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Nomographs (or nomograms, or alignment charts) are graphical representations of mathematical relationships (extending to empirical relationships of data) which are used by simply applying a straightedge across the plot through points on scales representing independent variables, which then crosses the corresponding datum point for the dependent variable; the choice among independent and dependent variable is arbitrary so that each variable may be determined in terms of the others. Examples of nomographs in common current use compute the lift available for a hot-air balloon, the boiling points of solvents under reduced pressure in the chemistry laboratory, and the relative forces in a centrifuge in a biochemical laboratory. Sundials represent another ancient yet widely familiar example. With the advent and ready accessibility of the computer, printed mathematical tables, slide rules and nomographs became generally redundant. However, nomographs provide insight into mathematical relationships, are useful for rapid and repeated application, even in the absence of calculational facilities, and can reliably be used in the field. Many nomographs for various purposes may be found online. This paper describes the origins and development of nomographs, illustrating their use with some relevant examples. A supplementary interactive Excel file demonstrates their application for some simple mathematical operations. [ABSTRACT FROM AUTHOR]

A method based on oblique projection is presented for construction of sundials. The derived formulas are classical, but usage of vectors and projections renders a coherent presentation rather than a number of special cases. The presented work is aimed to be useful for those taking a beginning module on vector algebra. [ABSTRACT FROM AUTHOR]

An ancient horizontal marble sundial unearthed at Pompeii is described and discussed in terms of the following: the meaning and astronomical significance of the Greek shorthand inscriptions on the object, and its design and functioning as a time-keeping device on the basis of hyperbolic shadow projection by a vertical gnomon. Detailed calculations are carried out for the epoch just prior to the volcanic eruption, of the astronomical coordinates of representative stars in the constellations recorded on the sundial, as well as the solar coordinates required for the evaluation of the shadow markings. These calculations not only confirm the high quality of the workmanship displayed in the construction of the sundial, but enable an accurate estimate to be made of the original length of the missing gnomon: 2 digiti = 1/8 pes in Imperial Roman units. [ABSTRACT FROM AUTHOR]

The author reflects on the presentation of architect Amir Freundlich regarding the sundial discovered by Lieutenant Henry Kitchener in Palestine in 1875. Topics discussed include the sundial is azimuth type with main upright of the instrument lying in the meridian plane, the sundial was surrounded by a green wooden fence, and the importance of Kitchener as pioneer in the archaeological exploration of Palestine.

An ‘infinite decreasing sequence of Gnomons’ is characteristic, according to Proclus, of incommensurability, hence David Fowler's idea to reconstruct Theodorus’ proofs of incommensurabilities, reported in theTheaetetus147d, employing Gnomons, is attractive and solidly based. The ‘preservation of the shape of the Gnomons’ is a form of the Pythagorean principle of the Limited according to Aristotle. In the present paper we propose a reconstruction that employs Gnomons but is free of the drawbacks present in Fowler's reconstruction. [ABSTRACT FROM PUBLISHER]

The article discusses the findings of the 2014 report of the Portable Antiquities Scheme (PAS). It offers detailed description of reported antiques includes ivory diptych sundial from the 16th or early 17th century found by Lara Maiklem, copper-alloy strap mounts from 17th century found by finder Tim Camm, and heart-shaped copper-alloy halfpenny trade token from the 17th century found by Kevin Gutteridge.

Like their students, teachers may hold a variety of naïve conceptions that have been hypothesized to limit their ability to support students’ learning. This study examines whether changes in elementary students’ conceptions are related to their teachers’ content knowledge, attitudes, and understanding of conceptual change. The study takes place in the context of the adoption of a new unit on seasonal change in which students build and use sundials to observe seasonal differences in the apparent motion of the Sun across the sky. A mixed-method approach is used. Data sources include pre- and post-tests for students and teacher interviews and questionnaires. Results indicate that changes in students’ conceptions may be related to their teachers’ knowledge of the content, attitudes toward science, and understanding of conceptual change. One teacher had low attitude toward science and limited knowledge of conceptual change. After instruction, her students’ responses became less accurate but more homogeneous than before instruction. The other teacher had high attitude and moderate knowledge of conceptual change. Her students showed gains from pre- to post-test, including responses that were more scientifically accurate than the teachers’ initial answers. [ABSTRACT FROM AUTHOR]

The first attempt at a classification of sundials appeared only in 1953, in the catalogue established by Henri Michel for the Museum of Liège. It was immediately followed, in the same year, by the article by Kathleen Higgins, exclusively dedicated to this topic. The influence of this second study has spread out throughout the numerous articles on sundials that have been subsequently published. The aim of the present paper is to bring some order to these two old classifications, which are in fact quite similar and were sufficiently valid at the time, and to propose a new approach to the problem based, for the first time, on principles directly linked to astronomy and geometry. Moreover, this latter approach has the advantage of a flexibility in its application to all kinds of sundial collections. [ABSTRACT FROM AUTHOR]

