Transformações expansivas em um curso de educação matemática a distância online

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Topologically correct intersection curves of tori and natural quadrics

This thesis provides efficient and robust algorithms for the computation of the intersection curve between a torus and a simple surface (e.g. a plane, a natural quadric or another torus), based on algebraic and numeric methods. The algebraic part includes the classification of the topological type of the intersection curve and the detection of degenerate situations like embedded conic sections and singularities. Moreover, reference points for each connected intersection curve component are determined. The required computations are realised efficiently by solving quartic polynomials at most and exactly by using exact arithmetic. The numeric part includes algorithms for the tracing of each intersection curve component, starting from the previously computed reference points. Using interval arithmetic, accidental incorrectness like jumping between branches or the skipping of parts are prevented. Furthermore, the environments of singularities are correctly treated. Our algorithms are complete in the sense that any kind of input can be handled including degenerate and singular configurations. They are verified, since the results are topologically correct and approximate the real intersection curve up to any arbitrary given error bound. The algorithms are robust, since no human intervention is required and they are efficient in the way that the treatment of algebraic equations of high degree is avoided.

Desarrollo de aprendizajes activos en primeros cursos universitarios: Workshop cónica.

Como ya es conocido, los profesores de Matemáticas utilizamos los ejemplos como recursos de aprendizaje para enseñar algún contenido matemático concreto, de modo que las generalizaciones y abstracciones sean más fácilmente entendidas por los alumnos, pasando de lo concreto a lo abstracto, como otra forma de enseñar y practicar en Matemáticas. Esta metodología de trabajo se ve potenciada por el uso de dispositivos móviles llamados mobile-learning (m-learning) o educación móvil (educación-m), en español. Siguiendo esta línea de trabajo, se ha realizado el workshop de cónicas que se presenta en este artículo, empleando estas nuevas tecnologías (TIC) y con el objetivo de desarrollar aprendizajes activos en Geometría a través de la resolución de problemas en los primeros cursos de Grado en las ingenierías. ABSTRACT: As it is already known, math teachers, use examples as learning resources, to teach some specific math contents, so that generalizations and abstractions are more easily understood by students, from concrete to abstract, as another way of Mathematics teaching and training. This methodology is enhanced by the use of mobile devices, called mobile-learning (m-learning) o “educación móvil” (educación-m), in Spanish. Following this strategy, the workshop of conic sections shown in this paper has been carried out, using these new technologies (ICT) and in order to develop active learning in Geometry through problem-solving at the first years of engineering degrees.

Student mathematical notebook of Thomas Noyes, 1793

This sewn volume contains Noyes’ mathematical exercises in geometry; trigonometry; surveying; measurement of heights and distances; plain, oblique, parallel, middle latitude, and mercator sailing; and dialing. Many of the exercises are illustrated by carefully hand-drawn diagrams, including a mariners’ compass and moon dials.

Student mathematical notebook of William Emerson Faulkner, 1795

Leather hardcover notebook with unruled pages containing the handwritten mathematical exercises of William Emerson Faulkner, begun in 1795 while he was an undergraduate at Harvard College. The volume contains rules, definitions, problems, drawings, and tables on geometry, trigonometry, surveying, calculating distances, sailing, and dialing. Some of the exercises are illustrated by unrefined hand-drawn diagrams, including some of buildings and trees.

Student mathematical notebook of William Tudor, 1795

Notebook containing the handwritten mathematical exercises of William Tudor, kept in 1795 while he was an undergraduate at Harvard College. The volume contains rules, definitions, problems, drawings, and tables on geometry, trigonometry, surveying, calculating distances, sailing, and dialing. Some of the exercises are illustrated with hand-drawn diagrams. The Menusration of Heights and Distances section contains color drawings of buildings and trees, and some have been altered with notes in different hands and with humorous additions. For instance, a drawing of a tower was drawn into a figure titled “Egyptian Mummy.” Some of the images are identified: “A rude sketch of the Middlesex canal,” Genl Warren’s monument on Bunker Hill,” “Noddles Island,” “the fields of Elysium,” and the “Roxbury Canal.” The annotations and additional drawings are unattributed.

Die analytische und höhere geometrie in ihren elementen, mit vorzüglicher berücksichtigung der theorie der kegelschnitte...Erste fortsetzung seiner reinen elementar-mathematik.

Added title-page: Algebraische, geometrische und trigonometrische uebungen im gewande einer analytischen geometrie.

A discussion by synthetic methods of two projective pencils of conies

Presented as author's thesis.

Teoremi di Chasles : sopra le proprietà dei sistemi di coniche ([mu], [nu]), che servono di base alla determinazione del numero di queste curve, che soddisfanno a cinque condizioni qualunque :nota /

Includes bibliographical references.

Encyclopaedia of pure mathematics.

Articles reprinted from Encyclopaedia metropolitana.

Vorlesungen über synthetische Geometrie.

v. 1 Die Theorie der Kegelschnitte in elementarer Darstellung. Bearb. von Dr. C. F. Geiser. 3 Aufl.--v. 2 Die Theorie der Kegelschnitte, gestützt auf projectivische Eigenschaften. Bearb. von Dr. Heinrich Schröter. 2 Aufl.

Analytische geometrie der kubischen kegelschnitte,

Available on demand as hard copy or computer file from Cornell University Library.

Researches on curves of the second order, also on cones and spherical conics treated analytically, in which the tangencies of Apollonius are investigated, and general geometrical constructions deduced from analysis; also several of the geometrical conclusions of M. Charles are analytically resolved, together with many properties entirely original.

Available on demand as hard copy or computer file from Cornell University Library.

Die Theorie der Kegelschnitte, gestutzt auf projektivische Eigenschaften.

Mode of access: Internet.

Compendio delle sezioni coniche d'Apollonio : con aggiunta di nuove proprietá delle medesime seizioni /

Mode of access: Internet.