This project is an example of Computational Reasoning. It acts as a geometric theorems prover. More specifically, it is designed to prove Morley's Trisector Theorem (as of June, 2016).
Execute run.py script.
Activity Diagram
Class Diagram
input.txt file serves as an input source for the project. It contains data about the vertices
and the angles of a triangulated figure.
The first number n on the first line in input.txt denotes a number of triangles in the triangulated figure.
The second number m on the first line in input.txt denotes a dimension of the angles that constitute those triangles.
The following n lines denote the points (vertices) and angles of each triangle in the triangulated figure.
The program will process first n+1 lines in input.txt and neglect the remaining part.
The points are written as 3 non-zero, distinct integer numbers in clockwise order separated by a comma.
Example: 1, 3, 5
The angle is written as m integer/float values a b c separated by space, each of which is a coefficient
of an angle of the form aα + bβ + c, where α and β are variables.
The program is able to work with unknown angles. Unknown angles are written with a symbol x.
Example: -0.5 -1 1 60.0, for m = 4
Please note that you need to provide m number of coefficients for each point (vertex),
otherwise, the program will fail to run.
One line contains information about one triangle: three points and three angles, where group of points is separated by a semicolon from a group of angles. Please note that points and angles correspond to each other via their indices in the list.
- This is an example of an information about triangle with all known angles for
m = 3:
1, 3, 5; -1 -1 60, 0 1 0, 1 0 120
Vertices:1, 3, 5
Angles:-α - β + 60, β, α + 120 - This is an example of an information about triangle with one
unknownangle:
1, 5, 4; -1 -1 60, 0 1 60, x
Vertices:1, 5, 4
Angles:-α - β + 60, β + 60, unknown
The program processes only the first triangle configuration in input.txt.
Thus, you may store all your configurations in input.txt, and move the one of interest to the top
before running the program.
Preparing an input file may be frustrating at the first time, because any missed detail will lead to improper program work. Below are some examples of triangle configurations with 3 variable angles:
- Simple triangle that requires pairing (CLASSIC PYRAMID): [link] (https://drive.google.com/open?id=1FBQ49obyUkgOncR4zO6KU7kQ88qRqlQWlRiMV95feHQ)
- Morley triangle that requires pairing (MORLEY INCOMPLETE): [link] (https://drive.google.com/open?id=172aspdJkZt9o6HyFKOKixCu8vuHe9FLwtaipAVcAuM4)
- Generalized Morley triangle with all angles known (GENERALIZED MORLEY): [link] (https://drive.google.com/open?id=1iNWpIilNH_K_C657zRd4lBOg7BdvI69nyTdTjkCqxfI)
Some triangulated figures come with constraints as demonstrated here: [link]
(https://drive.google.com/open?id=1Co-chfuKsFyROpgChfybuGml94_yjnKcEUJ0IBFB54o)
Our program does not support constraints yet.
See:
- angle.py
- triangle.py
- triangulated_figure.py
- Object attributes start with _ (underscore). G.e. _object_attribute
- Triangle vertices are called triangle points (or simply, points), for convenience
- interior point
- dimension of angle
- angle points (Triangle)