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Beautiful Mathematics is about beautiful mathematical concepts and creations. Mathematical ideas have an aesthetic appeal that can be appreciated by those who have the time and dedication to investigate. Mathematical topics are presented in the categories of words, images, formulas, theorems, proofs, solutions, and unsolved problems. Readers will investigate exciting mathematical topics ranging from complex numbers to arithmetic progressions, from Alcuin's sequence to the zeta function, and from hypercubes to infinity squared. Do you know that a lemniscate curve is the circular inversion of a hyperbola?   That Sierpiński’s triangle has fractal dimension 1.585… .?   That a regular septagon can be constructed with straightedge, compass, and an angle trisector?   Do you know how to prove Lagrange’s theorem that every positive integer is the sum of four squares?   Can you find the first three digits of the millionth Fibonacci number?  Discover the keys to these and many other mathematical problems.  In each case, the mathematics is compelling, elegant, simple, and beautiful. Who should read Beautiful Mathematics? There is something new for any mathematically-minded person. High school and college students will find motivation for their mathematical studies. Professional mathematicians will find fresh examples of mathematical beauty to pass along to others. Within each chapter, the topics require progressively more prerequisite knowledge. An appendix gives background definitions and theorems, while another gives challenging exercises (with solutions).

Mathematics. --- Math --- Science --- Mathematics --- Mathematics - Miscellanea --- Mathematics - Popular works

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« Amateur de sciences » comme on dit « amateur d’art », Bruno Latour a rédigé chaque mois pour la revue La Recherche son journal de passion en nous parlant de la science en train de se faire, du travail des disciplines, de la profession de chercheur, mais aussi de politique des sciences, de controverses, de vaches folles, de momie… D'un ton vif, tantôt allègre et tantôt polémique, ces courtes chroniques très imagées sont une initiation plaisante et synthétique pour ceux qui voudraient goûter à cette nouvelle approche des sciences sociales, la sociologie de la traduction, qui remet en cause l’ennuyeuse distinction entre « littéraire » et « matheux ».

Science --- Social aspects --- Sciences --- Aspect social. --- Miscellanea --- Aspect social --- Miscellanées --- Physical Sciences & Mathematics --- Sciences - General --- Miscellanées --- Social aspects. --- Science - Social aspects --- Science - Miscellanea --- chroniques --- histoire des sciences

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Sacred Thresholds. The Door to the Sanctuary in Late Antiquity offers a far-reaching account of boundaries within pagan and Christian sanctuaries: gateways in a precinct, outer doors of a temple or church, inner doors of a cella . The study of these liminal spaces within Late Antiquity – itself a key period of transition during the spread of Christianity, when cultural paradigms were redefined – demands an approach that is both interdisciplinary and diachronic. Emilie van Opstall brings together both upcoming and noted scholars of Greek and Latin literature and epigraphy, archaeology, art history, philosophy, and religion to discuss the experience of those who crossed from the worldly to the divine, both physically and symbolically. What did this passage from the profane to the sacred mean to them, on a sensory, emotive and intellectual level? Who was excluded, and who was admitted? The articles each offer a unique perspective on pagan and Christian sanctuary doors in the Late Antique Mediterranean.

Doors --- Senses and sensation in architecture --- Architecture and religion --- Boundaries --- Borders (Geography) --- Boundary lines --- Frontiers --- Geographical boundaries --- International boundaries --- Lines, Boundary --- Natural boundaries --- Perimeters (Boundaries) --- Political boundaries --- Borderlands --- Territory, National --- Religion and architecture --- Religion --- Architecture --- Religious aspects --- History --- Miscellanea --- Thresholds (Doorsills) --- Senses and sensation in architecture. --- Religious aspects. --- Miscellanea. --- Shrines --- Doors - Religious aspects. --- Architecture and religion - History - To 1500. --- Boundaries - Miscellanea. --- Thresholds (Doorsills).

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An inventive examination of a crucial but neglected aspect of architecture, by an architect writing to architects.

Architecture --- Buildings --- Edifices --- Halls --- Structures --- Human factors in architecture --- Human engineering --- Architecture and society --- Human factors. --- Maintenance and repair --- Environmental engineering --- Maintenance --- Miscellanea. --- ARCHITECTURE/Architectural Theory & Criticism --- ARCHITECTURE/Architectural History/Contemporary Architecture --- Constructions --- Miscellanea --- Facteurs humains --- Entretien --- Miscellanées --- 72.025 --- Monumentenzorg --- Restauratie (architectuur) --- Renovatie (architectuur) --- Design architectural --- Design architectural. --- Facteurs humains. --- Entretien. --- Entretien des bâtiments --- Processus de conception --- Art --- outdoor sculpture --- maintenance --- architecture [object genre] --- preserving --- architectural conservation --- Built environment

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The extraordinary array of images included in this volume reveals the full and rich history of the Middle Ages. Exploring material objects from the European, Byzantine and Islamic worlds, the book casts a new light on the cultures that formed them, each culture illuminated by its treasures. The objects are divided among four topics: The Holy and the Faithful; The Sinful and the Spectral; Daily Life and Its Fictions, and Death and Its Aftermath. Each section is organized chronologically, and every object is accompanied by a penetrating essay that focuses on its visual and cultural significance within the wider context in which the object was made and used. Spot maps add yet another way to visualize and consider the significance of the objects and the history that they reveal. Lavishly illustrated, this is an appealing and original guide to the cultural history of the Middle Ages.

Civilization, Medieval --- Civilization --- Barbarism --- Civilisation --- Auxiliary sciences of history --- Culture --- World Decade for Cultural Development, 1988-1997 --- Medieval civilization --- Middle Ages --- Chivalry --- Renaissance --- History --- Civilization, Medieval - Miscellanea --- Civilització medieval --- Miscel·lànies --- Civilització europea medieval --- Cultura europea medieval --- Cultura medieval --- Edat mitjana --- Cavallers i cavalleria --- Civilització --- Renaixement --- Història