DraggableProofs

Using Draggable Statements

This PG code shows how develop a proof with random statements that need to go in the correct order.

PG problem file	Explanation
DOCUMENT(); loadMacros( 'PGstandard.pl', 'MathObjects.pl', 'PGML.pl', 'draggableProof.pl', 'PGcourse.pl' ); TEXT(beginproblem());	Details of the draggableProof.pl macro can be found in [the POD].
$statements = [ 'Assume $\sqrt{2}=\frac{a}{b}$ where $a,b$ are integers, with $\text{gcd}(a,b)=1$ ', '$2 = \frac{a^2}{b^2}$', '$a^2 = 2b^2$', 'if $a^2$ is even, then $a$ must be even', 'Let $a=2k$ for $k$ some integer', 'We can then write $ 2 = \frac{4k^2}{b^2}$ or $b^2 = 2k^2$', 'Therefore $b^2$ is even, so $b$ is also even', 'If $a$ and $b$ are both even, then the initial assumption that $\text{gcd}(a,b)=1$ is contradicted.', '$\sqrt{2}$ is therefore not rational.' ]; # These are extra statements that are not needed. $extra = [ 'Then $a$ is odd', '$b^2$ cannot be rational.', 'therefore $a = 2b$' ]; $proof = DraggableProof( $statements, $extra );	The `DraggableProof` function takes an arrayref of correct statements, followed (optionally) by extra statements. See the POD for more options.
BEGIN_PGML [@ $proof->Print @]* END_PGML
ANS($proof->cmp);	Answer Evaluation:
BEGIN_PGML_SOLUTION Solution explanation goes here. END_PGML_SOLUTION COMMENT('Allows integration in either order. Uses PGML.'); ENDDOCUMENT();	Solution:

PG problem file	Explanation
DOCUMENT(); loadMacros( 'PGstandard.pl', 'MathObjects.pl', 'PGML.pl', 'draggableProof.pl', 'PGcourse.pl' ); TEXT(beginproblem());	Details of the draggableProof.pl macro can be found in [the POD].
$statements = [ 'Assume \(\sqrt{2}=\frac{a}{b}\) where \(a,b\) are integers, with \(\text{gcd}(a,b)=1\) ', '\(2 = \frac{a^2}{b^2}\)', '\(a^2 = 2b^2\)', 'if \(a^2\) is even, then \(a\) must be even', 'Let \(a=2k\) for \(k\) some integer', 'We can then write \( 2 = \frac{4k^2}{b^2}\) or \(b^2 = 2k^2\)', 'Therefore \(b^2\) is even, so \(b\) is also even', 'If \(a\) and \(b\) are both even, then the initial assumption that \(\text{gcd}(a,b)=1\) is contradicted.', '\(\sqrt{2}\) is therefore not rational.' ]; # These are extra statements that are not needed. $extra = [ 'Then \(a\) is odd', '\(b^2\) cannot be rational.', 'therefore \(a = 2b\)' ]; $proof = DraggableProof( $statements, $extra );	The `DraggableProof` function takes an arrayref of correct statements, followed (optionally) by extra statements. See the POD for more options.
BEGIN_PGML [@ $proof->Print @]* END_PGML
ANS($proof->cmp);	Answer Evaluation:
BEGIN_PGML_SOLUTION Solution explanation goes here. END_PGML_SOLUTION COMMENT('Allows integration in either order. Uses PGML.'); ENDDOCUMENT();	Solution: