Turtle Geometry presents an innovative program of mathematical discovery that demonstrates how the effective use of personal computers can profoundly change the nature of a student's contact with mathematics. Using this book and a few simple computer programs, students can explore the properties of space by following an imaginary turtle across the screen. The concept of turtle geometry grew out of the Logo Group at MIT. Directed by Seymour Papert, author of Mindstorms, this group has done extensive work with preschool children, high school students and university undergraduates.
This book is all about experiencing the awesome WHOLENESS power of God through a life of discipleship and prayer. The book is a call to get back to the simple basics of the Bible using the wholeness and oneness principles as a guide. In a few of the later chapters the book explores some simple, but remarkable number patterns such as the mathematical constants for light, time, gravity, creation fire, and many more, all of which were encoded in the Psalms 3000 years ago, about 2,900 years before they were known. These simple number patterns such as 19 for electricity, 27 for light, 29 for creation fire, and 38 for gravity, all have 'key words' in the first few verses of the Psalm number that is the same exact number of the math constant. The book also explores a few (ELS) or what is called Equidistant Lette! r Sequences to show hidden codes in the Bible. There also is a unique matrix code for the World Trade Center attack included. Many more interesting Bible numbers that equal modern day scientific theory and fact are found in the Tabernacle of Moses and other places in the Bible. The book brings out the wholeness principles contained in the Bible and how to apply them to your life. The book also validates the fact that the Bible contains the simple mathematical evidence for the existence of God with patterns of numbers that are way beyond chance.
This is a book about infinity — specifically the infinity of numbers, and how one kind of infinity is greater than all the rest. Along the way the author will demonstrate how infinity can be made to create beautiful ‘art’, and how this process can help us to understand the fundamental nature of numbers. This book will provide a fascinating read for anyone interested in number theory, infinity, math art, and/or generative art, and could be used a valuable supplement to any course on these topics. Features Beautiful examples of generative art. Accessible to anyone with a reasonable high school level of mathematics. Full of challenges and puzzles to engage readers.
What does it mean to know mathematics? How does meaning in mathematics education connect to common sense or to the meaning of mathematics itself? How are meanings constructed and communicated and what are the dilemmas related to these processes? There are many answers to these questions, some of which might appear to be contradictory. Thus understanding the complexity of meaning in mathematics education is a matter of huge importance. There are twin directions in which discussions have developed—theoretical and practical—and this book seeks to move the debate forward along both dimensions while seeking to relate them where appropriate. A discussion of meaning can start from a theoretical examination of mathematics and how mathematicians over time have made sense of their work. However, from a more practical perspective, anybody involved in teaching mathematics is faced with the need to orchestrate the myriad of meanings derived from multiple sources that students develop of mathematical knowledge. This book presents a wide variety of theoretical reflections and research results about meaning in mathematics and mathematics education based on long-term and collective reflection by the group of authors as a whole. It is the outcome of the work of the BACOMET (BAsic COmponents of Mathematics Education for Teachers) group who spent several years deliberating on this topic. The ten chapters in this book, both separately and together, provide a substantial contribution to clarifying the complex issue of meaning in mathematics education. This book is of interest to researchers in mathematics education, graduate students of mathematics education, under graduate students in mathematics, secondary mathematics teachers and primary teachers with an interest in mathematics.
In recent years geometry seems to have lost large parts of its former central position in mathematics teaching in most countries. However, new trends have begun to counteract this tendency. There is an increasing awareness that geometry plays a key role in mathematics and learning mathematics. Although geometry has been eclipsed in the mathematics curriculum, research in geometry has blossomed as new ideas have arisen from inside mathematics and other disciplines, including computer science. Due to reassessment of the role of geometry, mathematics educators and mathematicians face new challenges. In the present ICMI study, the whole spectrum of teaching and learning of geometry is analysed. Experts from all over the world took part in this study, which was conducted on the basis of recent international research, case studies, and reports on actual school practice. This book will be of particular interest to mathematics educators and mathematicians who are involved in the teaching of geometry at all educational levels, as well as to researchers in mathematics education.
This series is for people--adults and teenagers--who are interested in computer programming because it's fun. The three volumes use the Logo programming language as the vehicle for an exploration of computer science from the perspective of symbolic computation and artificial intelligence. Logo is a dialect of Lisp, a language used in the most advanced research projects in computer science, especially in artificial intelligence. Throughout the series, functional programming techniques (including higher order functions and recursion) are emphasized, but traditional sequential programming is also used when appropriate.In the second edition, the first two volumes have been rearranged so that illustrative case studies appear with the techniques they demonstrate. Volume 1 includes a new chapter about higher order functions, and the recursion chapters have been reorganized for greater clarity. Volume 2 includes a new tutorial chapter about macros, an exclusive capability of Berkeley Logo, and two new projects. Throughout the series, the larger program examples have been rewritten for greater readability by more extensive use of data abstraction.Volume 1 Symbolic Computing, is addressed to a reader who has used computers and wants to learn the ideas behind them. Symbolic computing is the manipulation of words and sentences, in contrast both to the graphics most people associate with Logo and to the numerical computation with which more traditional languages such as Pascal and C++ are most comfortable. This volume is well known for its clear and thorough presentation of recursion, a key idea in computer science that other texts treat as arcane and difficult.The Logo programs in these books and the author's free Berkeley Logo interpreter are available via the Internet or on diskette.
