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Draw diagram for proving the Pythagorean Theorem

[[wiki/img/pythagorean_diagram1.png]]

Draws a diagram suitable for proving the Pythagorean Theorem using turtle graphics..

It's possible to derive this diagram from any initial right triangle using only a compass and straight edge; though this construction is not yet used in the code.

This only exports one function draw_diagram taking two arguments, height, and width, and returning a reference to the (Turtle) screen created by the function. All constructions elements and labels/captions are derived from those two arguments.

The return value of this function can be used to further play with the resulting diagram. To do this start a Python (2.x) or iPython shell and issue the following commands:

>>> import pythy_turtle as pythy
>>> ## ... set height and width as desired: x and y
>>> screen = pythy.draw_diagram(x, y)
>>> turtle = screen.getturtles()[0]

As shown the single turtle used by this function can be obtained for further manipuation from the object returned by the draw_diagram() function.

To save the resulting image one can also use the canvasvg package (https://pypi.python.org/pypi/canvasvg/1.0.0) like so:

>>> ## (given the preceding environment)
>>> import canvasvg
>>> ## Choose a filename
>>> cavasvg.save_all(filename, screen.getcanvas())

... ignore the warning about how canvasvg doesn't support images; this code isn't using any of them and the exported SVG file looks fine and converts easily to PDF or PNG.

When called as a standalone programm this code takes optional command line arguments setting the height and width of the initial triangle. It does not control the size of the window opened by the Turtle/Tk system; so the resulting diagram might not all be visible and you may have to resize that window yourself. Also the function currently performs the drawing steps incrementally and pauses for the user to hit [Enter] several times. This is an artifact of the interactive development process used to write the code. When the diagram is complete __main__ calls the Turtle.mainloop() function to allow the user to view and manipulate the resulting window as desired. Closing that window will then drop out of __main__.

If a third command line argument is provided then it should be a filename to which you want the resulting diagram to be saved as an SVG (Scalable Vector Graphic).

If the program is called with arguments that cannot be converted to Python integers then the default triangle height and width (50x100) will be used.

Currently there are thick and thin lines, thick lines for outer (enclosing) square edges, thin lines for inner edges. Black for the first (rectangular) enclosing square; red for the second ("ring of triangles") square. The initial triangle is shaded in light grey and has a customary "right angle" mark. The "a" and "b" squares are filled in pink; the "c" square is filled in lavender; and the triangles are filled with a pale cyan.

This initial triangle is oriented in the manner customarily used to draw a "unit circle" ... to facilitate associating these related concepts.

Bugs and limitations:

  • Uses console text and raw_input to step through the construction (This is currently tightly interlaced into the function; need to make that optional and decoupled).
  • The steps used to draw the diagram do not show the hints necessary for c&s construction. It's illustrative rather than being a proof.
  • variable names in the function: w, t, wd, ht are horrible (they were used for the interactive session in which ai developed the code)
  • Colors (line and fill) are hard-coded into the function
  • Line thicknesses are hard-coded into the function
  • No scaling nor translation/placement is done ... calling the draw function with strange arguments can

To Do:

  • Refactor the local variable names
  • Offer iPython embedded shell option to call after image drawn (for use by programming students)
  • Move interaction from console into Turtle/Tk events!
    • Add controls for ratio or height and width
    • Add better input validation and error messages
    • Add loop/option to clear canvas and do another drawing
    • Optional audio record/playback? (For video tutorial use)
  • Add background image screen.bgpic()? Greyed out portrait of Pythagoras?
  • Use ratio option in lieu of absolute height/width
  • (Optionally?) scale (custom) triangles to canvas size
  • Add compass and straight edge sprites?
    • Animated?
  • Port to JavaScript on HTML5 canvas and post to custom web page