Descriptive geometry

At this point in the development, although geometry provided a common framework for all the forces, there was still no way to complete the unification by combining quantum theory and general relativity. Since quantum theory deals with the very small and general relativity with the very large, many physicists feel that, for all practical purposes, there is no need to attempt such an ultimate unification. Others however disagree, arguing that physicists should never give up on this ultimate search, and for these the hunt for this final unification is the ‘holy grail’. Michael Atiyah

The search for this “cup that overflow” is at the heart of all who venture for the lifeblood of the mystery of life. While Atiyah speaks to a unification of Quantum theory and Relativity, it is not without a understanding on Einstein’s part that having gained from Marcel Grossmann, that such a descriptive geometry could be leading Einstein to discover the very basis of General relativity?

Marcel Grossmann was a mathematician, and a friend and classmate of Albert Einstein. He became a Professor of Mathematics at the Federal Polytechnic Institute in Zurich, today the ETH Zurich, specialising in descriptive geometry.

So what use “this history” in face of the unification of the very large with the very small? How far back should one go to know that the steps previous were helping to shape perspective for the future. Allow for perspective to be changed, so that new avenues of research could spring forth

Gaspard Monge, Comte de Péluse-Portrait by Naigeon in the Musée de Beaune Born: 9 May 1746 in Beaune, Bourgogne, France
Died: 28 July 1818 in Paris, France-was a French mathematician and inventor of descriptive geometry.

Monge contributed (1770–1790) to the Memoirs of the Academy of Turin, the Mémoires des savantes étrangers of the Academy of Paris, the Mémoires of the same Academy, and the Annales de chimie, various mathematical and physical papers. Among these may be noticed the memoir “Sur la théorie des déblais et des remblais” (Mém. de l’acad. de Paris, 1781), which, while giving a remarkably elegant investigation in regard to the problem of earth-work referred to in the title, establishes in connection with it his capital discovery of the curves of curvature of a surface. Leonhard Euler, in his paper on curvature in the Berlin Memoirs for 1760, had considered, not the normals of the surface, but the normals of the plane sections through a particular normal, so that the question of the intersection of successive normals of the surface had never presented itself to him. Monge’s memoir just referred to gives the ordinary differential equation of the curves of curvature, and establishes the general theory in a very satisfactory manner; but the application to the interesting particular case of the ellipsoid was first made by him in a later paper in 1795. (Monge’s 1781 memoir is also the earliest known anticipation of Linear Programming type of problems, in particular of the transportation problem. Related to that, the Monge soil-transport problem leads to a weak-topology definition of a distance between distributions rediscovered many times since by such as L. V. Kantorovich, P. Levy, L. N. Wasserstein, and a number of others; and bearing their names in various combinations in various contexts.) A memoir in the volume for 1783 relates to the production of water by the combustion of hydrogen; but Monge’s results had been anticipated by Henry Cavendish.

Descriptive geometry

Example of four different 2D representations of the same 3D object

Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions, by using a specific set of procedures. The resulting techniques are important for engineering, architecture, design and in art. [1] The theoretical basis for descriptive geometry is provided by planar geometric projections. Gaspard Monge is usually considered the “father of descriptive geometry”. He first developed his techniques to solve geometric problems in 1765 while working as a draftsman for military fortifications, and later published his findings. [2]

Monge’s protocols allow an imaginary object to be drawn in such a way that it may be 3-D modeled. All geometric aspects of the imaginary object are accounted for in true size/to-scale and shape, and can be imaged as seen from any position in space. All images are represented on a two-dimensional drawing surface.

Descriptive geometry uses the image-creating technique of imaginary, parallel projectors emanating from an imaginary object and intersecting an imaginary plane of projection at right angles. The cumulative points of intersections create the desired image.

So given the tools, we learnt to see how objects within a referenced space, given to such coordinates, have been defined in that same space. Where is this point with in that reference frame?

What is born within that point, that through it is emergent product. Becomes a thing of expression from nothing? It’s design and all, manifested as a entropic valuation of the cooling period? Crystalline shapes born by design, and by element from whence it’s motivation come? An arrow of time?

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