Search

I purchased my first mechanical analog computer in 1962, when I was an electrical engineering freshman at the University of Illinois. It was distributed by The Fredrick Post Company of Chicago, but manufactured by The Hemmi Bamboo Slide Rule Company Ltd. in Japan. The model I obtained was the Versalog 1460 slide rule (slipstick) with the cordovan color leather case (Figure 1). This was the essential basic engineering tool for all mathematical computations required by students in the electrical engineering program at the university. Using the slide rule effectively required applying the fundamental rules of use coupled with one's intuitive engineering skills. You had to figure out where the place value of the decimal point was in your answer since the slide rule didn't keep track of this. Your intuition helped to quickly solve this issue.

Compensators are polarization microscopy accessories that enable precise measurements of optical retardation. The Berek compensator is a type of compensator invented in the early twentieth century. Despite being still widely in use today, a comprehensive description of its inner workings, derived from first principles, is absent from the modern literature, rendering this instrument inaccessible to students and researchers new to the field. In this tutorial article, we first establish through geometrical optics the fundamental relation giving the variable retardation induced by the compensator as a function of its tilt angle. We then shed light on the approximate relation that is still universally given in the manufacturers’ manuals—which seem to not have been updated since the slide rule era. We then discuss a third tilt–retardation relation, obtained within the more rigorous framework of wave optics. Lastly, we detail the principle of operation of the instrument. We hope that this article becomes a go-to resource for the new generation of scientists looking for an in-depth introduction to the Berek compensator.

Perhaps, in the Far Distant back of times, man in his need to somewhat quantify what he had collected to survive (animals or plants or fruits), needed to count, and his own fingers and toes became a good first instrument always available, so that easily got to 20 units. And his system was digital, quite advanced, in contrast with the slide rule we try to deal with herein, which is analogical, so that the figure above has nothing to do with the slide rule. An apology is kindly offered to the reader for the unintended mixture we got in.

Introduction: In persons with type 1 diabetes (T1D) insulin dosing can be adjusted based on trend arrows derived from continuous glucose monitoring (CGM). We propose a slide rule with narrower blood glucose intervals and more classes of insulin sensitivity than are available in current models. Methods: The slide rule was tested in silico, in which a meal was simulated in 100 virtual subjects and the insulin bolus was calculated either in the standard way based on the insulin-to-carbohydrate ratio and the correction factor or according to the slide rule, following which the percentage time spent in range (70–180 mg/dl; %TIR), hypoglycemia (< 70 mg/dl; %THYPO), and hyperglycemia (> 180 mg/dl; %THYPER) was compared between the methods during the 4 h after the meal. Slide rule performance was also tested in real life by analyzing the same variables at during the 4 h postprandial period in 27 individuals with T1D. Only meals starting while the rate of change was at least 1 mg/dl per minute (increasing or decreasing) were considered for analysis. Results: In silico, when the preprandial trend arrow was increasing, our slide rule reduced %THYPER and increased %TIR (p < 0.05), whereas when the preprandial trend arrow was decreasing, it reduced %THYPO and slightly increased %THYPER (p < 0.05). In real life, our slide rule kept subjects on target for 70.8 and 91.6% of postprandial time when preprandial trend arrows were increasing or decreasing, respectively. Conclusion: The proposed slide rule performed well both in silico and in real life, suggesting that it could be safely adopted by individuals with T1D to improve glucose control.

Diese Arbeit beschäftigt sich mit der Thematik der Regenwasserversickerung mithilfe von Bodenfiltermulden und wie die Dimensionierung dieser mittels eines Planungshilfsmittels vereinfacht werden könnte. Für jegliche Art von Bauwerken im urbanen Bereich ist Regenwasserentsorgung zunehmend von Bedeutung. Gute Ideen aus den Wettbewerben scheitern oft an der Umsetzbarkeit aufgrund von Platzmangel und hohen Kosten, die aber bei frühzeitiger Einbindung der Systeme, in der Vorentwurfsphase, planbar bzw. vermeidbar wären. Das Ziel der Arbeit ist die Konzeptionierung dieses Hilfsmittels und beschreibt die Zusammenhänge der einzelnen Parameter sowie die Anwendungsgrenzen und Voraussetzungen. This paper deals with the topic of rainwater infiltration with the help of soil filter troughs and how the dimensioning of these could be simplified by means of a planning aid. Rainwater disposal is becoming increasingly important for all kinds of buildings in urban areas. Good ideas from competitions often fail due to lack of space and high costs, which could be planned or avoided if the systems were integrated early on in the preliminary design phase. The aim of the work is to conceptualise this tool and describe the interrelationships of the individual parameters as well as the application limits and prerequisites.

