I have been intrigued by Euclid's Elements ever since I saw this website: http://aleph0.clarku.edu/~djoyce/java/elements/elements.html. I'd always thought it would be a cool way to explore geometry. Begin with the basics and then see what you could do with those things.
So, my idea for an iTextbook is based around those ideas. You begin with some "simple" definitions and postulates as in Euclid's book. Maybe give some reasoning behind the postulates by asking questions like, "Why do we need 2 points to draw a line? Challenge: I am thinking of a line in this window. See if you can guess it with zero hints. (Student draws random line and it won't match what's in the computer.) Here. I'll give you one hint: This point is on the line (point appears, kid draws another line, it won't match). You missed because here are some example lines that it could have been (show a bunch of lines through the point). Here is a second hint: This point is also on the line (connect the dots = winner)."
Expand by asking students to create some tools needed. For example, show a picture of a pile of items that you might find in a junk drawer. These include, but are not limited to, some string, some push-pins, a pen, tape, scissors, a straightedge of some sort, etc. Ask students "How could you create a perfect circle (see definitions 15-16) from these items?" Once they arrive at a correct answer, they "level up." A screen appears with something like, "You have acquired the circle tool!" and the glittery circle button appears in their tool-bar at the top which works like it would in any drawing program (click for the center point, then click again for a point on the circle to fix the size).
Basically, you build geogebra tools by finding out how to construct each thing. You have the line-segment tool and circle tool, so Challenge 1 is available to you: construct an equilateral triangle using the tools you have.
Once you show you can bisect a given line segment, you get a new "midpoint" tool. This unlocks new challenges in which you need to use the midpoint for other constructions.
After you construct an object, you get follow-up questions like: In constructing the midpoint, do the two circles need to be the same size? Is the bisecting segment always perpendicular to the original segment? Does the original segment bisect the segment you created? etc.
It'd be dynamic as with geogebra or sketchpad or anything like that, but you can only use the tools when you "level up" by figuring out how to get build them from more basic tools.
There's a "sandbox mode" where you can play around with tools you have or preview what will become available later. Challenges available are based on the tools you have acquired so far, so they are somewhat ordered, but not necessarily linear. They could be labeled with a difficulty level. Unlocking new tools unlocks new challenges. Hints can be available for the tougher constructions/proofs, like in most games, too.
Anyways, what do you think? The idea just struck me this afternoon, so I haven't thought through all the angles (pun intended), but it seemed like an interesting way to introduce parts of geometry.
