computational geometry

2012_01_19-text-th

Here is a simple explanation about the famous Euclidean Constructions: Why didn’t Euclid just measure things with a ruler and calculate lengths? For example, one of the basic constructions is bisecting a line (dividing it into two equal parts). Why not just measure it with a ruler and divide by two? One theory is the the Greeks could not easily do arithmetic. They had only whole numbers, no zero, and no negative numbers. This meant they could not for example divide 5 by 2 and get 2.5, because 2.5 is […]

2012_01_19-text-th

When I was younger, among the branches of philosophy, I had studied a little logic and, among the subjects of mathematics, geometrical analysis and algebra, three arts or sciences which looked as if they ought to contribute something to my project. But in looking at them, I took care, because, so far as logic is concerned, its syllogisms and most of its other instructions serve to explain to others what one already knows or even, as in the art of Lully, to speak without judgment of things about which one […]

2012_01_19-text-th

Here is the preface of the famous book “Architectural Geometry”. It simply encourages me to learn new things every day even sometimes it seems to become impossible. Geometry lies at the core of the architectural design process. It is omnipresent, from the initial form-finding stages to the actual construction. Modern constructive geometry provides a variety of tools for the efficient design, analysis, and manufacture of complex shapes. This results in new challenges for architecture. However, the architectural application also poses new problems to geometry. Architectural geometry is therefore an entire […]

2012_01_19-text-th

Here are two passages from Shamos’s dissertation thesis, where he is looking at history of geometry from perspective of a computer scientist. Egyptian and Greek geometry were masterpieces of applied mathematics. It is well established that the original motivation for tackling geometric problems was the need to tax lands accurately and fairly and to erect buildings (Eves, 72). As often happens, the mathematics that developed has permanence and significance that far transcends Pharaoh’s original revenue problem. It is a field in which intuition abounds and new discoveries are within the […]

2012_01_19-text-th

…While it is true that every curve which can be described by a continuous motion should ve recognized in geometry, this does not mean that we should use at random the first one that we meet in the construction of a given problem. We should always choose with care the simplest curve that can be used in the solution of a problem, but it should be noted that the simplest means not merely the one most easily described, nor the one that leads to the easiest demonstration or construction of […]

2012_01_19-text-th

Searching for a meaning to today’s popular design methods and concepts we are all going after. Most of the abstract problems, today described within architectural domains, are very paralell to another field defined by M. Ian Shamos in 1978. Here is the introduction paragraph of his phD thesis; Geometry is a subject that has captured the imagination of Man for at least 2500 years. It is at the very foundation of Art, Architecture, and Mathematics, and plays a central role in a host of other areas. Computer Science, by contrast, […]