Construct the intersection of 2 of the perpendicular bisectors.
5.) Hide the perpendicular bisectors and you have obtained the circumcenter.
Click HERE to view the circumcenter script tool.
circumcircle of a triangle
1.) Use your script tool to construct the circumcenter of the triangle.
2.) Construct a circle with the circumcenter as the center and the vertex as another point on the triangle.
Click HERE to view the circumcircle script tool.
Incenter of a circle
1.) Construct a triangle.
2.) Construct the three angle bisectors of the angles of the triangle.
3.) Construct the intersection of two of the angle bisectors. This is the incenter of the circle.
Click HERE to view the incenter script tool.
Incircle of the triangle
1.) Use your script tool to construct the incenter of a triangle.
2.) Use the incenter of a triangle as the center of the circle, construct the perpendiculars from the incenter of the triangle to the sides of the triangle.
3.) Construct the intersection of the sides of the triangle and the perpendiculars from the incenter.
4.) Construct a circle by center and point, using the incenter as the center and the intersection of one of the perpendiculars as the point.
Click HERE to view the incircle script tool.
Medial Triangle
1.) Construct a triangle
2.) Construct the midpoints of the three segments of a triangle.
3.) Construct the three segments that join the midpoints. These is the medial triangle and has the same centroid as the big triangle.
Click HERE to view the medial triangle script tool.
Orthic Triangle
1.) Construct a triangle
2.) Construct Perpendicular lines through the vertices of the triangle and the opposite sides.
3.) Construct the Intersection of the feet of the perpendicular lines and the sides of the triangle.
4.) Construct the segments that connect the three intersections.
5.) Hide the perpendicular lines.
6.) This is the orthic triangle
Click HERE to view the orthic triangle script tool.
Euhler Line
This is the line that contains the circumcenter, the centroid, and the orthocenter of a triangle.
1.) Construct a triangle
2.) Construct the orthocenter (H), the centroid (G), and the circumcenter (C) of a triangle. You can use your script tools for these constructions.
3.) Construct the line segment that connects these 3 centers. This is the Euhler Line of the triangle.
Click HERE to view the Euhler line script tool.
four centers of the triangle
1.) Construct a triangle
2.) Construct the orthocenter (H), centroid (G), circumcenter (C), and incenter of the triangle. You may use the script tools in order to do this or you may go through the construction of each one.
Click HERE to view the script tool for the four centers of a triangle.
Golden Ratio
1.) Construct a segment.
2.) Construct the midpoint of this segment.
3.) Construct the segment from the midpoint to one of the endpoints on the circle.
4.) Construct the circle by center and radius. Chose the center of the triangle to be one of the endpoints of the segment and the radius to be the distance from the midpoint of the circle to the endpoint.
5.) Then construct the Perpendicular line that goes through the endpoint.
6.) Construct the intersection of the circle and the perpendicular line.
7.) Construct the segment from intersection point on circle to opposite endpoint.
8.) Construct circle with center as the intersection of the perpendicular line and the triange and radius as the distance from the midpoint to one of the endpoints.
9.) Construct the intersection of the hypotenuse and the circle whose center is the intersection of the first circle and the perpendicular line.
10.) Construct a circle with the endpoint as the center and the distance from the center to your newly constructed intersection on the hypotenuse as the radius.
11.) Construct the intersection of the circle and your original segment, this marks off the Golden Ratio.
12.) Hide everything used for construction purposes.
Click HERE to view the Script Tool for the Golden Ratio.
midsegment triangle using the orthocenter
1.) Construct the triangle
2.) Construct the orthocenter (this may done using your script tool)
3.) Construct segments from orthocenter to the vertices of the triangle.
4.) Construct the midpoints of these segments.
5.) Construct segments connecting the three midpoints of the segments.
6.) Hide the segments from the orthocenters to the vertices. What results is the midsegment triangle which is constructed using the orthocenter.
Click HERE to view the Script tool for the orthocenter, midsegment triangle.
center of the circumcircle
1.) Construct a triangle
2.) Construct the medial triangle inside the triangle. This may be done using the script tool.
3.) Construct the circumcenter of the medial triangle, this may again be done using a script tool.
4.) The circumcenter of the medial triangle is the center of the 9 point circle.
Click HERE to view the Script tool for the center of the 9 point circle.
nine point circle
1.) Construct a triangle and the center of a nine point circle, this may be done using the script tool.
2.) Construct the orthocenter of the triangle (this may also be done using the script tool)
3.) Construct the segments from the orthocenter of the triangle to the corresponding vertices.
4.) Construct the midpoints of these segments and then hide the segments.
5.) Construct the altitudes of the triangle. Mark the intersection of the feet of the altitudes and the side of the triangles and then hide the altitudes.
6.) Construct the midpoints of the three sides of the triangle.
7.) Construct the circle whose center is the circumcenter of the medial triangle and has the midpoint of one of the triangle's segments on the circle. This is the ninepoint circle.
