Cactus: Calculator and computer technology user service.This is the second of two articles which describe how to use JavaSketchPad (JSP (JavaServer Page) An extension to the Java servlet technology from Sun that allows HTML to be combined with Java on the same page. The Java provides the processing, and the HTML provides the layout on the Web page. ) to explore the centres of a triangle. This introductory exercise is suggested in the GSP GSP Good Scientific Practice GSP Generalized System of Preferences GSP Gross State Product GSP German Shorthaired Pointer (dog breed) GSP Geometer's Sketchpad (KTP Technologies geometry software) GSP Georges St. Workshop Guide. The first article described how to construct the centroid centroid In geometry, the centre of mass of a two-dimensional figure or three-dimensional solid. Thus the centroid of a two-dimensional figure represents the point at which it could be balanced if it were cut out of, for example, sheet metal. (G) and the circumcentre (J) of a triangle ABC ABC in full American Broadcasting Co. Major U.S. television network. It began when the expanding national radio network NBC split into the separate Red and Blue networks in 1928. . This second article describes how to write instructions to find the orthocentre (K) and the in-centre (I), and then shows that three of these points are always co-linear. You can download these examples or use them online from users.on.net/~hhyde/cactus/jskpd. You can download versions of Java for various platforms from www.java.com. You can download the JSP Applet A small application, such as a utility program or limited-function spreadsheet or word processor. Java programs that are run from the browser are always known as applets. See midlet, crapplet and Java applet. from www.dynamicgeometry.com/JavaSketchpad/Download_Center.html as a zip file (1) A file that contains one or more files that have been compressed into the ZIP format. Also called a "ZIP archive," "zipped file" or "zipped archive," the ZIP algorithm is the most popular compression method in use. Not Just the . . Users must place the unpacked JSP folder In a graphical user interface (GUI), a simulated file folder that holds data, applications and other folders. Folders were introduced on the Xerox Star, then popularized on the Macintosh and later adapted to Windows and Unix. In Unix and Linux, as well as DOS and Windows 3. inside the project folder from which they will launch their html files. [ILLUSTRATION OMITTED]
from Orthocentre.html
<applet code="GSP.class"
codebase="jsp"
archive="JSP4.jar"
width="600" height="480"
align=center>
<param name=BackRed value=240>
<param name=BackGreen value=255>
<param name=BackBlue value=240>
<param name=LabelSize value=24>
<param name="Construction" value="
{1} Point(470,150) [red,label ('A (drag)')];
{2} Point(350,450) [red,label ('B')];
{3} Point(100,60) [red,label ('C')];
{4} Polygon(1,2,3) [white];
{5} Segment(1,2) [thick,black];
{6} Segment(2,3) [thick,black];
{7} Segment(3,1) [thick,black];
{8} Perpendicular(6,1) [magenta];
{9} Perpendicular(7,2) [magenta];
{10} Perpendicular(5,3) [magenta];
{11} Intersect(8,9) [magenta,label('K')];
">
Sorry, this page requires a Java-compatible
web browser.</applet>
All of the html files discussed in these articles are coded as simple 1 x 3 html tables An HTML structure for creating rows and columns. It is used for lists, specifications and other tabular data as well as to locate elements on the page. The table command gives the HTML designer reasonably precise control over placement of text and images. . The second cell of the code for Orthocentre.html contains the JSP applet shown above. The width and height of the JSP screen have been chosen so that it can be viewed using a VGA (Video Graphics Array) The display standard for the PC. All PC display adapters support VGA, and Windows machines boot up in "VGA mode" before switching to higher resolutions. screen and still be able to access an editor window to one side of the browser browser Software that allows a computer user to find and view information on the Internet. The first text-based browser for the World Wide Web became available in 1991; Web use expanded rapidly after the release in 1993 of a browser called Mosaic, which used screen. If your screens are larger, then it is easy to increase these dimensions. The BackRed, BackGreen and BackBlue parameters adjust the colour balance of the background of