The trisection of the angle
This article is a translation of the email sent by Walter Bender on the list Community-news of Sugar Labs , September 22, 2008. See the original article in English.
The trisection of angles: in three articles published in 1830, the French mathematician Evariste Galois laid the foundations of an algebraic proof of the fact that it is not possible to divide an angle into three with the rule and Compass, a fact known to the ancient Greeks but they were unable to prove. However, what is often forgotten is that the Greeks knew divide an angle into three using other instruments. What is the history lesson has to do with Sugar Labs? OLPC-Sur list was dominated by two threads, both separate and connected: the announcement of Microsoft on the Windows XP pilot in Peru, and the lack of function to extract the square root in Turtle Art, both discussions can be viewed through the lens of abstract algebra - apologies if this analogy too far.
Let me first summarize the discussion on Turtle Art. Some teachers in Uruguay teach the Pythagorean theorem and were blocked by the absence of square root function in Turtle Art. They wanted to demonstrate that the length of the diagonal of a square equals the square root of the sum of the square on each side. In pseudo-code, they wanted to build the following construction:
repeat 4 (forward 100 right-turn 90) 45-turn right advancing root-square ((100 * 100) + (100 * 100))
Many possibilities were discussed, including the use of Dr. Geo. My favorite comment is that Pato Acevedo, who said:
[Ironic mode ON] Sure, I can not understand how Pythagoras "discovered" his famous theorem without time calculator. [Irony mode off]
But in fact, despite some intervention on my part, the discussion has turned to how to change the Turtle Art activity. I made a tutorial (see http://sugarlabs.org/go/Patching_Turtle_Art , in English) with the hope not only to meet the immediate needs of teachers, but also show them that in fact they could make them themselves the necessary changes to the program so that it meets their needs. I hope I do not have them made it too easy, and some will take the chance to make changes - to create new instruments. The beauty of free software is that if a permutation group does not allow you to "trisecter an angle", you can always edit the group. Dialogue between teachers and developers began. The next step is that some teachers become developers.
What is the relationship with the announcement about Windows XP? It's just a shame that Microsoft does not use its vast resources to expand opportunities for children by going to places that are not already served by OLPC. Regardless of the merits of Windows XP, they could have an immediate impact and lasting covering space which is outside the Peruvian permutation group. Pamela Jones and Sean Daly wrote a more detailed analysis of history for XP Groklaw (see http://www.groklaw.net/article.php?story=20080920181151638 ).

















