In effective animation programming, one must be able to rely on theoretical knowledge as well as research-based insights in applicability. This updated version of Animation Maths contains an overview of both.
In addition to exploring collision detection, it also puts forward a discussion of programmable kinematics. These physics of motion, designed to complement programming, offer an invaluable tool in adding realism to games and animations. Furthermore, screen effects and image handling are taken to a professional level by a detailed outline of all the basic transformations.
The uniqueness of this book lies in its calculus-free approach. In order to cover the basics of the discipline, Animation Maths contains a brief summary of the fundamentals in arithmetics, solving systems and trigonometry. Animation Maths is accompanied by the website www.animationmaths.be which contains online support and useful downloads.
"Animation Maths achieves a perfect balance between deductive mathematics and broad accessibility, particularly through its interactive companion site." Leo Storme (Pure Mathematics and Computer Algebra, UGent) "With Animation Maths, Ivo De Pauw and Bieke Masselis present motion related mathematical subjects, ranging from trigonometry to quaternions and kinematics in an understandable fashion. It's a true game developers toolkit." Fries Carton (Guerrilla Games, Amsterdam)
Was there a beginning of time? Could time run backwards? Is the universe infinite or does it have boundaries? These are just some of the questions considered in an internationally acclaimed masterpiece by one of the world''s greatest thinkers. It begins by reviewing the great theories of the cosmos from Newton to Einstein, before delving into the secrets which still lie at the heart of space and time, from the Big Bang to black holes, via spiral galaxies and strong theory. To this day A Brief History of Time remains a staple of the scientific canon, and its succinct and clear language continues to introduce millions to the universe and its wonders.>
Près de 100 ans avant que Mondrian ne rende célèbres les lignes et formes géométriques rouges, jaunes et bleues, le mathématicien Oliver Byrne a utilisé un système chromatique similaire pour son édition de 1847 du traité de mathématique et de géométrie d'Euclide, Éléments. L'idée de Byrne était d'utiliser la couleur pour faciliter l'apprentissage et «diffuser un savoir permanent». Le résultat a été décrit comme l'un des livres les plus étranges et les plus beaux du XIXe siècle.
Le fac-similé de l'impressionnant ouvrage de Byrne est désormais disponible dans une magnifique édition. La beauté de ce chef-d'oeuvre artistique et scientifique vient autant de l'audace de ses calculs et diagrammes rouges, jaunes et bleus que de la précision mathématique et didactique des théories qu'il expose. La simplicité des formes et des couleurs annonce la vigueur future du Stijl et du Bauhaus. En rendant accessibles et esthétiquement plaisantes des informations complexes, ces graphiques sont aussi les précurseurs des infographies qui forment aujourd'hui largement les données que nous consommons.
As an introduction and history of geometric shapes that goes beyond shapes, the book offers thorough analyses on how geometric shapes emerge, develop and evolve in visual arts. How do shapes always successfully withstand the test of time? It is a secret hidden in the magnificent masterpieces by the great masters. Let's take a look in it and enjoy the beautifully constructed geometric visual language to the full.
In a study inspired by author's observation of the spiraling out of control use of mathematics by bankers, financiers and economists, the Western world's reliance on arithmetic and geometry is traced back, with support from the works of Medieval historian Alfred Crosby and of Anthropologist of Knowledge Paul Jorion, to its Medieval and Antiquity roots. The author bases on different areas such as philosophy with François Jullien's Chinese thought and Michel Bitbol with his epistemological reflections.
An exploration of one of the most celebrated and well-known theorems in mathematics.
By any measure, the Pythagorean theorem is the most famous statement in all of mathematics. In this book, Eli Maor reveals the full story of this ubiquitous geometric theorem. Although attributed to Pythagoras, the theorem was known to the Babylonians more than a thousand years earlier. Pythagoras may have been the first to prove it, but his proof-if indeed he had one-is lost to us. The theorem itself, however, is central to almost every branch of science, pure or applied. Maor brings to life many of the characters that played a role in its history, providing a fascinating backdrop to perhaps our oldest enduring mathematical legacy.
