2007-12-21 03:19:48 · 5 answers · asked by Alexander 6 in Science & Mathematics ➔ Mathematics
Yes. It's possible. Though you can't normally trisect a given angle, in this case you can. It has to do with the fact that a straight line through the origin is an angle of 180 degrees, but this also equals pi, which in turn equals 7pi / 7pi.
Thus, if you replicate the given angle on the opposite side of the origin, the remaining angle between 3pi/7 and the 4pi/7 line you created is equal to pi/7, which is 1/3 of your original angle. All you have to do is replicate it twice between 3pi/7 and 0.
2007-12-21 03:37:29 · answer #1 · answered by We left and returned! 7 · 6⤊ 0⤋
I really hate interruptions which keeps me from answering interesting questions like this. The method is simple. 2/7 Ï is the chord angle of a heptagon, so first draw a circle, draw in 3/7 Ï, then use the compass to repeatedly mark the chord lengths around the circle until there are 7 points in it, at which you'll have trisected the original chord angle 3/7 Ï.
2007-12-21 11:34:07 · answer #2 · answered by Scythian1950 7 · 3⤊ 1⤋
Yes, in this case it is possible, because it is equivalent to the problem of measuring out 1 pint using a 3 pint jug (the given angle) and a 7 pint jug (the semicircle).
Double the angle in the usual way, using the compass. The small angle between the result and a straight line is precisely one-third of the given angle.
2007-12-21 13:59:36 · answer #3 · answered by bh8153 7 · 2⤊ 0⤋
I do not believe that it is mathematiacally possible to trisect this angle. There are several methods which approximate the trisection to a very high degree, but an absolute trisection seems to have been proved impossible by Guass.
Astrobuf
2007-12-21 11:43:10 · answer #4 · answered by astrobuf 7 · 0⤊ 1⤋
You may get some idea here
http://www.geom.uiuc.edu/docs/forum/angtri/
2007-12-21 11:55:54 · answer #5 · answered by Pranil 7 · 1⤊ 0⤋