How does a single acorn produce an intricate structure of branches and leaves? How do migrating birds organize into sweeping patterns across the sky? How does a grounded caterpillar acquire wings and the gift of flight? These are just a few of many questions that arise by observing nature with a keen and watchful eye. By addressing these questions, Pierre Doucet and Paul Doucet are inspired to ask an even deeper question. Is the complexity of nature designed or the result of chance events over time?
Through an extensive inquiry into the natural world, they uncover a number of timeless principles that shed light on the question of design or chance. The authors show how these principles offer a rational explanation for the complexity of nature, and also how they apply to the unfolding of life. The Landscape of Reality provides an evidence-based perspective that is grounded in science and nature. From this framework readers are invited to examine their own lives. They will see how the timeless principles in nature—and the universe as a whole—have a profound influence on the nature of reality, and finally, on their unique life experience.
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these are indeed very true indeed and first important as is observed and well stated observed prof by prof dr mircea orasanu and prof drd horia orasanu and followed that this or these books influenced our considered as is can be observed and contributed at development of other domains or stimulated thus Euclid poses the five “requests” that, according to him, define planar geometry. These postulates would become the keystone for all of geometry, a system of absolute truths whose validity seemed irrefutable. One of the reasons for this faith is that these postulates seem obvious: the first of them stipulates that a straight line passes between two points, the second that any line segment can be indefinitely prolonged in both directions, the third that, given a point and an interval, it is always possible to trace out a circle having the point for its center and the interval as its radius, the fourth that all right angles are equal to each other.
now for the problem are considered other aspects as for BOOK or post observed prof dr mircea orasanu and prof drd horia orasanu and followed , of high standards for the field. They represent the judgement of an (anonymous) jury of distinguished scholars of international stature. The jury for the 2003 awards was chaired by Prof. Michèle Artigue of the University Paris 7.
ICMI is proud to announce the first awardees of the Klein and Freudenthal Medals.
The Felix Klein Medal for 2003 is awarded to Guy Brousseau, Professor Emeritus of the University Institute for Teacher Education of Aquitaine in Bordeaux, for his lifetime development of the theory of didactic situations, and its applications to the teaching and learning of mathematics.
The Hans Freudenthal Medal for 2003 is awarded to Celia Hoyles, Professor at the Institute of Education of the University of London, for her seminal research on instructional uses of technology in mathematics education.
Presentation of the medals, and invited addresses of the medallists, will occur at ICME-10 in Copenhagen, July 4-11, 2004.
1. here we see as say prof dr mircea orasanu and prof horia orasanu how followed
FUNDAMENTAL CONSIDERATIONS AND ANALYTICAL MECANICS
here must consider sime aspects alculus
approximated area is
By mean-value theorem,
where . As is chosen such that , the approximated area is
Thus, it is nature to ask if in general for a function with antiderivative
Theorem 15 (fundamental theorem of calculus):
Let be continuous on . If is any antiderivative of on , then
[justifications of theorem 15:]
Since be continuous on , then exists. Let
Then, by mean value theorem,