A stimulating intellectual history of Ptolemy's philosophy and his conception of a world in which mathematics reigns supreme.
The Greco-Roman mathematician Claudius Ptolemy is one of the most significant figures in the history of science. He is remembered today for his astronomy, but his philosophy is almost entirely lost to history. This groundbreaking book is the first to reconstruct Ptolemy's general philosophical system-including his metaphysics, epistemology, and ethics-and to explore its relationship to astronomy, harmonics, element theory, astrology, cosmology, psychology, and theology.
In this stimulating intellectual history, Jacqueline Feke uncovers references to a complex and sophisticated philosophical agenda scattered among Ptolemy's technical studies in the physical and mathematical sciences. She shows how he developed a philosophy that was radical and even subversive, appropriating ideas and turning them against the very philosophers from whom he drew influence. Feke reveals how Ptolemy's unique system is at once a critique of prevailing philosophical trends and a conception of the world in which mathematics reigns supreme.
A compelling work of scholarship, Ptolemy's Philosophy demonstrates how Ptolemy situated mathematics at the very foundation of all philosophy-theoretical and practical-and advanced the mathematical way of life as the true path to human perfection.
This cahier contains almost all the contributions to the two day meeting, commemorating the 70th year of the publication of Quine's seminal paper « New Foundations for Mathematical Logic », in which he describes for the first time the remarkable set theory NF. It contains also some other contributions which were prompted by this meeting.
This meeting follows the 50th meeting held in Oberwolfach in 1987, organized by M. Boffa and E. Specker in the presence of Quine, and the 60th anniversary meeting in Cambridge in 1997.
The two first papers are concerned with permutation techniques and unstratified formulae.
Next, R. M. Holmes shows a model of type theory wherein all elements are the denotations of closed terms.
In the two following articles, M. Crabbé and S. Tupailo show how to export results arising in NF to standard set theory.
Then, A. Tzouvaras explores different combinatorial techniques in order to reduce the consistency problem of NF.
The cahier ends with a tutorial on Constructive NF by T. E. Forster.
A négliger l'étude du langage pour aller directement aux choses, on ne fait que projeter dans l'être l'ombre portée du discours, de ses éléments, de ses articulations. Soutenu par cette conviction, Guillaume d'Ockham mène, au début du XIVe siècle, une analyse critique minutieuse des catégories logiques et métaphysiques léguées par Aristote, Porphyre et Boèce : entreprise de déréalisation qui ne conduit pas à un enfermement dans le langage, mais tout au contraire à une étude rigoureuse des modes selon lesquels les signes verbaux et conceptuels se rapportent aux choses existantes, dans leur réalité singulière. Les deux premières parties du troisième et dernier traité de la Somme de Logique correspondent aux Analytiques d'Aristote. L'étude du syllogisme en général est menée de façon systématique. II s'agit, en s'aidant de nombreux exemples, d'évaluer la validité des différentes combinaisons, selon les figures et modes traditionnels, mais aussi selon les diverses sortes de propositions. La théorie de la démonstration est quant à elle reformulée sur la base de la métaphysique de l'étant singulier et contingent, de la théorie de la connaissance comme contact direct avec la chose connue, et d'une conception purement logique de la nécessité.
If you could be invisible, what would you do? The chances are that it would have something to do with power, wealth or sex. Perhaps all three.
But there's no need to feel guilty. Impulses like these have always been at the heart of our fascination with invisibility: it points to realms beyond our senses, serves as a receptacle for fears and dreams, and hints at worlds where other rules apply. Invisibility is a mighty power and a terrible curse, a sexual promise, a spiritual condition.
This is a history of humanity's turbulent relationship with the invisible. It takes on the myths and morals of Plato, the occult obsessions of the Middle Ages, the trickeries and illusions of stage magic, the auras and ethers of Victorian physics, military strategies to camouflage armies and ships and the discovery of invisibly small worlds.
