Euclidean Geometry

Descartes is capable of illustrating a large number of plane geometry theorems. This can be achievd using mainly the tools: POINTS, SEGMENTS, ARCS and CONTROLS.

It is said that one example in enough (in spanish: "para muestra basta un botón"). Let's hope it is true.

Theorem. An arc of a circle spans the same angle from any point of the circle.

In this example the arc is AB. The student may drag the points P and Q and verify the statement of the theorem, that is, the angle AQB is always the same as the angle APB. The student can also drag A and B to modify the arc and thus the angle. The values of the angles are written in degrees. The user can verify that the angle APB is half the angle ACB, where C is the center of the circle. This fact was used in the applet configuration to simplify the calculations of the angles APB and AQB.

This example illustrates the use of constrictions on the controls. A constriction is an equation in x and y that defines the locus on which the CONTROL must stay. In this example the constriction is the circle centered at the origin with radius 3: x^2+y^2=9. This expression apears in the configuration of all the CONTROLS A, B, P and Q.

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	Ministerio de Educación, Cultura y Deporte. Año 2000