The advanced scientific lectures, in which the contents the learners had not yet learned are utilized, have been held in Naruto University of Education from 2013. The number of the students who finished the learning was almost one hundred in the previous course. Three students who were in the 5th，6th and 7th grade joined the advanced mathematics lecture course in 2016. In this paper, we show the contents of mathematics lecture course the three students attended, especially the consideration about the net of the torus and the principle of the slide rule. Through the experience of teaching them in the advanced mathematics lecture course, we reconstruct teaching materials − the net of torus and the principle of the slide rule − for higher grade school students. We also show teaching plans for the upper school year students in this paper. We already held the lesson of the net of the torus for high school students according our teaching plan. In our future work, we will try to make the lesson of the principle of the slide rule in high school and university, and we would like to discuss about teaching materials and teaching plans.

For the last decades approach to mathematical calculations has changed radically. On change by the account, to arithmometers, slide rules and calculators computers have come. The expert not able to put into practice knowledge to make mathematical calculations by means of the computer can be hardly considered as a high quality. In order that it was possible to use the computer for the solution of mathematical tasks it is necessary to construct at first mathematical, and then and computer model of this task. In article the analysis of a concept of model is carried out the place of the substantial line “Formalization and modeling” in a school course of informatics are analyzed and methodical recommendations for increase in learning efficiency of the substantial line “Formalization and modeling in a school course of informatics” are offered.In article the analysis of the basic concept of the Formalization and modeling in a school course of informatics is carried out features of studying of the Formalization and Modeling line in a school course of informatics in different textbooks. The article will be useful to teachers of informatics and also the student studying mathematics to teachers, and also the experts as obliges facing need of mathematical data processing, creation of mathematical and computer models and interpretation of the received results.

O presente trabalho tem como objetivo apresentar uma atividade contendo uma situação problema norteadora que descreve a taxa de crescimento da população infectada por uma doença viral. Sua solução envolve a função exponencial na criação de um modelo e a aproximação de valores de logaritmos de base 10 com a régua de cálculo. Essa atividade faz parte da dissertação de Mestrado de uma das autoras que busca voltar a atenção dos educadores para a utilização de situações-problema e material manipulativo como ferramentas que visam despertar o interesse e a participação dos discentes no processo de ensino e aprendizagem. Com o intuito de verificar a eficiência de tais estratégias didáticas no ensino da Matemática, realizou-se uma pesquisa com alunos do primeiro ano do Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS). Os resultados obtidos sugerem que os recursos didáticos utilizados são cativantes e capazes de aproximar o mundo matemático dos discentes.

In the December 2016 issue of I&M Magazine, there is a fine bit of history about the rise and fall of the slide rule [1]. The slide rule as used for multiplication and division qualifies as an analog computer, and analog computing will be the topic of this column. The best way to understand how a slide rule works is to make one. I started with a piece of semilog graph paper. Interestingly, some companies-Keuffel and Esser is an example-manufactured both slide rules and many styles of graph paper. I began with an image of semilog graph paper. The vertical axis of this paper is a logarithmic scale, while the horizontal axis is linear. I rotated the image clockwise by 90° and snipped it to produce Fig. 1. The logarithmic scale is now horizontal. I also reproduced the original labels on the top and bottom of the snippet.

Historically, the practice of medicine has been a physically intimate endeavor. Physicians have used their hands to palpate and reveal the secrets hidden within the body. Smelling the breath for the ketosis of diabetes or tasting the skin for the saltiness of cystic fibrosis were among the physician's essential practices. Today, perhaps the most defining characteristic of a brilliant clinician is the ability to synthesize many images-from electrocardiograms, ultrasounds, CT scans, and so forth-into a coherent picture that can guide our diagnosis and treatment. Yet this is rapidly becoming a Sisyphean task. Just as we are about to drown in a deluge of data, AI is throwing us a life preserver, to save not only our patients but ourselves. But where will AI take us?

Irrigated urban landscapes must increasingly maintain economic and ecosystem value with less water in response to drought amplified and shifted by climate change. Efficient landscape water management requires estimating water amount demanded by plants that can be replaced by irrigation to meet minimum performance expectations. The extant approach to estimating landscape water demand is conceptually muddled and often regionally inappropriate. Simplified Landscape Irrigation Demand Estimation (SLIDE) Rules distills scientifically credible assumptions about urban landscape biological and physical complexity into guidelines for estimating water demand that are conceptually accessible and operationally useful. SLIDE Rules are: 1) oasis urban reference evapotranspiration (ETo) effectively represents water use of urban turf seasonally and for day-to-day irrigation scheduling, but is less accurate for estimating water use of non-turf surfaces, especially in dry climates; 2) a discrete number of Plant Factors (PF) adjust ETo to estimate water demand of general landscape plant type categories—turf, non-turf, and desert—that are adjusted for temperature and drought responses; 3) a hydrozone controlled by one irrigation valve is the smallest landscape unit manageable for water, thus overall zone irrigation is governed by the highest water demand plant within that hydrozone; 4) for hydrozones

Figure 1 is a build-it-yourself contraption that could be used to add numbers. It consists of a dial numbered from 0 to 9.9 by tenths and a similarly numbered face upon which the dial is intended t...

