The role of spreadsheets in an investigation of Fibonacci numbers

We introduce a function Z(k) which measures the number of distinct ways in which a number can be expressed as the sum of Fibonacci numbers. Using a binary table and other devices, we explore the values that Z(k) can take and reveal a surprising relationship between the values of Z(k) and the Fibonacci numbers from which they were derived. The article shows the way in which standard spreadsheet functionalities makes it possible to reveal quite striking patterns in data.

Spreadsheets and Bulgarian goats

We consider a problem appearing in an Australian Mathematics Challenge in 2003. This article considers whether a spreadsheet might be used to model this problem, thus allowing students to explore its structure within the spreadsheet environment. It then goes on to reflect on some general principles of problem decomposition when the final goal is a successful and lucid spreadsheet implementation.

Applications of Spreadsheets in Education : The Amazing Power of a Simple Tool

This e-book is devoted to the use of spreadsheets in the service of education in a broad spectrum of disciplines: science, mathematics, engineering, business, and general education. The effort is aimed at collecting the works of prominent researchers and educators that make use of spreadsheets as a means to communicate concepts with high educational value. The e-book brings some of the most recent applications of spreadsheets in education and research to the fore. To offer the reader a broad overview of the diversity of applications, carefully chosen articles from engineering (power systems and control), mathematics (calculus, differential equations, and probability), science (physics and chemistry), and education are provided. Some of these applications make use of Visual Basic for Applications (VBA), a versatile computer language that further expands the functionality of spreadsheets. The material included in this e-book should inspire readers to devise their own applications and enhance their teaching and/or learning experience.

Discrete phase-locked loop systems and spreadsheets

This paper demonstrates the use of a spreadsheet in exploring non-linear difference equations that describe digital control systems used in radio engineering, communication and computer architecture. These systems, being the focus of intensive studies of mathematicians and engineers over the last 40 years, may exhibit extremely complicated behaviour interpreted in contemporary terms as transition from global asymptotic stability to chaos through period-doubling bifurcations. The authors argue that embedding advanced mathematical ideas in the technological tool enables one to introduce fundamentals of discrete control systems in tertiary curricula without learners having to deal with complex machinery that rigorous mathematical methods of investigation require. In particular, in the appropriately designed spreadsheet environment, one can effectively visualize a qualitative difference in the behviour of systems with different types of non-linear characteristic.

Life cycle modelling and design knowledge development in 3D virtual environments : final report

Experience plays an important role in building management. “How often will this asset need repair?” or “How much time is this repair going to take?” are types of questions that project and facility managers face daily in planning activities. Failure or success in developing good schedules, budgets and other project management tasks depend on the project manager's ability to obtain reliable information to be able to answer these types of questions. Young practitioners tend to rely on information that is based on regional averages and provided by publishing companies. This is in contrast to experienced project managers who tend to rely heavily on personal experience. Another aspect of building management is that many practitioners are seeking to improve available scheduling algorithms, estimating spreadsheets and other project management tools. Such “micro-scale” levels of research are important in providing the required tools for the project manager's tasks. However, even with such tools, low quality input information will produce inaccurate schedules and budgets as output. Thus, it is also important to have a broad approach to research at a more “macro-scale.” Recent trends show that the Architectural, Engineering, Construction (AEC) industry is experiencing explosive growth in its capabilities to generate and collect data. There is a great deal of valuable knowledge that can be obtained from the appropriate use of this data and therefore the need has arisen to analyse this increasing amount of available data. Data Mining can be applied as a powerful tool to extract relevant and useful information from this sea of data. Knowledge Discovery in Databases (KDD) and Data Mining (DM) are tools that allow identification of valid, useful, and previously unknown patterns so large amounts of project data may be analysed. These technologies combine techniques from machine learning, artificial intelligence, pattern recognition, statistics, databases, and visualization to automatically extract concepts, interrelationships, and patterns of interest from large databases. The project involves the development of a prototype tool to support facility managers, building owners and designers. This final report presents the AIMMTM prototype system and documents how and what data mining techniques can be applied, the results of their application and the benefits gained from the system. The AIMMTM system is capable of searching for useful patterns of knowledge and correlations within the existing building maintenance data to support decision making about future maintenance operations. The application of the AIMMTM prototype system on building models and their maintenance data (supplied by industry partners) utilises various data mining algorithms and the maintenance data is analysed using interactive visual tools. The application of the AIMMTM prototype system to help in improving maintenance management and building life cycle includes: (i) data preparation and cleaning, (ii) integrating meaningful domain attributes, (iii) performing extensive data mining experiments in which visual analysis (using stacked histograms), classification and clustering techniques, associative rule mining algorithm such as “Apriori” and (iv) filtering and refining data mining results, including the potential implications of these results for improving maintenance management. Maintenance data of a variety of asset types were selected for demonstration with the aim of discovering meaningful patterns to assist facility managers in strategic planning and provide a knowledge base to help shape future requirements and design briefing. Utilising the prototype system developed here, positive and interesting results regarding patterns and structures of data have been obtained.