From the medieval to the cutting-edge, fairy tales to telecommunications, from beliefs about the supernatural to the discovery of dark energy, Philip Ball reveals the universe of the invisible.
"Lorsque la poésie critique entre en action dans la critique poétique, la chance d apprendre à penser mieux, c est-à-dire librement, s accroît. Les équations du bien penser et du bien parler s enivrent jusqu à faire surgir un écrire tendant vers l infini dans une explosion des temps. C est pareille tempête que nous propose la poésie de José Muchnik, nous invitant à « palper » de tout notre être-lecteur. (Traduction de l espagnol de Sara Yamila Muchnik et Yann Ludovic Henaff)"
For over fourty years, choosing a statistical model thanks to data consisted in optimizing a criterion based on penalized likelihood (H. Akaike, 1973) or penalized least squares (C. Mallows, 1973). These methods are valid for predictive model choice (regression, classification) and for descriptive models (clustering, mixtures). Most of their properties are asymptotic, but a non asymptotic theory has emerged at the end of the last century (Birgé-Massart, 1997). Instead of choosing the best model among several candidates, model aggregation combines different models, often linearly, allowing better predictions. Bayesian statistics provide a useful framework for model choice and model aggregation with Bayesian Model Averaging.
In a purely predictive context and with very few assumptions, ensemble methods or meta-algorithms, such as boosting and random forests, have proven their efficiency.
This volume originates from the collaboration of high-level specialists: Christophe Biernacki (Université de Lille I), Jean-Michel Marin (Université de Montpellier), Pascal Massart (Université de Paris-Sud), Cathy Maugis-Rabusseau (INSA de Toulouse), Mathilde Mougeot (Université Paris Diderot), and Nicolas Vayatis (École Normale Supérieure de Cachan) who were all speakers at the 16th biennal workshop on advanced statistics organized by the French Statistical Society. In this book, the reader will find a synthesis of the methodologies' foundations and of recent work and applications in various fields.
The French Statistical Society (SFdS) is a non-profit organization that promotes the development of statistics, as well as a professional body for all kinds of statisticians working in public and private sectors. Founded in 1997, SFdS is the heir of the Société de Statistique de Paris, established in 1860. SFdS is a corporate member of the International Statistical Institute and a founding member of FENStatS-the Federation of European National Statistical Societies.
MATHEMATICS IN CHINESE is aimed at Chinese language students with an elementary proficiency who want to be able to use Chinese to communicate about numbers, geometrical objects, coordinates, mathematical models, statistics, probabilities and calendars.
The book contains Chinese-English and English-Chinese lexicons.
MATHÉMATIQUES EN CHINOIS s'adresse aux élèves et étudiants qui possèdent un niveau élémentaire en chinois et souhaitent pouvoir communiquer dans cette langue sur les nombres, les objets géométriques, les coordonnées, les modèles mathématiques, les statistiques, les probabilités et les calendriers.
Ce livre contient des lexiques chinois-français et français-chinois.
Is headbanging a mathematical certainty? Can you turn a pile of batteries into a new proof? Can you use a cannon to beat Googol? What does a mathematician have against giant peas?
In his first book, David Eelbode uses mathematics - served with a more than generous splash of humour - to answer these questions, and much more. Using space as a metaphor and a captivating thread, he invites you to embark on a delightful trip to an absurd universe, where numbers and formulas meet low flying pianos and drunk wombats. So buckle up for this funny voyage to Planet Maths and its inhabitants!
Entre 1946 et 1953, les Conférences Macy ont réuni une communauté de chercheurs interdisciplinaires dont les travaux conjoints ont permis de définir les bases d'une science nouvelle, la cybernétique. Cette publication propose une transcription complète des contributions et des protocoles des dix conférences parmi les plus importantes de l'histoire contemporaine de la science.
An inviting, intuitive, and visual exploration of differential geometry and forms.
Visual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton's geometrical methods to provide geometrical explanations of the classical results. In the fifth act, he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner.
