Let us consider a hypothetical trisection analytical engine (as shown in the Figure below), consisting of
three equal straight line members,of length 2L each ,in the following configuration - the central arm AB being
stationary,with its two end-arms AC and BD free to rotate about it in the same plane.
Further,for convenience, let us assume the half-lengths (L) of the three arms to be of unit distance-eg.1cm.
and the initial starting position of the three arms to be perfectly aligned,ie. in-line.
Now, for an angular displacement of 1degree of each of the rotating arms,the end-points of the three line members
are directed towards a single point in the plane,having a displacement
x=OA=OB=OC'=OD'=1.1459301348013030973037736012513 metres.( This follows from the relation
Sin(theta)= (half-length of arm) / (displacement) = (L/x) , in triangle AOF')
For 1 millidegree ,or 0.001degree of rotation (equivalent to 3.6 seconds)
x= 1,145.9155902761908279693783984458 metres.
For 0.0001degree of rotation,
x=11,459.155902617918616402959700024 metres.
for 0.00001degree of rotation ,
x=1,144,591.55902616478719770064248914 metres.
For 1 micro-degree ,or 0.000001degree of rotation,(equivalent to 3.6 milli-seconds)
x= 1145915.5902616464320803735295682 metres.
For very fine angles of rotation of nano-degree,femto-degree,atto-degree and less .... the displacements
can be computed.
Thus it is a computational machine that very finely divides space(for the Paramanidean monist
who believes in the infinite divisibility of space!).A complete Nomogram of angle of rotation versus
displacement is impossible because of the infinite sheet of paper needed!
If such a fine mechanism exists in reality,then theoretcally it is possible to direct to
very distant points many light years away(!).And even without any digital
computer ,just by fractional changes of rotation and using a simple formula i
suggest viz. Sin(n x theta )= n x Sin (theta) where n and theta are very small quantities.
The trisection theorem,iterative trisection construction and trisection analytical
engine,are original creations of Professor Suresh Robert Norman.