Create animated figures

With OK Geometry you can create animated HTML figures. An animated figure is a group of ordinary figures that are displayed in a temporal sequence. Animated figures allow to represent in a single figure, for example, the steps of a euclidean construction, the properties of a given geometric configuration, the frame of a proof, etc.

The easiest way to obtain an animated figure that shows the construction steps of a configuration or the geometric properties of a given configuration, is to create an icon from a construction with scenes. However, you can also obtain an animated figure by aggregating icons.

In adition to the manual creation of scenes, there are three simplified ways for obtaining them. The incremental method is suitable for displaying construction steps. The differential method is suitable for adding various sets of objects to a fixed configuration. And there is a third method aimed for showing selected properties observed by OK Geometry.   

We illustrate the animated figures with some examples, which all refer to the isodynamic points of a triangle.

Isodynamic centres of a triangle



For a scalene triangle ?ABC there exist two points X with the property that the distance from X to the vertices of ABC are inversely proportional to the respective sidelengths, i.e.,

       |XA|•|BC| = |XB|•|CA| = |XC|•|AB|

One of the two points lays inside the circumcircle of the triangle ABC, the other lays outside the circumcircle. The first point, X15, is called the first isodynamic centre of ABC. The other, X16, is called the second isodynamic centre of ABC.

A construction of isodynamic points

The figure illustrates a lesser known Euclidean construction of the isodynamic points X15 and X16 of ABC. Here, the animated figure was obtained by incremental scenes.
 

Some properties of the circumcevian triangle of the isodynamic point


The figure shows some properties of the circumcevian triangle  of the first isodynamic point (i.e., the vertices of the triangle A'B'C' are the projections of X15 onto the circumcircle of ABC). The properties, observed by OK Geometry, were added as property scenes to the basic configuration. 

The isodynamic point and some triangle objects


The figure shows some triangle objects related to the first isodynamic point of the triangle ABC. The animated figure was created using differential scenes.

Download construction (.pro)