Geometry for elementary academy Bisecting an bend

 11 September 19:03   

    In this chapter, we will apprentice how to bifurcate an angle. Accustomed an bend $angle\; ABC$ we will bisect it to two according angles. The architecture is based on [http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI9.html book I, hypothesis 9]




    # Accept an approximate point D on the articulation $overline$.





    # $circ\; B,overline$.





    # Let E be the circle point of $overline$ and $circ\; B,overline$.





    # $overline$.





    # on $overline$ with third acme F and get $riangle\; DEF$.





    # $overline$.





    # The angles $angle\; ABF$, $angle\; FBC$ according to bisected of $angle\; ABC$.

    # $overline$ is a articulation from the centermost to the ambit of $circ\; B,overline$ and accordingly equals its radius.

    # Hence, $overline$ equals $overline$.

    # $overline$ and $overline$ are abandon of the boxlike triangle $riangle\; DEF$.

    # Hence, $overline$ equals $overline$.

    # The articulation $overline$ equals to itself

    # Due to the triangles $riangle\; ABF$ and $riangle\; FBC$ congruent.

    # Hence, the angles $angle\; ABF$, $angle\; FBC$ according to bisected of $angle\; ABC$.

    We showed a simple adjustment to bisect an bend to two. A accustomed catechism that rises is how to bisect an bend into additional numbers.

    Since Euclid’s days, mathematicians looked for a adjustment for , adding it into 3. Alone afterwards years of trials it was accurate that no such adjustment exists back such a architecture is impossible, using alone adjudicator and compass.

    # Acquisition a architecture for adding an bend to 4.

    # Acquisition a architecture for adding an bend to 8.

    # For which additional amount you can acquisition such constructions?