Geometrical Construction

Geometrical Construction


the solution of certain geometry problems with the aid of auxiliary instruments (straightedge, compass, and others) that are assumed to be absolutely precise. Investigations of geometrical constructions have elucidated the range of problems that are solvable with the aid of an assigned set of instruments and have indicated the methods for solving these problems. Geometrical constructions are usually broken down into constructions on a plane and in space. Certain problems of geometrical constructions on a plane had been considered even in antiquity (for example, the famous problems of trisecting an angle, duplicating a cube, and squaring a circle). Like many others, they belong to problems of geometrical constructions with the aid of a compass and a straightedge. Geometrical constructions on a plane have a rich history. The theory of these constructions was worked out by the Dutch geometer G. Mohr (1672) and by the Italian engineer L. Mascheroni (1797). A considerable contribution to the theory of geometrical constructions was made by the Swiss scientist J. Steiner (1833). Only in the 19th century was the range of problems that are solvable with the aid of the aforementioned instruments ascertained. Specifically, the foregoing famous problems of antiquity are not solvable with the use of a compass and a straightedge.

Geometrical constructions on a Lobachevskii plane were studied by N. I. Lobachevskii himself. The general theory of such constructions and constructions on a sphere was developed by the Soviet geometer D. D. Mordukhai-Boltovskii.

Geometrical constructions in space are associated with the methods of descriptive geometry. The theory of geometrical constructions is of interest in that aspect related to practical applications in descriptive geometry.


Adler, A. Teoriia geometricheskikh postroenii, 3rd ed. Leningrad, 1940. (Translated from German.)
Chetverukhin, N. F. Metody geometricheskikh postroenii. Moscow, 1938.
Steiner, J. Geometricheskie postroeniia, vypolniaemye s pomoshch’iu priamoi linii i nepodvizhnogo kruga. Moscow, 1939. (Translated from German.)
Aleksandrov, I. I. Sbornik geometricheskikh zadach na postroenie s resheniiami, 18th ed. Moscow, 1950.


References in periodicals archive ?
Little more than a sturdy geometrical construction remains, suggestive of the skeletal remains of a skyscraper.
In a central statement, Raman describes the inevitability of the Sidney-Descartes connection: "If, for Descartes, geometrical construction converts the formal logic of algebraic analysis into an intuitive grasp of truth akin to divination, the turn inward to the heart in this sonnet [by Sidney] likewise achieves a re-vision; it changes the very mode of seeing: from the observation of a series of mechanical movements between causes and effects into an almost vatic insight into the totality of their deeper, underlying connectedness" (236).
Properties of a knitted fabric are determined by the internal geometrical construction of the yarn and fabric, as well as by chemical and mechanical treatment, applied to the yarn.
When is a geometrical construction exact and elegant?
In its symmetry and geometrical construction, "1001 Pages" wears its Islamic influences on its sleeve.
The main purpose of this research is to determine to what extent preservice teachers use visual elements and mathematical properties when they are dealing with a geometrical construction activity.
This is the world of Norman Cornish where paintings and drawings depict routine environments in an instinctive manner that outflanks their studied, geometrical construction.
The geometrical construction of the part model; identifying and defining the material properties; definition of finite elements; the definition of contour conditions and loadings for each heat transfer mode (convection, conduction or radiation) processing of nonlinear analysis and diagrams drawing of time variation.
In fact, even as they propose a geometrical construction that transforms the site architecturally, Verjux's works create a sensory experience that evolves according to one's mood or according to the time of day; the intensity of the electric light is softer in the natural light of day, and denser, more brilliant at night.
Like Panofsky, Damisch is impressed with the capacity of perspective--the geometrical construction used by artists to obtain the illusion of space--to correspond with "our" perceptual experience of the world.