Unique features of the first four acts include: four distinct geometrical proofs of the fundamentally important Global Gauss-Bonnet theorem, providing a stunning link between local geometry and global topology; a simple, geometrical proof of Gauss's famous Theorema Egregium; a complete geometrical treatment of the Riemann curvature tensor of an n-manifold; and a detailed geometrical treatment of Einstein's field equation, describing gravity as curved spacetime (General Relativity), together with its implications for gravitational waves, black holes, and cosmology. The final act elucidates such topics as the unification of all the integral theorems of vector calculus; the elegant reformulation of Maxwell's equations of electromagnetism in terms of 2-forms; de Rham cohomology; differential geometry via Cartan's method of moving frames; and the calculation of the Riemann tensor using curvature 2-forms. Six of the seven chapters of Act V can be read completely independently from the rest of the book.
Requiring only basic calculus and geometry, Visual Differential Geometry and Forms provocatively rethinks the way this important area of mathematics should be considered and taught.
This book is devoted to Archimedes' modern works: direct consequences of his ideas, leading to progresses in presently unexplored, or poorly explored, domains of science.
This, at first sight, may look quite strange, because Archimedes died more than 2 200 years ago, and most people think that everything he did, no matter how clever he was, has been long ago incorporated by modern science, and that he belongs to the past. Certainly, he is considered as one of the greatest geniuses of all times, but people think that his heritage must be simply of historical value.
But this is not true at all, as this book clearly demonstrates. Two main ideas, namely the "Archimedes Maps" and "the Method", lead to completely new approaches of present problems, with far more powerful tools than the ones which were produced otherwise.
The present book is organized as follows:
We start with a quick and simple historical presentation, just in order to remind the reader about Archimedes' times. This book is not intended to address any preoccupation about history of mathematics. In the First Part, we present Archimedes Maps, and their applications to modern problems, such as monitoring, surveillance, resource allocation, and many others, with concrete examples to present concerns.
Archimedes' approaches provide interesting and relevant research subjects, the kind of research subject which will be appreciated by all Governments and funded by all Agencies. It relates deep old mathematics to new socially important preoccupations. The most hostile project director, hearing such topics, will fall onto his knees, start crying, and draw his checkbook.
The impatient reader, who wants to return to his modern computations, will ask: "Is that all?". Of course, a vast majority of scientists would be more than happy to see that their work is still useful 2 200 years after their death, and that it is used for socially important questions, carries unsolved problems and generates new research topics. A vast majority of scientists... But remember that here we deal with one of the greatest geniuses of all times. So it is not all, you have seen nothing yet. The benediction of the Governments and of the Agencies is not enough; Satan is in charge and Archimedes drives the show.
A second line of thought, developed in the second part of the present book, deals with the "weighing methods". The idea is to compare an unknown information to an artificially produced one (thus well known). Archimedes himself considered the "Method" as his masterpiece, and asked that the result (a sphere and a cylinder) should be engraved on his tomb. The Method was lost for more than 2 000 years, and, strangely enough, the mathematical contents were not rediscovered by anyone else during that time. This is strange indeed, because all classical concepts in mathematics, such as equations, polynomials, differential or integral calculus, were discovered independently many times, by many people, at many places. The Method is certainly not a classical concept; it does not fit with anything we know. It was discovered only once, and then lost.
The Method is a special case of general Greek Comparison Methods. But it is very special. Nobody knows how such an idea came to his mind, because there are no other examples. But the Method, as we see, is extremely powerful, and brings direct solutions to modern problems, such as electricity production. We present it in modern terms (which has never been done before) and investigate its modern applications to probabilities, systems of polynomial equations, optics, non destructive testing, and so on.
Then we give, for the reader's convenience, the few texts which present Archimedes life (mostly about the siege of Syracuse, 212 BC, when he died), and some comments about his abilities, compared to the abilities of modern mathematicians.
