The perfect compass: conics, movement and mathematics around the 10th century.

International audienceGeometry instruments certainly exist since men are interested in mathematics. These theoretical and practical tools are at the crossroads of the sensible world and mathematical abstractions. In the second half of the 10th century, the Arabic scholar al-Sijzı wrote a treatise on a new instrument: the perfect compass. At that time, several other mathematicians have studied this tool presumably invented by al-Quhı. Many works are now available in French and English translations. After an historical presentation of the perfect compass, this article deals with a few passages of al-Sijzı's treatise which show the importance of continuous tracing of curves and provide interesting elements on the role of instruments in the mathematical research process. All these texts can help to understand the importance of motion in geometry which can be easily simulated by geometry softwares and used in a geometry lesson or in teacher training sessions

Renaissance theories of vision

A collection of essays by leading art and architectural historians which examine treatises and works of art produced throughout Europe during the Renaissance in order to understand how artists and writers conceived of processes of vision and perception, and how those conceptions influenced the works of art. Keywords: Renaissance, vision, perception, optics, Plato (Meno, Republic, Symposium, Timaeus), Aristotle (De anima, Metaphysics, Nicomachean Ethics, Physics), Plotinus (Enneads), Saint Augustine (De Civitate Dei), Ibn Sina (Avicenna, Liber canonis), Ibn al-Haytham (Alhazen, De Aspectibus), Ibn Sahl, Marsilio Ficino (De amore, Theologia Platonica), Nicholas of Cusa (On Conjecture, On Learned Ignorance, On the Vision of God), Leon Battista Alberti (De pictura), Gian Paolo Lomazzo (Trattato della pittura), Gregorio Comanini (Il Figino), John Davies (Nosce Teipsum, Orchestra), René Descartes (Optics), Samuel van Hoogstraten, George Berkeley (A New Theory of Vision), Florence, Rome, Venice, England, Austria, Netherlands, Fra Angelico (Annunciation, Lamentation, Lamentation Over the Dead Christ), Donatello (Chellini Madonna, Coronation of the Virgin, Crucifix, Piot Madonna), Leonardo da Vinci (Last Supper, Notebooks, Treatise on Painting, Two Views of the Skull, Uffizi Annunciation, Vitruvian Man), Filippino Lippi (Delphic Sibyl), Giovanni Bellini (Agony in the Garden, Coronation of the Virgin), Raphael (Disputa, Holy Family, Jurisprudence, Madonna di Foligno, Parnassus, School of Athens, Sistine Madonna), Parmigianino (Self Portrait in a Convex Mirror), Titian (Assunta, Salome), Bronzino (Pygmalion and Galatea), Johannes Gumpp (Self Portrait), Rembrandt van Rijn (Bathsheba at Her Bath, Jeremiah Lamenting the Destruction of Jerusalem, The Jewish Bride, Lucretia, The Night Watch, Salome, Self Portrait, The Syndics, Titus, A Woman Bathing), Svetlana Alpers (The Art of Describing, Rembrandt’s Enterprise, The Vexations of Art), Thomas Aquinas (Summa Theologica, Commentary on the Sentences), Roger Bacon, Francesco Barozzi, Celeste Brusati (Artifice and Illusion), Norman Bryson (Looking at the Overlooked, Vision and Painting), Baldessare Castiglione (Libro del cortegiano), catoptrics, dioptrics, extramission, intromission, Benvenuto Cellini (Perseus), Giovanni Chellini, Antonio Correggio (Assumption of the Virgin), Georges Didi-Huberman (Fra Angelico), Samuel Edgerton (The Heritage of Giotto’s Geometry), Euclid (Elements of Geometry, Optica), Kamāl al-Dīn al-Fārisī (The Revision of Optics), Giovan Ambrogio Figino, Fra Bartolommeo, Fra Filippo Lippi (Annunciation), Piero della Francesca (De prospectiva pingendi), Galileo (Sidereus Nuncius), Galleria degli Uffizi, Galleria Doria Pamphili, Lorenzo Ghiberti (Commentaries), Domenico Ghirlandaio (Annunciation), Giles of Viterbo, Giorgione (Adoration of the Shepherds), Herbert Grabes (The Mutable Glass), Anthony Grafton (Leon Battista Alberti), Martin Heidegger (Poetry, Language, Thought), Edmund Husserl, Cristiaan Huygens, Immanuel Kant (Critique of Pure Reason), Martin Kemp (The Science of Art), Johannes Kepler, Alkindi (De Aspectibus), Murray Krieger (Ekphrasis), Diogenes Laertius (On the Lives of Philosophers), John Locke, Andrea Mantegna (Friedsam Madonna, St. Sebastion, Trivulzio Altarpiece), Giambattista Marino (La galeria), Masaccio (Tribute Money, Trinity), Museo San Marco, Narcissus, Neoplatonism, Agrippa von Nettesheim (De occulta philosophia), Erwin Panofsky, Platonic Academy, Pliny the Elder, Proclus (Commentary on the First Book of Euclid’s Elements), Ptolemy, Pythagoras, Peter Paul Rubens (Judith with the Head of Holofernes), William Shakespeare (The Rape of Lucrece, Venus and Adonis), Stanza della Segnatura, Giorgio Vasari (Vite), Vatican, Diego Velázquez (The Spinners), Johannes Vermeer (The Artist in His Studio, Girl with a Pearl Earring, View of Delft), Ernst van de Wetering (Rembrandt), Joost van den Vondel, Erasmus Witelo (Perspectivae), Heinrich Wölfflin (Principles of Art History