the JSP screen. Since each colour has 256 values, the JSP screen background can be matched against the table background in 248 different ways. If you wish your students to learn geometry, I suggest you do not mention colour matching options. [ILLUSTRATION OMITTED] The value of the Construction parameter (1) Any value passed to a program by the user or by another program in order to customize the program for a particular purpose. A parameter may be anything; for example, a file name, a coordinate, a range of values, a money amount or a code of some kind. comprises the list of numbered commands. Items {1}, {2} and {3} define three points labelled A, B and C, based on a coordinate system coordinate system Arrangement of reference lines or curves used to identify the location of points in space. In two dimensions, the most common system is the Cartesian (after René Descartes) system. that counts from the top left-hand corner of the JSP screen. The size of these labels is determined by the LabelSize value. Item {4} draws a white triangle that makes it easier to distinguish the original triangle amid subsequent construction lines. Item {5} draws a thick black line segment between the points defined in items {1} and {2}. Items {6} and {7} add the other two sides. Item {8} draws a magenta construction line through the point A defined in item {1} and perpendicular to the line segment BC defined in item {6}. This is the altitude altitude, vertical distance of an object above some datum plane, such as mean sea level or a reference point on the earth's surface. It is usually measured by the reduction in atmospheric pressure with height, as shown on a barometer or altimeter. from A to BC. Items {9} and {10} draw the other two altitudes. Item {11} finds the intersection (K) of two of the altitudes and we observe that as we drag the vertices The plural of vertex. See vertex. of the triangle, the altitudes remain concurrent at the orthocentre K. If, instead of a triangle, you get the message, "Sorry, this page requires a Java-compatible web browser The program that serves as your front end to the Web on the Internet. In order to view a site, you type its address (URL) into the browser's Location field; for example, www.computerlanguage.com, and the home page of that site is downloaded to you. ," then JSP is not working. There are several possible causes. Visit my website and attempt to view these same examples online. If this does not work then Java is not enabled in your browser. You need to install Java from www.java.com or you need to enable it (switch it on) using your browser preferences. Finding the in-centre of the triangle should be easy; however, the designers of JSP have not included a simple command to find an angle bisector.
from In-centre.html
{1} Point(470,150) [red,label ('A (drag)')];
{2} Point(350,450) [red,label ('B')];
{3} Point(100,60) [red,label ('C')];
{4} Polygon(1,2,3) [white];
{5} Ray(1,2) [hidden,black];
{6} Ray(2,3) [hidden,black];
{7} Ray(3,1) [hidden,black];
{8} Segment(1,2) [thick,black];
{9} Segment(2,3) [thick,black];
{10} Segment(3,1) [thick,black];
{11} Circle(1,2) [hidden,black];
{12} Circle(2,3) [hidden,black];
{13} Circle(3,1) [hidden,black];
{14} Intersect2(7,11) [hidden,black];
{15} Intersect2(5,12) [hidden,black];
{16} Intersect2(6,13) [hidden,black];
{17} Segment(16,1) [hidden,black];
{18} Segment(14,2) [hidden,black];
{19} Segment(15,3) [hidden,black];
{20} Midpoint(17) [hidden,black];
{21} Midpoint(18) [hidden,black];
{22} Midpoint(19) [hidden,black];
{23} Ray(21,1) [red];
{24} Ray(22,2) [red];
{25} Ray(20,3) [red];
{26} Intersect(23,24) [green,label ('I')];
{27} Perpendicular(9,26) [hidden,black];
{28} Intersect(27,9) [hidden,blue];
{29} Circle(26,28) [black];
Consider the In-centre.html Java applet A Java program that is downloaded from the server and run from the browser. The Java Virtual Machine built into the browser is interpreting the instructions. Contrast with Java application. listed above. To bisect bi·sect v. bi·sect·ed, bi·sect·ing, bi·sects v.tr. To cut or divide into two parts, especially two equal parts. v.intr. To split; fork. the vertex A corner point of a triangle or other geometric image. Vertices is the plural form of this term. See vertex shader. at A, draw the ray AC {7} in case AC is shorter than AB. Then draw a circle {11} with centre A and radius AB. At {14} we find where the circle cuts the ray AC and draw a segment {18} from this point back to B. A ray {23} drawn from A through the midpoint mid·point n. 1. Mathematics The point of a line segment or curvilinear arc that divides it into two parts of the same length. 