DESARGUES' THEOREM: PROOF ON A PLANE USING THE COORDINATE METHOD
Rubrics: MATHEMATICS AND MECHANICS
Authors:
1.
Bauman Moscow State Technical University
(Asssociate Professor)
Russian Federation
Russian Federation
Type:
Article
Pages:
from 73
to 76
Status:
Published
Received:
17.02.2026
Accepted:
17.02.2026
Published:
17.02.2026
Subject area:
UDC 514.146.01
Language:
Russian
Keywords:
Desargues' theorem, projection onto a plane, coordinate method
Abstract:
The proof of Desargues' theorem on the plane is obtained in the computer's model space using the coordinate method of space transformation. The essence of the method [3] is the regular reduction of the dimensionality of the finite 3D geometric model of the shape that defines this space when visualized in an axonometric view. This allows for solving problems on a two-dimensional plane, avoiding the classical method of projecting space onto a projection plane. To fulfill the conditions of Desargues' theorem, two related triangles are constructed in the standard isometric form: one of them is the base of any straight prism, and the second triangle is the section of this prism. Graphical constructions have found, and mathematical calculations have confirmed, the intersection of the related sides of the triangles at points belonging to the axis of kinship 𝑠𝑠 0 .
The proof of Desargues' theorem on the plane is obtained in the computer's model space using the coordinate method of space transformation. The essence of the method [3] is the regular reduction of the dimensionality of the finite 3D geometric model of the shape that defines this space when visualized in an axonometric view. This allows for solving problems on a two-dimensional plane, avoiding the classical method of projecting space onto a projection plane. To fulfill the conditions of Desargues' theorem, two related triangles are constructed in the standard isometric form: one of them is the base of any straight prism, and the second triangle is the section of this prism. Graphical constructions have found, and mathematical calculations have confirmed, the intersection of the related sides of the triangles at points belonging to the axis of kinship 𝑠𝑠 0 .
Keywords:
Desargues' theorem, projection onto a plane, coordinate method
Desargues' theorem, projection onto a plane, coordinate method
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