Can Classic Greek Problems Be Solved with Basic Geometry?

[gravenewworld]

I have to give a presentation for geometry, and I chose to do my presentation on the impossiblity of squaring the circle, doubling the volume of a cube, and trisection of an arbitrary angle with Euclidean tools. The problem is though, that I am certain the majority of the class has never been exposed to any field theory at all. Does anyone have any ideas of how I can possibly explain the proofs of why these problems are impossible without having to go to field theory? I mean I will go to field theory if I have to, but then again, no one would understand unless there is a way to easily explain field theory without using heavy duty concepts, like using polynomials etc.

 

[NeutronStar]

I don't know if these will help or not,...


http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Squaring_the_circle.html

http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Doubling_the_cube.html

http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Trisecting_an_angle.html

 

[fourier jr]

I have to give a presentation for geometry, and I chose to do my presentation on the impossiblity of squaring the circle, doubling the volume of a cube, and trisection of an arbitrary angle with Euclidean tools. The problem is though, that I am certain the majority of the class has never been exposed to any field theory at all. Does anyone have any ideas of how I can possibly explain the proofs of why these problems are impossible without having to go to field theory? I mean I will go to field theory if I have to, but then again, no one would understand unless there is a way to easily explain field theory without using heavy duty concepts, like using polynomials etc.

it looks like that hist of math site has done all your research for you. just look up 1/2 dozen of the references & you're 90% of the way there. all you've got to do is write it up!

 

[gravenewworld]

Thanks a lot for your help. LOL while doing research on these problems, I found this interesting journal article. The legislature in Indiana actually tried to pass legislation in order to change the value of pi first to 4 and then to 3.2 so that the squaring the circle problem could be solved. The legislation actually made it through the House unanimously, but the Senate postponed voting on the bill indefinitely (it can still be voted on today).

 

[robert Ihnot]

I pointed this out before, but Archemedies did trisect the angle by using a paper strip.http://www.cut-the-knot.org/pythagoras/archi.shtml

The method is called "illicit," in the article, as if mathematicians were more busy inventing restrictions than solving problems. Quote from above: "It's thus specifically forbidden to use a ruler for the sake of measurement," WHY? Every student has one today.

This also leads to the fact, that in my day, some students believed that they would astonish the mathematical world by trisecting the angle and spent a great deal of time on that. Actually nobody in my high school class understood the difference between a straight edge and a ruler anyway, which was never gone into.

 

[matt grime]

There is also a theory of those constructions which allow a marked straight edge (ruler).