About the author : Bernard Beauzamy is a French mathematician, born 1949. He has been University Professor, 1979-1995. He established SCM SA in 1995, a company which does mathematical models. He has been chairman and CEO of this company since then. Among his previous books, "Introduction to Banach Spaces and their Geometry" and "Introduction to Operator Theory and Invariant Subspaces" have become classics.
In real life situations, one rarely has desirably detailed information. It is sometimes incomplete, sometimes corrupted, or with missing or erroneous data. Conversely, some pieces of information do exist. Therefore, there is a natural wish: to try to use the existing information in order to reconstruct some missing items. However, this should be done with two constraints:
First, one should not add any artificial information, such as model assumptions (for instance, that some growth is linear, or that some law is gaussian) ;
Second, the result should be of probabilistic nature: we do not want a precise value for the reconstruction, but a probability law, which allows estimation of the uncertainties.
This is precisely the topic of this book. We show how to "propagate" the information, from a place where it exists to a place where we want to use it; this propagation deteriorates with the distance, somewhat as a gravitational field decreases with the distance.
The book is organized in three parts: the first part presents the basic rules, accessible with no specific expertise in probabilities; the second presents the applications to real world problems, and the third part gives the theory.
This theory comes from a situation which is rather rare these days: a new mathematical theory, entirely developed by SCM in order to meet a need which was originally expressed by the Industry, namely Framatome ANP (today Areva) in 2003. Since then, the tool was used in many cases: classifying industrial objects (Air Liquide), evaluation of pollutions (Total), estimates for water quality in European rivers (European Environment Agency), applications to the safety of nuclear reactors (Institut de Radioprotection et de Sûreté Nucléaire), and so on.
About the authors :
Olga Zeydina, PhD in Probabilistic Methods for Nuclear Safety, has been Research Engineer at the Société de Calcul Mathématique SA, since 2006.
Bernard Beauzamy, University Professor (1979-1995), founded SCM SA in 1995 and since then has been Chairman of this company.
Le livre présente un thème important, qui se développe actuellement de façon intense, de l'analyse et la théorie stochastique contemporaines : les opérateurs, les semi-groupes et les processus stochastiques de Dunkl. Les motivations et les applications de ces sujets, à l'origine en provenance de la Physique (modèles quantiques intégrables), s'étendent aujourd'hui à de vastes domaines de l'analyse harmonique et du calcul stochastique, y compris les espaces symétriques, et les processus de diffusion à valeurs dans ces espaces.
Les auteurs du livre ont obtenu des résultats importants de la théorie de Dunkl. Le livre est écrit de façon accessible à des chercheurs ayant des connaissances standard en analyse harmonique et calcul stochastique.
The significance of the existence of the system is to realize its function and maintain its stability, that is, the reliability and stability of the reliability. Reliability is affected by factors, component properties and system structure, and its changes are complex. In order to solve this problem, the authors proposed the space fault tree theory in 2012. This book is the first time that the fundamental part of the theory has been presented internationally. The authors of the book are Pro. Tiejun Cui and Dr. Shasha Li.
The book introduces a hot topic of mathematics and computer science at the edge of hyperbolic geometry and cellular automata.
A hyperbolic space is a geometric model where through a given point, there are two distinct parallels to a given line. A cellular automaton is a set of cells which are uniformly distributed in a space, connected locally and update their states by the same rule.
The volume presents novel results on location of tiles in many tilings of the hyperbolic place. These results are employed to implement emerging non-classical types of cellular automata and offer insights of accessing and transferring information in hyperbolic spaces.
Hyperbolic geometry is an essential part of theoretical astrophysicists and cosmology, therefore ideas discussed in the book will play an important role in the theory of relativity.
Besides specialists of these traditional fields of application, many specialists of new domains start to show a growing interest both, to hyperbolic geometry and to cellular automata. This is especially the case in biology and in computer science.
The book is unique because it skilfully hybridizes two different domains of geometry and computation in a way beneficial for mathematics, computer science and engineering. The book is an outstanding treatise of concepts and implementations which will last for decades.