Click HERE to view the Script tool for the 9 point circle.
pentagon given the radius
1.) Find the golden ratio of the given radius (you may do this using the script tool).
2.) Construct a circle with center as endpoint of the radius, and radius length from endpoint to Golden Ratio point.
3.) Construct another circle with with the same radius and center as golden ratio point.
4.) Construct the intersection of the two circles.
5.) Construct segments from the intersection of the circles to the two endpoints of the given radius.
6.) Reflect the two sides of the newly formed triangle about the given radius.
7.) Connect the endpoint of the newly reflected triangle and the original opposite endpoint of radius.
8.) Reflect the triangle about the center fou times.
9.) Hide radii in the center, this is your pentagon.
This explanation may be a little confusing, so you can see the steps in the following script tool by undoing and redoing steps under the edit menu.
Click HERE to see the script tool for the construction of a pentagon given its radius.
pedal triangle
1.) Construct a triangle using lines.
2.) Put an arbitrary pt. anywhere in plane.
3.) Construct perpendicular lines from the pedal point to the sides of the triangle.
4.) Construct the intersections of the perpendicular lines and the sides of the triangle.
5.) Constrcut the segments that connect the three intersections of the triangle.
6.) Hide the perpendicular lines. The resulting triangle is the pedal triangle.
Click HERE to see the script tool for the construction of the pedal triangle.
square given the length of a side
1.) Using one of the endpoints of the given side of the square as the endpoint of the circle and the distance from the two endpoints as the radius of the circle, construct a circle by center and radius.
2.) Construct a perpendicular line through the endpoint of the circle.
3.) Construct the intersection of the circle and the endpoint.
4.) Construct a line through the point of intersection that is parallel to the given side of the square.
5.) Construct a circle with center as the intersection of the circle and perpendicular line and radius as the length of the given side of the square.
6.) Construct the intersection of the circle and the parallel line.
7.) Construct the segment from the intersection to the endpoint of the given side of the square.
8.) Hide all circles and lines that were used for construction. This is a square constructed from a given side.
Click HERE to see the script tool for the construction of a square given a side.
equilateral triangle given a side
1.) Construct a circle using one endpoint of the given side as the center of the circle and the distance between the segments as the radius of the circle.
2.) Using the other endpoint construct a second circle with the same radius.
3.) Construct the intersection of the two circles.
4.) Construct the segments connecting the endpoints of the given side to the intersections of the triangle. This is your equilateral triangle.
Click HERE to view the script tool for the construction of an equilateral triangle given a side.
Trisecting a line segment
1.) Construct your given line segment, segment AB.
2.) Construct a line perpendicular to segment AB through A.
3.) Construct another line perpendicular to segment AB through B.
4.) Construct an arbitrary point on the perpendicular line through pt. A
5.) Construct the segment between the arbitrary point and point A.
6.) Construct a circle centered at point B with radius equal to the newly constructed segment.
7.) Construct the intersection of the perpendicular line through point B and the circle.
8.) Construct circle with center as the intersection and the same radius as before.
9.) Construct the intersection of the perpendicular line through pt. B and this newly constructed circle.
10.) Construct a circle centered at new intersection with the same radius.
11.) Construct the segment from the third intersection and the arbitrary point selected on line j.
12.) Construct the intersection of segment AB and newly constructed segment.
13.) Construct the segment between A and the intersection.
14.) Construct the segment between the intersection and B.
15.) Take the midpoint of the segment between the intersection and B.
16.) Construct the segment between the intersection and the midpoint.
17.) Construct the segment between the midpoint and pt. B. This should trisect your line segment.
Click HERE to view a gsp sketch of the construction of a trisected line segment.
regular hexagon
There are a lot of steps to this construction. You can view these steps under show script view after choosing the hexagon tool on the following GSP sketch:
Click HERE to view a gsp sketch of the construction of a regular hexagon.
isosceles triangle given the base and the altitude of the triangle
1.) Given segment AB as the base of the triangle and segment CD as the altitude of the triangle, Construct E the midpoint of AB.
2.) Construct circle with center E and radius equal in length to segment CD.
3.) Construct a perpendicular line to AB through E.
4.) Construct the intersection of the perpendicular line and the circle.
5.) Construct the segment from A to the intersection.
6.) Construct the segment from B to the intersection. Hide unnecessary circles, lines, and points, used for construction purposes only and you will have the construction of an isosceles triangle given the length of the base and the length of the altitude.
Click HERE to view the gsp sketch of an isosceles triangle given the base and the altitude.
octagon
1.) Construct a square given the length of the side of the octagon. This may be done using the script tool.
2.) Construct the diagonals of the square
3.) Construct the intersection of the diagonals.
4.) Using that length as x, and the length of the base of the square as x times the square root of two, construct circles by center and radius in order to complete the construction of the octagon.
Click HERE to view the gsp sketch of an octagon given a side.
Author & Contact:
Jennifer Shea
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