x-start or x-finish for 2D graph as a variable?

[cliverlong]

I'm trying to use your "step function" to create some Autograph "minimax" demonstrations.

The starting idea is this. Set the perimeter of a shape to a fixed value, say 20. The initial shapes would be a rectangle or a sector. The objective is to find the length, l, of a side (rectangle) or angle (of sector) that gives the largest area. Algebraically this would be done by expressing the area, A as a function of length, l, then determining and solving dA/dl = 0.

My idea to use Autograph is to create the shape where the length of the parameter, length l or angle, is an Autograph variable. In the attached example I have created the rectangle using both "shape" and a small modification of the step function above (the function has value +1 over a small range of values of x starting at zero). I can create the rectangle either way and it responds as I want, i.e. re-shapes, when I vary the value of the parameter, a. However, the "shape" option does not offer a right-click option to calculate/estimate the area within the shape. The rectangle based on the "step" functions does offer the option to calculate the area but when it is selected Autograph just says this is an "invalid area". Is there a different approach to this?

Regards,

Clive

  minimax.agg (Size: 4.9 KB / Downloads: 2)

  minimax2.agg (Size: 8.81 KB / Downloads: 3)

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A rider to this.

If I can get a value for the area then I would like to be able to plot the area (dependent) against the variable (independent) so I can see/show the graph actually has a maximum or minimum at a particular value of the variable that (hopefully) corresponds to the value determined algebraically (using differentiation).

Thanks

clive