Geometry Explorer Help
Getting Started with Geometry Explorer:

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First Exploration- Building an equilateral triangle:

We will start out with an example that is actually the first demonstration in Book I of Euclid's classic work The Elements. In this example we first construct two circles, with the center of one being the radial point of the other, and vice-versa.

To do this, go to the Create Panel and click on the circle tool. Then, click and drag anywhere in the canvas to make a circle. You will notice that the first place that you clicked becomes the center point of the circle and the dragged point becomes a radius point for the circle.

ex1

Now create a second circle with the center point being the radius of the first circle, and the new radius point being the center point of the first circle. You can tell that you have clicked on a point by the point being highlighted ( a little circle surrounds it). Your picture should now look like this:

ex2

Now we will construct the intersection of these two circles. Select both circles by 1) Clicking on the select arrow in the Create Panel, and 2)Clicking on each circle. If both circles are selected, the Intersection tool in the Construct Panel should be enabled (black), as well as the Filled Circle tool.

ex3

To construct the two intersection pts, we just click on the intersect tool. The two intersection points should now be visible. Next we will select the top intersection point and the two circle centers.

ex4

With these three points selected, many construction tools are enabled. In particular the closed polygon tool (second from left in the bottom row) is enabled. Click on this to construct an equilateral triangle. (For fun: why must the triangle be an equilateral triangle?) Now select either of the centers in the canvas and drag them around. Does the triangle remain equilateral? All of the constructions that we made - circles, intersections, polygons, etc are preserved under dynamic changes to the centers. That is what makes this geometry exploration environment so powerful -- a virtually endless number of examples can be explored to give insight into a mathematical result.