Equations

The applets are started by clicking the red buttons.

 The applet Equivalence transformations is a puzzle in which equations that emerge from each other by equivalence transformations shall be recognized. The goal here is not to solve the equations! The applet shall help to understand what equations are and that the usual way to solve them invokes a good portion of mathematical logic, even in the simplest cases. It is started from the red button in its own window.

 The applet Quadratic equations 1 is a puzzle in which various mathematical statements shall be glued together so as to represent a proof for the solution formula for quadratic equations (i.e. for equations of the type x2+ p x + q = 0). Since the derivation of this formula very often provides the first contact with "true" mathematical reasoning, it is of major importance. This applet serves to test the degree of understanding for the situation. It is started from the red button in its own window.

 The applet Quadratic equations 2 summarizes three ways to solve equations of the type x2+ p x + q = 0. It is emphasized that any choice of p and q gives rise to a concrete equation. The third method is a graphical one and may be ignored if appropriate. The user should already know a little bit about quadratic equations. The applet is started from the red button in its own window.