Life Cycle Modelling and Design Knowledge Development in 3D Virtual Environments

Experience plays an important role in building management. “How often will this asset need repair?” or “How much time is this repair going to take?” are types of questions that project and facility managers face daily in planning activities. Failure or success in developing good schedules, budgets and other project management tasks depend on the project manager's ability to obtain reliable information to be able to answer these types of questions. Young practitioners tend to rely on information that is based on regional averages and provided by publishing companies. This is in contrast to experienced project managers who tend to rely heavily on personal experience. Another aspect of building management is that many practitioners are seeking to improve available scheduling algorithms, estimating spreadsheets and other project management tools. Such “micro-scale” levels of research are important in providing the required tools for the project manager's tasks. However, even with such tools, low quality input information will produce inaccurate schedules and budgets as output. Thus, it is also important to have a broad approach to research at a more “macro-scale.” Recent trends show that the Architectural, Engineering, Construction (AEC) industry is experiencing explosive growth in its capabilities to generate and collect data. There is a great deal of valuable knowledge that can be obtained from the appropriate use of this data and therefore the need has arisen to analyse this increasing amount of available data. Data Mining can be applied as a powerful tool to extract relevant and useful information from this sea of data. Knowledge Discovery in Databases (KDD) and Data Mining (DM) are tools that allow identification of valid, useful, and previously unknown patterns so large amounts of project data may be analysed. These technologies combine techniques from machine learning, artificial intelligence, pattern recognition, statistics, databases, and visualization to automatically extract concepts, interrelationships, and patterns of interest from large databases. The project involves the development of a prototype tool to support facility managers, building owners and designers. This Industry focused report presents the AIMMTM prototype system and documents how and what data mining techniques can be applied, the results of their application and the benefits gained from the system. The AIMMTM system is capable of searching for useful patterns of knowledge and correlations within the existing building maintenance data to support decision making about future maintenance operations. The application of the AIMMTM prototype system on building models and their maintenance data (supplied by industry partners) utilises various data mining algorithms and the maintenance data is analysed using interactive visual tools. The application of the AIMMTM prototype system to help in improving maintenance management and building life cycle includes: (i) data preparation and cleaning, (ii) integrating meaningful domain attributes, (iii) performing extensive data mining experiments in which visual analysis (using stacked histograms), classification and clustering techniques, associative rule mining algorithm such as “Apriori” and (iv) filtering and refining data mining results, including the potential implications of these results for improving maintenance management. Maintenance data of a variety of asset types were selected for demonstration with the aim of discovering meaningful patterns to assist facility managers in strategic planning and provide a knowledge base to help shape future requirements and design briefing. Utilising the prototype system developed here, positive and interesting results regarding patterns and structures of data have been obtained.

GPFlow: an intuitive environment for web-based scientific workflow

Increasingly scientists are using collections of software tools in their research. These tools are typically used in concert, often necessitating laborious and error-prone manual data reformatting and transfer. We present an intuitive workflow environment to support scientists with their research. The workflow, GPFlow, wraps legacy tools, presenting a high level, interactive web-based front end to scientists. The workflow backend is realized by a commercial grade workflow engine (Windows Workflow Foundation). The workflow model is inspired by spreadsheets and is novel in its support for an intuitive method of interaction enabling experimentation as required by many scientists, e.g. bioinformaticians. We apply GPFlow to two bioinformatics experiments and demonstrate its flexibility and simplicity.

