GRAPHICAL TRISECTION OF AN ANGLE1

Trisection, Pythagorean Angles, and Gaussian Integers

Pythagorean angles, that is angles with rational sines and cosines, provide an interesting environment for studying the question of characterizing trisectable angles. The main result of this paper shows that a Pythagorean angle is trisectable if and only if it is three times some other Pythagorean angle. Using the Euclidean parametrization of Pythagorean angles, this result allows an effective ...

Angle Trisection with Origami and Related Topics

It is well known that the trisection of an angle with compass and ruler is not possible in general. What is not so well known (even if it is folklore in the community of geometric constructions and mathematical paper folding) is that angle trisection can be done with other tools, especially by an Origami construction. In this paper we briefly discuss this construction and give a geometric and a...

development and implementation of an optimized control strategy for induction machine in an electric vehicle

in the area of automotive engineering there is a tendency to more electrification of power train. in this work control of an induction machine for the application of electric vehicle is investigated. through the changing operating point of the machine, adapting the rotor magnetization current seems to be useful to increase the machines efficiency. in the literature there are many approaches wh...

Graphical Abstracts

"square Trisection". Dissection of a Square in Three Congruent Partitions

A square trisection is a problem of assembling three identical squares from a larger square, using a minimal number of pieces. This paper presents an historical overview of the square trisection problem starting with its origins in the third century. We detail the reasoning behind some of the main known solutions. Finally, we give a new solution and three ruler-and-compass constructions. We con...