I began writing this applet in Feb. 1996, and it's still under development, and probably will be until I get tired of modifying it.
I'm using it to illustate Euclid's Elements. Above you see an illustration from Euclid's Elements Book I Propostion 22.
Another example using this Geometry Applet illustrates the Euler line of a triangle.
I'm still developing the Geometry Applet on which the figures in the Elements are based, and there will be changes needed in it. The most recent is a way to lift the diagram off the page into a separate window.
Here's how you can manipulate the figures that appear. If you click on a point in the figure, you can usually move it in some way. The free points, colored red, can be freely dragged about, and as they move, the rest of the diagram (except the other free points) will adjust appropriately. Sliding points, colored orange, can be dragged about like the free points, except their motion is limited to either a straight line or a circle, depending on the point. If you drag the pivot point, colored green, the entire diagram will be translated along with it. Other points can be dragged, too, if there is a pivot point showing, and the diagram will be rotated and dilated around the pivot point. Also, if you type r or the space key while the cursor is over the diagram, then the diagram will be reset to its original configuration. If you type u or return the figure will be lifted off the page into a separate window. Typing d or return while the cursor is over the original window will return the diagram to the page. (Netscape has some problems getting it back into the right position.) Note that you can resize the floating window to make the diagram larger.
It needs a lot of documentation, and I'll get to that. Soon, I hope. Note that if you type any key while the cursor is over the diagram, then the diagram will be set to its original configuration.
name=e[1] value="A;point;free;50,50;black;magenta"Each element has a number, a name, an element class, a construction method, and construction data. Optionally colors may be specified. The number of this element is 1, which means that it is the first element to be created. Its name is A. Its class is point. Its construction method is free, which means it can be freely dragged about. Its construction data is 50,50, which means that it will be initially places at pixel coordinates (50,50). When it is displayed, its name A will be colored black, but the dot representing the point will be magenta.
Elements come in five different classes: point, line, circle, polygon, and sector. Each of these classes has several construction methods. Most of the construction methods can only use one list of construction data, but some can use alternate lists.
| Element class point | ||
| Construction method | Construction data | Description |
| free | 2 integers | a freely dragable point with initial coordinates |
| midpoint | 2 points line |
the midpoint C of a line AB |
| intersection | 4 points 2 lines |
the intersection E of two lines AB and CD |
| first | line | the first end A of the line AB |
| last | line | the last end B of the line AB |
| center | circle | the center of a circle |
| lineSlider | 2 points, 2 integers line, 2 integers |
a point that slides along a line AB with initial coordinates |
| circleSlider | circle, 2 integers | a point that slides along a circle with initial coordinates |
| circumcenter | 3 points | the center of a circle ABC passing through 3 points A, B, and C |
| vertex | polygon, integer | a vertex Ai of a polygon A1A2...An with index i |
| foot | 3 points point, line |
the foot D of a perpendicular AD drawn to a line BC |
| cutoff | 4 points 2 lines |
the point E on a line AB so that AE = CD |
| extend | 4 points 2 lines |
the point E on a line AB so that BE = CD |
| parallelogram | 3 points point, line |
the 4th vertex D of a parallelogram ABCD given 3 vertices A, B, and C |
| similar | 5 points line, 3 points |
the point F so that triangle ABF is similar to CDE |
| perpendicular | 2 points line |
the point C so that AC is equal and perpendicular to AB |
| proportion | 8 points 4 lines |
the point I on GH so that AB:CD = EF:GI |
| invert | point, circle | the image of a point A inverted in a circle |
| meanProportional | 6 points 3 lines |
the point G on EF so that AB:CD = CD:EG |
| Element class line | ||
| Construction method | Construction data | Description |
| connect | 2 points | the line AB connecting two points A and B |
| angleBisector | 3 points | the line AD bisecting angle BAC with D on BC |
| angleDivider | 3 points, integer | the line AD with D on BC so that BAD is the nth part of the angle BAC |
| foot | 3 points point, line |
the line AD drawn perpendicular to BC |
| chord | 2 points, circle line, circle |
the intersection of a line AB in a circle |
| bichord | 2 circles | the common chord connecting the two intersections of circles |
| perpendicular | 2 points line |
the line AC equal and perpendicular to AB |
| cutoff | 4 points 2 lines |
the line AE equal to CD along the line AB |
| extend | 4 points 2 lines |
the line BE equal to CD so that A, B, and C are collinear with B between A and C |
| parallel | 3 points point, line |
the line AD parallel and equal to BC |
| similar | 5 points line, 3 points |
the line AF so that triangle ABF is similar to CDE |
| proportion | 8 points 4 lines |
the line GI along GH so that AB:CD = EF:GI |
| meanProportional | 6 points 3 lines |
the line EG along EF so that AB:CD = CD:EG |
| Element class circle | ||
| Construction method | Construction data | Description |
| radius | 2 points line |
the circle with center A and radius AB |
| 3 points point, line |
the circle with center A and radius BC | |
| circumcircle | 3 points | the circle passing through 3 points A, B, and C |
| invert | 2 circles | the image of the first circle inverted in the second |
| Element class polygon | ||
| Construction method | Construction data | Description |
| square | 2 points line |
the square ABCD on a side AB |
| triangle | 3 points | the triangle ABC given 3 vertices A, B, and C |
| quadrilateral | 4 points | the quadrilateral ABCD given 4 vertices A, B, C, and D |
| pentagon | 5 points | the pentagon given 5 vertices |
| hexagon | 6 points | the hexagon given 6 vertices |
| equilateralTriangle | 2 points line |
the equilateral triangle ABC on a side AB |
| parallelogram | point, line 3 points |
the parallelogram ABCD given A, B, and C |
| regularPolygon | 2 points, integer line, integer |
the regular polygon on a side AB given the number of vertices n |
| starPolygon | 2 points, 2integers line, 2 integers |
the star polygon on a side AB given the number of vertices n and the density d |
| similar | 5 points line, 3 points |
the triangle ABF similar to CDE |
| application | polygon, 3 points | given points B, C, and D, the parallelogram equal to the given polygon with one side BC and one angle BCD |
| Element class sector | ||
| Construction method | Construction data | Description |
| sector | 3 points | the sector of a circle given the center and two points on the circumference |
| arc | 3 points | the sector of a circle whose arc passes through three points |
David E. Joyce
Department of Mathematics and Computer Science
Clark University
Worcester, MA 01610
Email: djoyce@clarku.edu
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