Difference between revisions of "Prove Command"
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Normally, GeoGebra decides whether a [[Boolean_values|boolean expression]] is true or not by using numerical computations. However, the Prove command uses [[w:Symbolic_computation|symbolic methods]] to determine whether a statement is ''true'' or ''false'' in general. If GeoGebra cannot determine the answer, the result is ''undefined''. | Normally, GeoGebra decides whether a [[Boolean_values|boolean expression]] is true or not by using numerical computations. However, the Prove command uses [[w:Symbolic_computation|symbolic methods]] to determine whether a statement is ''true'' or ''false'' in general. If GeoGebra cannot determine the answer, the result is ''undefined''. | ||
{{example| 1=<div>We define three free points, <code><nowiki>A=(1,2)</nowiki></code>, <code><nowiki>B=(3,4)</nowiki></code>, <code><nowiki>C=(5,6)</nowiki></code>. The command <code><nowiki>AreCollinear[A,B,C]</nowiki></code> yields ''true'', since a numerical check is used on the current coordinates of the points. Using <code><nowiki>Prove[AreCollinear[A,B,C]]</nowiki></code> you will get ''false'' as an answer, since the three points are not collinear in general, i.e. when we change the points.</div>}} | {{example| 1=<div>We define three free points, <code><nowiki>A=(1,2)</nowiki></code>, <code><nowiki>B=(3,4)</nowiki></code>, <code><nowiki>C=(5,6)</nowiki></code>. The command <code><nowiki>AreCollinear[A,B,C]</nowiki></code> yields ''true'', since a numerical check is used on the current coordinates of the points. Using <code><nowiki>Prove[AreCollinear[A,B,C]]</nowiki></code> you will get ''false'' as an answer, since the three points are not collinear in general, i.e. when we change the points.</div>}} | ||
| − | {{example| 1=<div>Let us define a triangle with vertices ''A'', ''B'' and ''C'', and define <code><nowiki>D=MidPoint[B,C]</nowiki></code>, <code><nowiki>E=MidPoint[A,C]</nowiki></code>, <code><nowiki>p=Line[A,B]</nowiki></code>, <code><nowiki>q=Line[D,E]</nowiki></code>. Now both <code><nowiki>p∥q</nowiki></code> and <code><nowiki>Prove[p∥q]</nowiki></code> yield ''true'', since a midline of a triangle will always be parallel to the appropriate side.</div>}} | + | {{example| 1=<div>Let us define a triangle with vertices ''A'', ''B'' and ''C'', and define <code><nowiki>D=MidPoint[B,C]</nowiki></code>, <code><nowiki>E=MidPoint[A,C]</nowiki></code>, <code><nowiki>p=Line[A,B]</nowiki></code>, <code><nowiki>q=Line[D,E]</nowiki></code>. Now both <code><nowiki>p∥q</nowiki></code> and <code><nowiki>Prove[p∥q]</nowiki></code> yield ''true'', since a midline of a triangle will always be parallel to the appropriate side. |
| + | <ggb_applet width="525" height="366" version="5.0" id="40121" enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="false" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="false"/> | ||
| + | </div>}} | ||
{{Note| See also [[ProveDetails Command|ProveDetails]] command, [[Boolean values|Boolean values]] and [http://dev.geogebra.org/trac/wiki/TheoremProving technical details of the algorithms].}} | {{Note| See also [[ProveDetails Command|ProveDetails]] command, [[Boolean values|Boolean values]] and [http://dev.geogebra.org/trac/wiki/TheoremProving technical details of the algorithms].}} | ||
Revision as of 10:57, 30 May 2013
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This page is about a feature that is supported only in GeoGebra 5.0. |
 Warning: | This GeoGebra command is heavily under construction. Expect to encounter various problems when trying it out. The syntax or the output of this command may be subject to change. |
- Prove[ <Boolean Expression> ]
- Returns whether the given boolean expression is true or false in general.
Normally, GeoGebra decides whether a boolean expression is true or not by using numerical computations. However, the Prove command uses symbolic methods to determine whether a statement is true or false in general. If GeoGebra cannot determine the answer, the result is undefined.
Example:
We define three free points,
A=(1,2), B=(3,4), C=(5,6). The command AreCollinear[A,B,C] yields true, since a numerical check is used on the current coordinates of the points. Using Prove[AreCollinear[A,B,C]] you will get false as an answer, since the three points are not collinear in general, i.e. when we change the points.Example:
Let us define a triangle with vertices A, B and C, and define
D=MidPoint[B,C], E=MidPoint[A,C], p=Line[A,B], q=Line[D,E]. Now both p∥q and Prove[p∥q] yield true, since a midline of a triangle will always be parallel to the appropriate side.
Note: See also ProveDetails command, Boolean values and technical details of the algorithms.
