This volume is based on lectures delivered at the 2022 AMS Short Course “3D Printing: Challenges and Applications” held virtually from January 3–4, 2022. Access to 3D printing facilities is quickly becoming ubiquitous across college campuses. However, while equipment training is readily available, the process of taking a mathematical idea and making it into a printable model presents a big hurdle for most mathematicians. Additionally, there are still many open questions around what objects are possible to print, how to design algorithms for doing so, and what kinds of geometries have desired kinematic properties. This volume is focused on the process and applications of 3D printing for mathematical education, research, and visualization, alongside a discussion of the challenges and open mathematical problems that arise in the design and algorithmic aspects of 3D printing. The articles in this volume are focused on two main topics. The first is to make a bridge between mathematical ideas and 3D visualization. The second is to describe methods and techniques for including 3D printing in mathematical education at different levels— from pedagogy to research and from demonstrations to individual projects. We hope to establish the groundwork for engaged academic discourse on the intersections between mathematics, 3D printing and education.

The volume presents a collection of articles on the use of 3D printing technology in mathematics education and in mathematics teacher training. It contains both basic research-oriented contributions as well as reflected descriptions of concrete developments for teaching. The authors of this compilation share a positive attitude towards the possibilities that the use of 3D printing technology (understood as an interplay of software and hardware) can unfold for mathematics education, but critically evaluate from a mathematics education research perspective when, where and how an application can enable an added value for the learning of a mathematical content.

The first book to explain mathematics using 3D printed models. Winner of the Technical Text of the Washington Publishers Wouldn’t it be great to experience three-dimensional ideas in three dimensions? In this book—the first of its kind—mathematician and mathematical artist Henry Segerman takes readers on a fascinating tour of two-, three-, and four-dimensional mathematics, exploring Euclidean and non-Euclidean geometries, symmetry, knots, tilings, and soap films. Visualizing Mathematics with 3D Printing includes more than 100 color photographs of 3D printed models. Readers can take the book’s insights to a new level by visiting its sister website, 3dprintmath.com, which features virtual three-dimensional versions of the models for readers to explore. These models can also be ordered online or downloaded to print on a 3D printer. Combining the strengths of book and website, this volume pulls higher geometry and topology out of the realm of the abstract and puts it into the hands of anyone fascinated by mathematical relationships of shape. With the book in one hand and a 3D printed model in the other, readers can find deeper meaning while holding a hyperbolic honeycomb, touching the twists of a torus knot, or caressing the curves of a Klein quartic.

Additive Manufacturing 3D Printing & Design The 4th Revolution Not ever previously consumer has had a technology where we so easily interpret the concepts into a touchable object with little concern to the machinery or talents available. If “seeing is believing!-” 3D printing technology is the perfect object image to see, touch, and feel! It is the wings to lift the well sought product, after laboring and toiling in several design iterations to bring the novel product to be a successful implementation. Now it is promising to become familiar with the product prototype and physically test it to find the flaws in the design. If a flaw is detected, the designer can easily modify the CAD file and print out a new unit. On Demand Custom Part Additive manufacturing has become a mainstream manufacturing process. It builds up parts by adding materials one layer at a time based on a computerized 3D solid model. It does not require the use of fixtures, cutting tools, coolants, and other auxiliary resources. It allows design optimization and the producing of customized parts on-demand. Its advantages over conventional manufacturing have captivated the imagination of the public, reflected in recent corporate implementations and in many academic publications that call additive manufacturing the “fourth industrial revolution.” Digital Model Layer by Layer 3D additive manufacturing is a process tailored for making three-dimensional objects of varieties of different shapes created from digital models. The objects are produced using an additive process, where successive layers of materials are deposited down in different shapes. The 3D Additive Manufacturing is considered diverse from traditional machining techniques, which depends primarily on the removal of material by cutting or drilling. The removal of material is referred to as a “subtractive process.” In a fast-paced, pressure-filled business atmosphere, it is clear that decreasing delivery by days is exceptionally valuable. Digital Manufacturing 3D printing - additive manufacturing, produces 3D solid items from a digital computer file. The printing occurs in an additive process, where a solid object is generated through the consecutive layering of material. There are