CCI-CCI Creative City Index 2012

The CCI-Creative City Index was commissioned in 2010 by the Beijing Academy of Science & Technology's Beijing Research Center for the Science of Science. John Hartley was asked to develop a new creative global city index. The brief was to improve on the existing indexes with a specific focus on creative industries and the sources of creative development. This report, by John Hartley, Jason Potts, Trent MacDonald, with Chris Erkunt and Carl Kufleitner, sets out the new model we have developed, which we call the CCI Creative City Index (CCI-CCI). It presents the results of a pilot application of the index to six cities: London, Cardiff, Berlin, Bremen, Melbourne and Brisbane. The index incorporates many elements from other global and creative city indexes, but also adds several new dimensions relating to creative industries scope, micro-productivity, and the economy of attention. The report and Excel spreadsheets of index calculations can be found on this site.

Daylighting design and simulation : ease of use analysis of digital tools for architects

Good daylighting design in buildings not only provides a comfortable luminous environment, but also delivers energy savings and comfortable and healthy environments for building occupants. Yet, there is still no consensus on how to assess what constitutes good daylighting design. Currently amongst building performance guidelines, Daylighting factors (DF) or minimum illuminance values are the standard; however, previous research has shown the shortcomings of these metrics. New computer software for daylighting analysis contains new more advanced metrics for daylighting (Climate Base Daylight Metrics-CBDM). Yet, these tools (new metrics or simulation tools) are not currently understood by architects and are not used within architectural firms in Australia. A survey of architectural firms in Brisbane showed the most relevant tools used by industry. The purpose of this paper is to assess and compare these computer simulation tools and new tools available architects and designers for daylighting. The tools are assessed in terms of their ease of use (e.g. previous knowledge required, complexity of geometry input, etc.), efficiency (e.g. speed, render capabilities, etc.) and outcomes (e.g. presentation of results, etc. The study shows tools that are most accessible for architects, are those that import a wide variety of files, or can be integrated into the current 3d modelling software or package. These software’s need to be able to calculate for point in times simulations, and annual analysis. There is a current need in these software solutions for an open source program able to read raw data (in the form of spreadsheets) and show that graphically within a 3D medium. Currently, development into plug-in based software’s are trying to solve this need through third party analysis, however some of these packages are heavily reliant and their host program. These programs however which allow dynamic daylighting simulation, which will make it easier to calculate accurate daylighting no matter which modelling platform the designer uses, while producing more tangible analysis today, without the need to process raw data.

Letters and numbers in Excel : fostering student engagement in fundamentals of maths & computing

The television quiz program Letters and Numbers, broadcast on the SBS network, has recently become quite popular in Australia. This paper considers an implementation in Excel 2010 and its potential as a vehicle to showcase a range of mathematical and computing concepts and principles.

Colour by numbers in Excel 2007 : solving algebraic equations without algebra

This is an update of an earlier paper, and is written for Excel 2007. A series of Excel 2007 models is described. The more advanced versions allow solution of f(x)=0 by examining change of sign of function values. The function is graphed and change of sign easily detected by a change of colour. Relevant features of Excel 2007 used are Names, Scatter Chart and Conditional Formatting. Several sample Excel 2007 models are available for download, and the paper is intended to be used as a lesson plan for students having some familiarity with derivatives. For comparison and reference purposes, the paper also presents a brief outline of several common equation-solving strategies as an Appendix.

Diophantine equations as a context for technology-enhanced training in conjecturing and proving

Solving indeterminate algebraic equations in integers is a classic topic in the mathematics curricula across grades. At the undergraduate level, the study of solutions of non-linear equations of this kind can be motivated by the use of technology. This article shows how the unity of geometric contextualization and spreadsheet-based amplification of this topic can provide a discovery experience for prospective secondary teachers and information technology students. Such experience can be extended to include a transition from a computationally driven conjecturing to a formal proof based on a number of simple yet useful techniques.

Fun with Fibonacci

We introduce a function which measures the number of distinct ways in which a number can be expressed as the sum of Fibonacci numbers. Using a binary table and other devices, we explore the values that can take and reveal some interesting patterns. The article shows how standard spreadsheet functionalities make it possible to reveal quite striking patterns in data, and is intended to be used in the classroom.

The slumbarumba jumbuck problem

The potential for simple linear relationships arising from a computer game to build student modelling and "world problem" skills is explored. The fundamental capability of the spreadsheet to tabulate and graph possible solutions is used to lay bare the problem structure for the students.