Trisecting a right angle with compass+straightedge

[G037H3]

I know the current impossibility of trisecting a random given angle with straightedge+compass.

My question is: is it possible to trisect a right angle using straightedge+compass, perhaps by creating a 60 degree and 30 degree angle, and then bisecting the 60 degree angle

or

by bisecting the right angle and then discerning a 15 degree angle one each side of the bisection so that three 30 degree angles are produced?

My last question wasn't answered, maybe this one will be ^_^

 

[Bill Simpson]

A well written summary of methods to trisect angles:

http://en.wikipedia.org/wiki/Angle_trisection

 

[G037H3]

Okay, so my idea of creating a 60 degree angle (1 angle in an equilateral triangle) is the correct method, it seems. I'm not going to go into depth about geometric constructions, as I am going to wait until after I've mastered Euclid's Elements and La Geometrie. :)

It was just a random thing that popped into my mind.

 

[JJacquelin]

For French readers, two reviews for general public :
" Trisection " : a brief review of the Ancient Greec problem of the angle trisection.
" Tracé d'un angle quelconque à la règle et au compas" : A very simple and accurate (but not theoretically exact) method.
http://www.scribd.com/JJacquelin/documents

 

[G037H3]

thank you for contributing to my thread

I unfortunately have not yet learned French, though I intend on doing so after Deutsch and perhaps Latin :)

 

[HallsofIvy]

I know the current impossibility of trisecting a random given angle with straightedge+compass.

Not just "current"- it is impossible and with the restriction to "straight edge and compass" will always be impossible.

My question is: is it possible to trisect a right angle using straightedge+compass, perhaps by creating a 60 degree and 30 degree angle, and then bisecting the 60 degree angle

or

by bisecting the right angle and then discerning a 15 degree angle one each side of the bisection so that three 30 degree angles are produced?

My last question wasn't answered, maybe this one will be ^_^

What are you talking about? Trisecting a right angle specifically? That's trivial. When we say it is impossible to trisect an angle with straight edge and compass we mean it is not possible to trisect an arbitrary angle that way- that there exist angles which cannot be trisected that way.

 

[G037H3]

Not just "current"- it is impossible and with the restriction to "straight edge and compass" will always be impossible.

I know, but I keep an open mind regarding the term "impossible".

What are you talking about? Trisecting a right angle specifically? That's trivial. When we say it is impossible to trisect an angle with straight edge and compass we mean it is not possible to trisect an arbitrary angle that way- that there exist angles which cannot be trisected that way.

Yes, what I wrote in the OP is exactly what I meant. As for the rest, I know.

What I was asking for was a specific method of trisecting a right angle, nothing else.

 

[g_edgar]

Euclid provided a method for constructing a right angle, and for constructing a 60 degree angle, thus for constructing a 30 degree angle. Thus it is possible to construct a 30 degree angle. This answers your question.

There are, more interestingly, certain cases where neither angle A nor angle A/3 can be constructed, but when A is given, then angle A/3 can be constructed from it.