Figure 8 - uploaded by Dominique Tournès
Content may be subject to copyright.
Source publication
Graphical tables (abaques and nomograms) can give rise to original activities for 16- to 18-year-olds with a strong historical and cross-curricular element. These activities lend themselves to a practical way of dealing with information and highlighting the changes in presentation (graphic, numerical, algebraic and geometric) as well as offering a...
Similar publications
The objective of this study was to analyze the conceptualization process in solving graph function problems based on the student perspective. Samples in this study were three students from the sains program in one of the best high school in West Jakarta region by the reason of testing results. This study has explored the completion of the problem a...
Citations
... We thus expect nomograms to easily fit in existing courses; in particular, nomography extends graphical approaches for computation to any equation that can be written in determinant form as in Eq. (3). Some personal experiences on nomograms for math education in high schools were reported in (Tournès, 2018); a test on their usefulness for university-level education would then be worthwhile to understand their strengths and limitations. We also believe that mentioning examples of nomograms, together with their uses and applications, within a course in Mechanics of Machines, could also enhance interest among students in historical methods for engineering analysis and in its broader historical development. ...
Computing formulae and solving equations are essential elements of scientific analysis. While today digital tools are almost always applied, analog computing is a rich part of the larger history of science and technology. Graphical methods are an integral element of computing history and still find some use today. This paper presents the history of nomograms, a historically-relevant tool for solving mathematical problems in various branches of science and engineering; in particular, we consider their role in mechanical engineering, especially for education, and discuss their mathematical properties. Each nomogram is a graphical description of a specific mathematical equation, designed such that the solution can be found through a simple geometric construction that can be performed with a straightedge. By design, using nomograms requires little skills and can be done even in adverse environments; a solution of sufficient accuracy for most purposes can then be found in a very short time. Another important advantage of nomograms is that they offer clear insight on the relationships between the variables, an insight which can be lost by looking at a complex equation. First introduced in the late \(19^{\textrm{th}}\) century, nomograms were used by engineers and scientists due to their speed with respect to manual calculations, before being superseded by computers. While now mostly obsolete in practice, nomograms can still prove useful in workshops and teaching classes: we thus also discuss their educational applications and present a few original examples.
... When entered in XY coordinates, the quadratic equation or parabolic equation will form a parabolic graph. On the coe cient, values a, b, and c determine the parabolic shape of the quadratic equation function in the XY coordinate (15). ...
... The coe cient c determines the intersection of the quadratic function formed by the y-axis or the value x = 0. If each function enters the value x = 0, it causes the intersection of the y-axis (15). The results of the zygomatic bone arch form a parabolic graph that opens downward so that it can determine the coe cient (a), which will be the benchmark of the average value in this study. ...
OBJECTIVE
Conventional methods for sex determination, such as zygomatic arch geometry and morphometry, are based on visual and linear anthropometric measurements. Considering the geographical condition of Indonesia, simple materials and methods for sex determination are important. Bali is a population that can represent the genetic population of Southeast Asia as it is one of the migration meeting points, and it has a unique O2a chromosomal lineage. Therefore the objective of this study was to verify a new simple method for sex determination using the zygomatic arch curvature. METHODS: A cross-sectional research was conducted involving 50 male and 50 female participants between the ages of 16 to 18. Brass wires were used to measure zygomatic arch curvatures. The data were processed using Microsoft Excel to produce a curve equation for sex determination and the size range of zygomatic bone arch length. RESULTS: The average yield and ranges right male zygomatic bone were coefficient a (-0.128 – -0.103), coefficient b (0.734–1.025), coefficient c (0.056–0.248), while the left were coefficient a (-0.138 – -0.098), coefficient b (-0.965 – -0.709), coefficient c (0.087–0.196). The right female range yields were coefficient a (-0.165 – -0.110), coefficient b (0.785–1.121), coefficient c (0.101–0.179), while the left were coefficient a (-0.142 – -0.111), coefficient b (-0.980 – -0.799), coefficient c (0.086–0.184). CONCLUSION: This new simple method can be used for forensic sex determination using zygomatic arch curvature based on a validated curve equation.
... (3). An experience on nomograms for math education in high schools was reported in [31]; a test on their usefulness for university-level education would then be worthwile to understand their strengths and limitations. We also believe that mentioning examples of nomograms, together with their uses and applications, within a course in Machine Mechanics, could also enhance students' interest in historical methods for engineering analysis and in the broader historical development of our field. ...
In this paper, we consider the history of nomograms as a computational tool in mechanical engineering, together with their potential applications for teaching purposes, and summarize the mathematical methods used to derive them. Nomograms are graphical descriptions of a mathematical problem, such that the desired solution may be derived through a simple geometric construction, which usually requires nothing more than a straightedge. This way, a reasonably accurate solution to a complex problem can be quickly obtained even in adverse environmental conditions by low-skilled users; moreover, a nomogram can provide immediate insight on the relationship between the variables. Nomograms date back to the 1800s and have been used by engineers for decades, due to their convenience over manual computation, before computers became widespread. While nomograms have now been largely superseded as engineering tools, our analysis shows that they can still have some applications in workshops and for teaching purposes.
