Since the time that this blog is dormant, I experimented with other objects. This idea
activity m has been blown by Danielle Salles group geometry IREM de Basse Normandie : Machine trisection angles. Share
an angle into two equal angles is possible with ruler and compass, all students remember the bisector. Cut at an angle into 4 or 8 is not much more complicated and just requires some precision. But cut at any angle into three equal angles is not possible using only ruler and compass. This is an old problem, also known as construction with ruler and compass of squaring the circle and duplicating the cube.
By cons, other technical solutions, using other tools provide solutions to this problem. After this
introdution history, I suggest to my students get in groups of 3 and use the following tools, using the manual to understand how they work. Before the end of the day, students must turn on all the workshops, making the angle trisection in each case, and validated by the teacher the proper use of the object, then choose two of these objects and sketch a figure to illustrate the geometric object. The study of these figures is presented at the session next module, after we had discussed what should be a mathematical figure, as a basis for effective demonstration.
objects trisection are to:
The tomahawk (or trisector Bergeryís)
manufacturing: a board cut with a jigsaw
manufacturing: a curtain rod, a screw that fits into this groove.
The geometric figure is almost visible, but I do not think I could hide it.
It should be noted that these first three tools come down to exactly the same geometric figure and same reasoning. Of the two tools that students must study, he should consider a mandatory among these three, the second choice among the three following demonstrations that lead to quite different.
Double bisector:
bars and plastic fasteners. We can operate a slot on the bars of trisector, but can also cope by superimposing two bisectors.
Inspired trisector MacLaurin found on the site Geogebra
Made mecanno bars and elastics.
With bars mécanno:
Technique: two strips revolve around a groove. The angle formed at the end by these two brackets is the third of an angle formed by the triangle built with bars mécanno.
The instructions are on this PDF
After discussing the mathematical figure of it must contain (name of points, equal in length, angles), students needed to demonstrate the operation of two of them (one of the first 3 and the last three).
The results were somewhat disappointing, although there were some very interesting ideas of ownership of the problem. Given some mistakes, I realized that having just the photo does not always suffice to make the figure. So if I start this activity very rich, I will leave these objects available to my students at the bottom of my room, so they can handle it again if they feel the need to verify some properties and they have interviews.
Excerpts Copy:
folds to represent the transformations of the triangles into the tee:
passage of drawing the figure in three stages:
Just a drawing not when it interesting
Ultimately, this work has led students to think and move, to paraphrase Ruben Rodriguez, a passage from one universe to be experienced machines to a formalized world figures, then to a world of ideas and demonstrations.
An example:
Universe formalized the mathematical figure:
ED = DC so the triangle is isosceles D EDC.
Even if it was rewarding, even if the necessary background to the level of fourth, it was not an exercise easier for students because it requires a lot of hindsight, the more difficult, as the saying one of my very good students, there was no solution on the Internet.
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