Esta dissertação busca voltar à atenção dos educadores para a utilização de quatro metodologias de ensino: Situações Problema, Tecnologias da Informação e Comunicação, História da Matemática e Material Concreto, tendo como objetivo apresentar atividades diferenciadas envolvendo o estudo de funções exponenciais e logarítmicas. Estas ferramentas visam despertar o interesse e a participação dos discentes no processo de ensino e aprendizagem. Com o intuito de verificar a eficiência de tais estratégias didáticas no ensino da Matemática, realizou-se uma pesquisa com alunos do primeiro ano do Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS). Os resultados obtidos sugerem que os recursos didáticos utilizados são cativantes e capazes de aproximar o mundo matemático dos discentes. This dissertation intends to show the use of four teaching methodologies: problem solving, information and communication technologies, History of Mathematics and manipulatives. This study aims to present differentiated activities involving the teaching of exponential and logarithmic functions. The use of these methodologies should enhance students interest on the learning process. In order to verify the efficiency of the practice and the didactic strategies applied to build the activities, students of the first year of the Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS) were invited to solve them. The results obtained suggest that the didactic resources used are attractive and capable of bringing the mathematical world closer to the students.

Printed accounts of the appearance and use of various forms of slide rule appear in a variety of 18th and early 19th American printed sources. Based largely on British work, these texts reveal both confidence in the practical potential of the instrument and the slow diffusion of the device.

A main goal in DNA computing is to build DNA circuits to compute designated functions using a minimal number of DNA strands. Here, we propose a novel architecture to build compact DNA strand displacement circuits to compute a broad scope of functions in an analog fashion. A circuit by this architecture is composed of three autocatalytic amplifiers, and the amplifiers interact to perform computation. We show DNA circuits to compute functions sqrt(x), ln(x) and exp(x) for x in tunable ranges with simulation results. A key innovation in our architecture, inspired by Napier's use of logarithm transforms to compute square roots on a slide rule, is to make use of autocatalytic amplifiers to do logarithmic and exponential transforms in concentration and time. In particular, we convert from the input that is encoded by the initial concentration of the input DNA strand, to time, and then back again to the output encoded by the concentration of the output DNA strand at equilibrium. This combined use of strand-concentration and time encoding of computational values may have impact on other forms of molecular computation.

Q uick and accurate tree height measurement has always been a goal of foresters. The techniques and technology to measure height were developed long ago—even the earliest textbooks on mensuration showcased hypsometers (e.g., Schlich 1895, Mlodziansky 1898, Schenck 1905, Graves 1906), and approaches to refine these sometimes remarkable tools appeared in the first issues of Forestry Quarterly, Proceedings of the Society of American Foresters, and the Journal of Forestry. For example, one such hypsometer based on the geometric principle of similar triangles (top of Figure 1) employed rotary mirrors to allow the user to simultaneously see the top and bottom of the tree in “proper parallax” (Tieman 1904). Other early hypsometers applied different approaches that used angles and distance (e.g., Graves 1906, Detwiler 1915, Noyes 1916, Krauch 1918). Of these trigonometric hypsometers, those that calculated total tree height (HT) as a function of the tangent of the angles to the top (B2) and bottom (B1) of the tree and a baseline horizontal distance (b) to the stem were most common (Figure 1). Because they are easy to apply and required only simple technology, these approaches (hereafter, the similar triangles and tangent methods) have dominated tree height measurement. That is not to say the challenge of accurate tree height measurement was solved— many early foresters reported problems with getting consistent data in uneven terrain or dense understories or with the use of different types of hypsometers. Good measurement practices usually mitigated these issues and became standard components of forester training programs. Others addressed these challenges by designing new techniques based on different trigonometric relationships. As an example, Haig (1925) proposed a slide rule solution that calculated tree height using the sine law and slope distance from the observer to the tree base (s1)

Older readers will remember using a slide rule to carry out multiplication and division in the days before calculators. There was also a graphical tool called a nomogram, which was used for evaluating certain functions. Although such devices have little practical use nowadays, I was interested in investigating which classes of functions with two independent variables could be calculated using this type of device.Figure 1 shows how a slide rule was used to multiply 3 by 4 (or equivalently to divide 12 by 4). To do this, you align the 1 on the upper scale with the 3 on the lower scale and then read off the value below the 4 on the upper scale to get 12 (or, for division, you line up the 4 above the 12 and read off the answer 3 on the lower scale).