Résumé Le cadran solaire analemmatique est présenté pour la première fois par un mathématicien français, appelé Vaulezard, dans un petit fascicule publié en 1640. Suit un deuxième ouvrage, plus complet, en 1644. Dernier venu, ce cadran attire l'attention d'importants savants tels que Foster et Lalande. Parfait dès le départ, il a néanmoins la singulière particularité d'inspirer diverses tentatives d'amélioration, plutôt infructueuses, et d'être à l'origine de quelques variétés de cadrans analemmatiques qui, elles, connaissent un franc succès. Nous apportons la preuve trigonométrique et, pour la première fois semble‐t‐il, la preuve géométrique de sa validité astronomique en suivant fidèlement la méthode de construction indiquée par Vaulezard. Nous effectuons, en outre, un survol aussi exhaustif que possible des différents modèles dérivés de ce cadran ainsi que de la littérature les concernant. Summary The analemmatic sundial was briefly presented for the first time in 1640 by the French mathematician Vaulezard and was described in more detail by him in 1644. The analemmatic dial is the last genuine sundial to be invented and it has attracted the attention of some important scholars such as Foster and Lalande. Although perfect from the very beginning, it had the unusual particularity of inspiring several unfortunate attempts at its improvement as well as being at the origin of a few other types of analemmatic dials, which met with a certain success. We provide here the trigonometric proof and for the first time, the geometric proof of its astronomical validity by closely following the construction method of Vaulezard. We also make a comprehensive survey of the different kinds of analemmatic sundials and of their literature. [ABSTRACT FROM AUTHOR]

The article focuses on activity programs in science education for increasing students' understanding of the sun. The Shadow Play activity is meant to be the first step to help eventual conceptual understanding of shadows. The activity includes posters that have suggestions for children's books on shadows and the sun in other cultures that can be linked to language arts and fine arts, as well as an obvious physical education link to "shadow tag." Measuring shadow lengths and making bar graphs may help the students make predictions. Technological design is a minor element in the Equatorial Sundial activity. Middle level students already know how to tell time and have noticed the sun's apparent motion across the sky. They may have studied seasons or wondered about daylight savings time. The sundial is one of mankind's oldest inventions, but few students realize it is more than a decoration in public spots and gardens. Students in the field test expected that "clock time" and "sun-dial" time would match. Links to social studies and geography and to mathematics have been suggested.

Provides a historical overview of the sundial. Construction of sundials in Egypt; Influence of the development of geometry and trigonometry; Applications of sundials during the Middle Ages; Types and craftsmanship of sundials.

Presents a design of a portable sundial which does not require a compass. Premise in Kepler's first law; Measurement of time in the portable sundial.

Describes the use of altitude sundials for seasonal and equal hours. Determination of the corresponding dial patterns; Advantages of altitude dials; Usability of pocket electronic calculator.

Focuses on the seasonal-hour sundials on vertical and horizontal planes. Characteristics of seasonal-hour planar dials; Comparison between true and equiangular dial patterns; Difficulty of ancient timekeeping system.

Focuses on the acquisition of four fragments of a portable sundial with associated calendrical gearing. Description of the sundials; Influence of the Byzantine mathematical gearing on the Islamic tradition; Historical significance of the sundials.

Two Islamic brass scientific instruments, each bearing a map of the world for finding the direction and distance to Mecca, have come to light since 1989. They both appear to date from Safavid Iran, possibly from the late seventeenth century. Each is a copy of a different earlier map of the same kind, and both these derive from a more elaborate prototype. They are the only known surviving Islamic world maps with localities properly marked on a competently drawn coordinate grid. Serious activity in mathematical cartography, including the preparation of detailed world maps, is known to have started in Baghdad in the ninth century, and it is likely that the highly sophisticated cartographic grids on the Safavid world maps were first developed several centuries before these two maps were made. [ABSTRACT FROM PUBLISHER]

The article focuses on children's activities for teaching basic astronomy concepts with the help of two trade books "The Moon Book," by Gail Gibbons and "Anno's Sundial," by Mitsumasa Anno. Students can get information about the Moon from the book "The Moon Book." With the help of the book "Anno's Sundial," students can learn about the Sun's apparent movement. Students can learn about the Earth's movements by examining shadows through the use of sundials. The first activity is for grade 3, and requires the students to draw the Moon's shape for each evening. Then they can compare the various shapes of the moon over several weeks. The second activity is for grade 4-6 students in which they need to observe the movement of a shadow and how it changes over time. This observation can then be used to understand the pattern of sunrise and sunset.

A correction to an article about Kitchener's sundial published in a 2016 issue is presented.

Presents information on the activity of building a sundial in the classroom for students to watch instead of a clock. What the sundial is made up of; Explanation of basic ideas involved in the constructing of the sundial.

Presents various information related to literature. Details of Howard Mumford Jones' compression of American literature; Information on the replicas of ancient Greek sundials.

The article reports that the American Association of Textile Chemists and Colorists (AATCC) in the U.S. recently dedicated what it hopes will be a thousand year tribute to its 270 charter members. A bronze sundial bearing the name of each member was formally installed on the north lawn of the AATCC Technical Center in research Triangle Park in North Carolina during the association's regular spring meetings on April 27, 1972. On the other hand, a gift from the association's Golden Jubilee Conference in Boston was presented on behalf of the conference committee by E. J. Chornyei of Bradford Dyeing Association, chairman of the Boston conference.