Difference between revisions of "Prove Command"
From GeoGebra Manual
(add link to gg-art-doc) |
m (Text replace - ";(.*)\[(.*)\]" to ";$1($2)") |
||
| Line 1: | Line 1: | ||
<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|logical}} | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|logical}} | ||
| − | ;Prove | + | ;Prove( <Boolean Expression> ): Returns whether the given boolean expression is true or false in general. |
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>}} | ||
Revision as of 17:15, 7 October 2017
- 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, GeoGebra Automated Reasoning Tools: A Tutorial and technical details of the algorithms.
