Thesis (Ph.D.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / The present stuqy is an investigation of the effects of two parameters of the spiral aftereffect. Clinical psychologists have been interested in aftereffect research because of the possibility of utilizing the phenomenon as a diagnostic tool for brain damage. The parameters which were studied are frequoocy of stmulation (FS) and boundary velocity (BV). Frequency of stimulation is the frequency with which a given retinal element is stimulated by a contour (boundary) of the moving stimulus. The frequency of stimulation for the spiral is defined as the product of number of spiral arms and rotational velocity. In this study, variations in frequenqy of stimulation were effected by varying the number of spiral arms. Boundary velocity is the velocity with which a given contour (boundary) passes across a retinal element. In the spiral, boundary velocity corresponds to the rate of expansion or contraction, and it is proportional to: [(Rotational Velocity) x (Visual Angle Subtended by Spiral)]/(Number of Spiral Turns) Variations in boundary velocity were effected by simultaneously varying number of spiral arms and rotational velocity in such a way that frequency of stimulation remained constant and boundary velocity varied. In this study, a population of responses was sampled from two male subjects, each of Whom viewed five Archimedes spirals rotated at four rotational velocities. The spirals were drawn with one, two, four, eight, and sixteen arms, and were rotated at 40 rpm, 80 rpm, 160 rpn, and (all except the sixteen arm spiral) at 320 rpm. Each spiral-speed combination was repeated three times each day for eight days, resulting in a total of 24 replications for each spiral-speed combination. The dependent variable was the aftereffect, as measured by extent and duration. [TRUNCATED] / 2031-01-01

Thesis--Copenhagen. / "De arenae numero" (p.[169]-200) is in Greek.

The Conics of Apollonius remains a central work of Greek mathematics to this day. Despite this, much recent scholarship has neglected the Conics in favor of works of Archimedes. While these are no less important in their own right, a full understanding of the Greek mathematical corpus cannot be bereft of systematic studies of the Conics. However, recent scholarship on Archimedes has revealed that the role of secondary commentaries is also important. In this thesis, I provide a translation of Eutocius' commentary on the Conics, demonstrating the interplay between the two works and their authors as what I call conjugate. I also give a treatment on the duplication problem and on compound ratios, topics which are tightly linked to the Conics and the rest of the Greek mathematical corpus. My discussion of the duplication problem also includes two computer programs useful for visualizing Archytas' and Eratosthenes' solutions.

No description available.

This dissertation investigates the appropriation of material from one scientific field into another in the early Hellenistic period, 300-150 BCE. Appropriation from one science into another led to the emergence of new concepts in a community of scientists. Herophilus of Chalcedon’s appropriation of musical rhythms led to the emergence of the pulse as a materio-semiotic object for Rationalist physicians. Archimedes of Syracuse’s appropriation of mechanical concepts of weighing led to the emergence of the mechanical method as a scientific way of seeing for practicing mathematicians. But objects and concepts emerging from cross-scientific appropriation had ideological consequences for scientific methodology within individual scientific communities. Archimedes prioritized a formal Euclidean proof over that offered by the mechanical method because of the standards of proof demanded by the community of practicing mathematicians. The sect of Empiricist physicians rejected Rationalist medicine and promoted the individual doctor’s role and authority as a medical caregiver. The dissertation’s sum tells a story of increasing but limited strategies of naturalization within the sciences of the early Hellenistic period. / text

Thesis (Ph.D.)--Rochester Institute of Technology, 2008. / Typescript. Includes bibliographical references (p. 175-179) and index.

This diploma thesis suggests some ideas how to use historical mathematical texts in today's mathematics teaching. The theoretical part introduces the historical context of original texts which have become the basis for this thesis. In the practical part, several ideas how to implement these texts are suggested, designed and tested.