an extensive variety of materials to select from countless lists of polymers and metals. The process begins with the generation of a 3D digital file such as CAD file. The 3D digital file is then directed to a 3D printer for printing using a simple print command. Freed of the constraints of traditional factories, additive manufacturing allows designers to produce parts that were previously considered far too complex to make economically. Engineers and Biologists are finding practical applications to use 3D additive manufacturing. It permits novel designs to become matchless rare-products that were not likely with preceding manufacturing methods. It is poised to transform medicine and biology with bio-manufacturing. This technology has the possibility to upsurge the well-being of a nation’s citizens. Additive manufacturing may progress the worldwide resources and energy effectiveness in ground, sea and air. This 3D Printing & Design book will enable you to develop and 3D print your own unique object using myriads of worldwide materials. Galilee Galileo & Isaac Newton Galileo Galilei and Isaac Newton have changed our understanding of not only our own solar system, but also the whole universe through the invention of their telescope. The telescope steered a novel and captivating scientific discipline of “astronomy” —observing and studying the planets, stars, and other objects in the universe. The Nebula, for example, could not be observed prior to the invention of the telescope. No one could have estimated how many planets were in our solar system. Thanks to the technology of the telescope, the knowledge of universe was revealed. Thanks to a simple piece of glass made of silica, and to a simple lens made of glass. Similarly, 3D printing technology is a simple approach to open a flood gate to our Fourth Industrial Revolution. One-off Prototype One-off prototypes can be hideously expensive to produce, but a 3D printer can bring down the cost by a sizable margin. Many consumers goods, mechanical parts, aerospace, automobiles, robots, shoes, fashions, architects' models, dentures, hearing aids, cell biology, now appear in a 3D-printed form for appraisal by engineers, stylists, biologist, and clients before obtaining the final approval. Any changes can be swiftly reprinted in a few hours or overnight, whereas waiting for a new prototype to emerge from a machine shop could take weeks, and sometimes months. Some designers are already printing ready-to-wear shoes, dresses, and prosthetics, from metals, plastic and nylon materials. 3D printing’s utmost advantage is making discrete parts rapidly, autonomous of design complications. That speed delivers rapid reaction on the first prototype, and the capability to modify the design and speedily re-manufacture the part. As an alternative of waiting days or weeks for a CNC-machined prototype, a 3D printer can manufacture the part overnight. Development Cycle The 3D printer provides the additional advantage of removing many overhead manufacturing costs and time-delay by 3D printing parts that withstand a machine shop environment. Several tooling, fixtures, and work-holding jaws may be easily developed and 3D printed without extensive lead time and overhead cost. Its speed and quality shorten the product development cycle, permitting manufacturing aesthetically appealing, and high-performance parts in less than a day. Many instances testify that 3D printers offer substantial flexibility to yield parts with the adequate tensile strength and quality, desired to prosper the technology at a reasonable speed and cost. The rewards of applying 3D printing are substantial, as 3D printing permits product development teams to effortlessly, rapidly, and cost effectively yield models, prototypes, and patterns. Parts can be manufactured in hours or days rather than weeks. Nano-bots 3D additive manufacturing may be the only known method for constructing nanobots, which will overcome the speed disadvantage of 3D additive printing, thereby enabling the technology to be widely deployed in every manufacturing aspect. If millions of nanobots worked together, they might be able to do amazing manufacturing takes. Microscopic Surgery Scientists and researchers constructed teams of nanobots able to perform microscopic surgery inside a patient’s body. Some groups of nanobots have been programmed to build objects by arranging atoms precisely so there would be no waste. Other nanobots might even be designed to build more nanobots to replace ones that wear out! Compared to other areas of science like manufacturing and biology, nanotechnology is a very new area of 3D printing research. Working with microns and nanometers is still a very slow and difficult task. Carbon Fiber Also, material scientists and metallurgists are constantly providing engineers, and manufacturers with new and superior materials to make parts in the most economical and effective means. Carbon-fiber composites, for instance, are replacing steel and aluminum in products ranging from simple mountain bikes to sophisticated airliners. Sometimes the materials are farmed, cultivated and may be grown from biological substances and from micro-organisms that have been genetically engineered for the task of fabricating useful parts. Facing the benefits of the current evolution of 3D printing technology, companies from all parts in the supply chain are experiencing the opportunities and threatens it may bring. First, to traditional logistic companies, 3D printing is causing a decline in the cargo industry, reducing the demand for long-distance transportation such as air, sea and rail freight industries. The logistic companies which did not realize the current evolution may not adapt rapidly enough to the new situation. As every coin has two sides, with 3D Printing, logistics companies could also become able to act as the manufacturers. The ability to produce highly complex designs with powerful computer software and turn them into real objects with 3D printing is creating a new design language. 