I know there is a proof that angles can not be TRISECTED,but does it really mean we should give up the search for any possible method?
Below is a TRISECTION procedure(I ever sent to a Board of Discussion ).
And I need the comments of this Board's members:either in FAVOUR or AGAINST with REASONS:
I need to reserve the calculations involved in the proof of the Trisection Procedure and go straight to an Undisputable(Practical) proof:
It is not by chance/guess that an(y) angle can be TRISECTED ; but has a Concrete Proof from a familiar but hidden Rule/Law I have Discovered which Scientists/Mathematecians have failed to Notice/Apply since the Dawn of maths to Trisect angles.
It States: The radius of any circle divides its own circumference into six(6) equal parts,when turned/rotated around it.In the TRISECTION sense:"The radius of any semi-circle divides its arc(i.e.,semi-circle) into three(3) equal parts"and hence the angle it sub-tends.
Did you know this? Because whoever knew this(Theorem) and would still argue that an angle can not be TRISECTED is denying himsef of knowledge.
TRISECTION OF ANGLES 2ND VERSION:where the angle is 180 degrees or less
This procedure is Similar to the first version but gives a very CLEAR PICTURE of the THEOREM stated above:
To Trisect angle OAB:
With O as a centre use any reasonable radius to mark an arc accross angle OAB.
With a straight edge join the arc intersects with line OA and OB,name this line alpha(line A).
Now bisect angle OAB and name the bisector line beta(line B),preferably short-dashes line.
Use the point of intersection of the two(2) lines as a centre and adjust the compass to the radius of half(1/2) line alpha and construct a semi-circle/circle between the lines OA & OB.
With the same radius use line alpha intersection line OA as a centre and mark arc alpha along the circle and next,arc alpha as a centre mark another arc beta towards line OB.
[you can decide to repeat this procedure from line OB to obtain arc gamma(arc G) and arc omega(arc W) to ascertain accuracy].
Now join the arc(s) intersects along the circle/semi- circle to centre O with a straight edge and measure the three(3) seperate angles.
[if Construction/Drawing were possible on this board,my illustrations would have cleared all the doubts].
Now your comments.
NOTE:
There is SCARCELY perfection in DIVISIONS(esp.,Angles):
For the division of an angle into "n" equal parts;beside Human Error,a deviation of ±[n/n1/n]° is an avoidable is some special Cases; where n=No. of divisions.
And for multiple/repeated divisions,
deviation=±[(n/n1/n)x (n1/n)r],where r=No. of repetitions.
eg for trisection deviation maximum=±[3/31/3]=2.08°.
If an angle is bisected and again (bisected)a deviation of [(2/21/2)x(21/2)11]°=2° is possible.
Dark Orange Text means index or raised to the power
Thank you.
Its Domayele,
Greeting(s) from Ghana.