2. A position midway between two extremes. {21} of the segment will bisect the vertex at A. All of these construction lines, except the bisector {23}, are hidden for the sake of clarity. The rays {23-25} are coincident co·in·ci·dent adj. 1. Occupying the same area in space or happening at the same time: a series of coincident events. See Synonyms at contemporary. 2. at the in-centre (I). If we draw the in-circle {29} we can see that it touches each side of the triangle. [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED]
from Euler_Segment.html
{1} Point(480,170) [red,label ('A (drag)')];
{2} Point(350,450) [red,label ('B')];
{3} Point(100,60) [red,label ('C')];
{4} Polygon(1,2,3) [white];
{5} Segment(1,2) [thick,black];
{6} Segment(2,3) [thick,black];
{7} Segment(3,1) [thick,black];
{8} Midpoint(6) [black,label ('D')];
{9} Midpoint(7) [black,label ('E')];
{10} Midpoint(5) [black,label ('F')];
{11} Perpendicular(5,10) [hidden,magenta];
{12} Perpendicular(6,8) [hidden,magenta];
{13} Perpendicular(7,9) [hidden,magenta];
{14} Intersect(11,12) [magenta,label ('J')];
{15} Perpendicular(5,3) [hidden,blue];
{16} Perpendicular(6,1) [hidden,blue];
{17} Perpendicular(7,2) [hidden,blue];
{18} Intersect(15,16) [blue,label ('K')];
{19} Segment(1,8) [hidden,green];
{20} Segment(2,9) [hidden,green];
{21} Segment(3,10) [hidden,green];
{22} Intersect(19,20) [green,label ('G')];
{23} Ray(1,2) [hidden,black];
{24} Ray(2,3) [hidden,black];
{25} Ray(3,1) [hidden,black];
{26} Circle(1,2) [hidden,black];
{27} Circle(2,3) [hidden,black];
{28} Circle(3,1) [hidden,black];
{29} Intersect2(25,26) [hidden,black];
{30} Intersect2(23,27) [hidden,black];
{31} Intersect2(24,28) [hidden,black];
{32} Segment(31,1) [hidden,black];
{33} Segment(29,2) [hidden,black];
{34} Segment(30,3) [hidden,black];
{35} Midpoint(32) [hidden,black];
{36} Midpoint(33) [hidden,black];
{37} Midpoint(34) [hidden,black];
{38} Ray(36,1) [hidden,red];
{39} Ray(37,2) [hidden,red];
{40} Ray(35,3) [hidden,red];
{41} Intersect(38,39) [red,label ('I')];
{42} Segment(14,18) [thick,black];
{43} Segment(22,14) [thick,black];
{44} Ratio/Segments (42,43,420,450,'Ratio
JK/JG = ')
{45} Circle(14,1) [hidden,magenta];
{46} Perpendicular(5,41) [hidden,black];
{47} Intersect(5,46) [hidden,black];
{48} Circle(41,47) [hidden,magenta];
{49} ShowButton(10,270,'Show
Centroid')(19,20,21) [black];
{50} ShowButton(10,310,'Show InCentre')(38,39,40,48)
[black];
{51} ShowButton(10,350,'Show
Orthocentre')(15,16,17) [black];
{52} ShowButton(10,390,'Show
Circumcentre') (11,12,13,45) [black];
{53} HideButton(10,430,'Hide All
Construction Lines')
(11,12,13,15,16,17,19,20,21,38,39,40,
45,48) [black];
Finally, all of the constructions can be incorporated into one model as shown above. If you move points A, B or C you will notice that the points J, G and K are always on a line and the point G is always a third of the distance from J to K. The segment JK is called the Euler Segment. The code for the Euler_Segment.html applet is shown at left. Near the bottom you will see where five buttons have been defined. Clicking the ShowButtons will reveal the constructions listed in brackets brackets: see punctuation. . For example, the "Show Centroid" button {49} is placed at coordinates (10, 270) and reveals the otherwise hidden constructions {19}, {20} and {21}. Reference to these buttons therefore lets you find the section of code which builds each part of the model. The HideButton command restores the model to its simpler form by removing all the construction lines. Obviously, larger construction tasks would be easier to build and understand if we could define subroutines. Even an ability to space the instructions {10}, {20}, {30} etc., thereby leaving room to make subsequent changes as we did with numbered commands in BASIC, would make JSP much easier to use. However, JSP is not a programming language. The advantages of JSP are that it is free, most students enjoy using it, and it allows dynamic geometry to be added to web pages that can be viewed with most browsers. Hartley Hyde users.on.net/~hhyde/cactuscactus.pages@internode in·ter·node n. 1. A section or part between two nodes. 2. An internodal segment. in .on.net |
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