In this paper, we investigate what appears to be an intermediate developmental stage in geometrical thinking according to Sfard’s commognitive framework. More specifically, we examine the change in three middle-school students’ mathematical discourse as they worked on a geometry construction problem within a virtual collaborative dynamic-geometry environment. We trace how their word use, use of...

The gradually varied surface was introduced and studied in digital and discrete spaces by Chen. The basic idea of introducing gradually varied surfaces is to employ a purely discrete interpolation algorithm to fit a discrete surface when the desired surface is not required to be “smooth.” In this paper, we generalize the concept of gradually varied surfaces. A digital surface is defined as a ma...

Over the last 50 years the world’s population and industrialization have soared leading to increased resource use, pollution and waste, and in turn to problems including raw materials shortage and unsustainable increases in landfill areas environmental, social and economic expectation stakeholders of the company every day more and more. Designing products with reuse at end of life in mind is a ...

[1] Humans are willful creatures. No other species on this planet has gained so much mastery over its own fate. We have neutralized countless threats that once killed us in the millions: we have learned to protect ourselves from the elements and predators in the wild; we have developed cures and treatments for many deadly diseases; we have transformed the small gardens of our agrarian ancestors...

The Universe could be spatially flat, positively curved or negatively curved. Each option has been popular at various times, partly affected by an understanding that models tend to evolve away from flatness. The curvature of the Universe is amenable to measurement, through tests such as the determination of the angles of sufficiently large triangles. The angle subtended by the characteristic sc...

This paper shows that the development from an agricultural regime through industrialization to a manufacturing regime occurs simultaneously to the demographic transition and the change in labor structure towards an increasing fraction of skilled labor due to technological progress. The manufacturing sector is economically viable when the technological level is sufficiently high. During the indu...

The industrial revolution transformed the cottage industry into mass production. In this chapter, the authors trace the recent advancement of the software industry and establish that it is following a similar route followed by the manufacturing industry towards industrialization. The chapter positions the concept of Software Product Lines (http://www.sei.cmu.edu/productlines/), as a possible fo...

New updated! The latest book from a very famous author finally comes out. Book of still crazy after all these years, as an amazing reference becomes what you need to get. What's for is this book? Are you still thinking for what the book is? Well, this is what you probably will get. You should have made proper choices for your better life. Book, as a source that may involve the facts, opinion, l...