## Application to simulate ruler and compass constructions together with the underlying algebra.

The application opens showing two points (0,0) and (1,0). The line y = 0 and the unit circle have also been constructed. The underlying field is the rational integers Q. When you select an object by choosing from the drop down lists, it is coloured red and the algebraic form of the object is shown below.

To carry out a construction click on that appropriate button and then select the objects in the order indicated by the instructions shown. If you select an incorrect object clicking on it a second time will normally deselect it. Alternatively reclicking the button will deselect all the selected objects. When you are happy with your selection, click the 'Do the construction' button. Some constructions require an extension to the field. If this, is the case, you are given the option to allow the extension or cancel the construction. The underlying field is shown as a quadratic extension of Q.

Clicking the 'Construct pentagon' button will enable an animated version of a construction of the pentagon