Experimental analysis of the breakage of a liquid bridge under microgravity conditions.

The experimental results obtained of the experiment \STACO" made on board the Spacelab D-2 Mission are analyzed. The conguration consisted of a liquid bridge between two solid supporting disks. An expected breakage occurred during the experiment. The recorded images are analyzed and the measured behaviour compared with the results of three dimensional model

Perception and Extramission in De quantitate animae

Augustine is commonly interpreted as endorsing an extramission theory of perception in De quantitate animae. A close examination of the text shows, instead, that he is committed to its rejection. I end with some remarks about what it takes for an account of perception to be an extramission theory and with a review of the strength of evidence for attributing the extramission the- ory to Augustine on the basis of his other works

Absorption and Screening in Phycomyces

In vivo absorption measurements were made through the photosensitive zones of Phycomyces sporangiophores and absorption spectra are presented for various growth media and for wavelengths between 400 and 580 mµ. As in mycelia, ß-carotene was the major pigment ordinarily found. The addition of diphenylamine to the growth media caused a decrease in ß-carotene and an increase in certain other carotenoids. Growth in the dark substantially reduced the amount of ß-carotene in the photosensitive zone; however, growth on a lactate medium failed to suppress ß-carotene in the growing zone although the mycelia appeared almost colorless. Also when diphenylamine was added to the medium the absorption in the growing zone at 460 mµ was not diminished although the colored carotenoids in the bulk of the sporangiophore were drastically reduced. Absorption which is characteristic of the action spectra was not found. Sporangiophores immersed in fluids with a critical refractive index show neither positive nor negative tropism. Measurements were made of the critical refractive indices for light at 495 and 510 mµ. The critical indices differed only slightly. Assuming primary photoreceptors at the cell wall, the change in screening due to absorption appears too large to be counterbalanced solely by a simple effect of the focusing change. The possibility is therefore advanced that the receptors are internal to most of the cytoplasm; i.e., near the vacuole

The geometry of sound rays in a wind

We survey the close relationship between sound and light rays and geometry. In the case where the medium is at rest, the geometry is the classical geometry of Riemann. In the case where the medium is moving, the more general geometry known as Finsler geometry is needed. We develop these geometries ab initio, with examples, and in particular show how sound rays in a stratified atmosphere with a wind can be mapped to a problem of circles and straight lines.Comment: Popular review article to appear in Contemporary Physic