Orientador: Otília Terezinha Wiermann Paques / Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-26T19:52:15Z (GMT). No. of bitstreams: 1 Roveran_AdilsonPedro_M.pdf: 4768820 bytes, checksum: c1af27275416644cbfcfa08f6a1c3bd4 (MD5) Previous issue date: 2015 / Resumo: Este estudo tem por objetivo construir um caminho, norteado pelo pensamento geométrico grego, partindo da ideia de equivalência de figuras planas até chegar a estimativas do número pi, conquista de Arquimedes, passando pelas quadraturas de figuras planas e pela busca da quadratura do círculo. Uma conquista importante, a quadratura das lúnulas de Hipócrates de Chios ao lado do cálculo da área do círculo, pelo método de Arquimedes servem de incentivo ao uso da História da Matemática no Ensino de Matemática, que é o tema central dessa pesquisa. As atividades propostas no terceiro capítulo pretendem refazer um caminho, por construções geométricas e raciocínio algébrico dessa busca, desde as quadraturas de polígonos, até a estimativa do valor do número pi, para a sala de aula / Abstract: This study aims to build a path, guided the Greek geometric thought, based on the idea of equivalence between areas of plane figures to the estimate of the number pi, achievement of Archimedes, through the squaring polygons and the pursuit of squaring the circle. An important achievement, the squaring of the lunulae Hippocrates of Chios and the calculating of the circle area, by Archimedes method, serve to encourage the use of the History of Mathematics in Mathematics Teaching, which is the central theme of this research. The activities proposed in the third chapter intend to retrace a path for geometric constructions and algebric reasoning that quest, since the squaring of polygons, to determine the value of the number pi, for the use in the classroom / Mestrado / Matemática em Rede Nacional / Mestre

This diploma thesis describes historical evolution of calculation of sphere's volume and surface and provides an analysis of textbooks for secondary and primary schools. It is made with the intention to inspire high school teachers with various approaches of teaching the volume and surface of solid bodies. It can help teachers with motivation of students as well as with selection of textbook and teaching methods for the issue. This thesis is meant to inspire high school students interested in history of mathematics, too. It includes analysis of preserved exercises on the topic from ancient Egypt and Mesopotamia as well as findings from Archimedes' works, which were devoted to this topic. Moreover it describes contribution of enlighteners on the subject and shows exact procedures of derivation of formulas using integral calculus.

Syftet med studien är att bidra med kunskap om hur elever i årskurs 1–3 förståroch förklarar det fysikaliska fenomenet flyta och sjunka. Studien ämnar ävenatt utforska hur en praktisk aktivitet kan bidra till att synliggöra och skapa endjupare förståelse för begreppen Arkimedes princip och densitet för elever pålågstadiet. För att besvara studiens syfte valdes en designbaserad forskningsansats där en aktivitet designades och utfördes med 31 elever i årskurserna 1–3. Aktiviteten spelades in på video- och röstfiler som senare analyserades tematiskt.Resultaten visar att eleverna har viss kunskap om varför vissa saker flyter ochandra sjunker. Resultaten visar även att den praktiska aktiviteten bidrar till attsynliggöra begreppen Arkimedes princip och densitet på ett tydligt sätt vilketvisar att även de yngsta eleverna kan närma sig fysikens begrepp och teorier.När lärare i de lägre årskurserna låter eleverna tidigt börja närma sig och arbetamed naturvetenskapliga begrepp så läggs en bra grund inför kommande studieri de naturvetenskapliga ämnena. / The purpose of this study is to contribute with knowledge about how pupils ingrades 1-3, understands and explain the physical phenomenon of floating andsinking. The study also aims to explore how a practical activity can help tomake the physical phenomenon visible and create a deeper understanding ofthe concepts of Archimedes' principle and density for pupils in primary school.To answer the purpose of the study, a design-based research approach waschosen where an activity was created and performed with 31 pupils in grades1-3 in Sweden. The activity was recorded on video and voice files which werelater analyzed thematically.The results show that the pupils have some knowledge of why some thingsfloat and others sink. The results also show that the practical activity contributes to making the concepts of Archimedes' principle and density visible in aclearer way, which shows that even the youngest pupils can approach physicalconcepts and theories. When teachers in the lower grades allow pupils to startapproaching and working with scientific concepts at an early stage, a goodfoundation is laid for future studies in the natural science subjects.