Ever needed to measure something and all you had was a piece of paper?  This leads us to how we can use maple to figure out what we can measure using a sheet of standard 8-1/2" x 11" paper.

Can we measure 6" with a sheet of paper?

> eq := (17/2)*x+11*y = 6;
                                  17             
                            eq := -- x + 11 y = 6
                                  2              
> eq2 := isolve(eq, a);
                   eq2 := {x = -20 - 22 a, y = 16 + 17 a}
> subs(a = 0, b = 0, eq2);
                              {x = -20, y = 16}

So that is the simplest case, stacking up 16 pieces on the long side and subtracting 20 on the short side.  A total of toppling the piece of paper over 36 times.  That's a high percentage of of error. 

But wait!  haha.   Wouldn't a fold make it simpler?  Sure!  Fold the 8.5" across and we now have 2.5" to work with.

> eq := (17/2)*x+11*y+(5/2)*z = 6;
                               17            5      
                         eq := -- x + 11 y + - z = 6
                               2             2      
> eq2 := isolve(eq, {a, b});
           eq2 := {x = a, y = 1 + 4 a + 5 b, z = -2 - 21 a - 22 b}
> subs(a = 0, b = 0, eq2);
                           {x = 0, y = 1, z = -2}

Less toppling of pieces of paper and much less error. 

 

 


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