3D-printed items often have an organic, natural look. “Nature has come up with some very efficient designs, Figure 1.3. Often it is prudent to mimic them,” particularly in medical devices. By incorporating the fine, lattice-like internal structure of natural bone into a metal implant, for instance, the implant can be made lighter than a machined one without any loss of strength. It can integrate more easily with the patient's own bones and be grafted precisely to fit the intended patient. Surgeons printed a new titanium jaw for a woman suffering from a chronic bone infection. 3D additive manufacturing promises sizable savings in material costs. In the aerospace industry, metal parts are often machined from a solid billet of costly high-grade titanium. This constitutes 90% of material that is wasted. However, titanium powder can be used to print parts such as a bracket for an aircraft door or part of a satellite. These can be as strong as a machined part, but use only 10% of the raw material. A Boeing F-18 fighter contains a number of printed parts such as air ducts, reducing part weight by at least 30%. Remote Manufacturing 3D Printers Replicator can scan an object in one place while simultaneously communicating to another machine, locally or globally, developed to build a replica object. For example, urgently needed spares could be produced in remote places without having to ship the original object. Even parts that are no longer available could be replicated by scanning a broken item, repairing it virtually, and then printing a new one. It is likely digital libraries will appear online for parts and products that are no longer available. Just as the emergence of e-books means books may never go out of print, components could always remain available. Service mechanics could have portable 3D printers in their vans and hardware stores could offer part-printing services. DIY Market Some entrepreneurs already have desktop 3D printers at home. Industrial desktop 3D printing machines are creating an entirely new market. This market is made up of hobbyists, do-it-yourself enthusiasts, tinkerers, inventors, researchers, and entrepreneurs. Some 3D-printing systems can be built from kits and use open-source software. Machinists may be replaced someday by software technicians who service production machines. 3D printers would be invaluable in remote areas. Rather than waiting days for the correct tool to be delivered, you could instantly print the tool on the job. Printing Materials However, each method has its own benefits and downsides. Some 3D printer manufacturers consequently offer a choice between powder and polymer for the material from which the object is built. Some manufacturer use standard, off-the-shelf business paper as the build material to produce a durable prototype. Speed, cost of the 3D printer, cost of the printed prototype, and the cost of choice materials and color capabilities are the main considerations in selecting a 3D printing machine. SLA – DLP - FDM – SLS - SLM & EBM The expansive world of 3D printing machines has become a confusing place for beginners and professionals alike. The most well-known 3D printing techniques and types of 3D printing machines are stated below. The 3D printing technology is categorized according to the type of technology utilized. The categories are stated as follows: Stereolithography(SLA) Digital Light Processing(DLP) Fused deposition modeling (FDM) Selective Laser Sintering (SLS) Selective laser melting (SLM) Electronic Beam Melting (EBM) Laminated object manufacturing (LOM) Also, the book provides a detailed guide and optimum implementations to each of the stated 3D printing technology, the basic understanding of its operation, and the similarity as well as the dissimilarity functions of each printer. School Students, University undergraduates, and post graduate students will find the book of immense value to equip them not only with the fundamental in design and implementation but also will encourage them to acquire a system and practice creating their own innovative samples. Furthermore, professionals and educators will be well prepared to use the knowledge and the expertise to practice and advance the technology for the ultimate good of their respective organizations. Global Equal Standing Manufacturers large and small play a significant part in the any country’s economy. The U.S. economy; rendering to the United States Census Bureau, manufacturers are the nation’s fourth-largest employer, and ship several trillions of dollars in goods per annum. It may be a large automotive enterprise manufacturing vehicles or an institution with less than 50 employees. Manufacturers are vital to the country’s global success. However, many societies have misunderstandings about the manufacturing jobs are undesirable jobs and offers low-paying compensations. Other countries may be discouraged to compete against USA. Additive Manufacturing Technology – 3D Printing would level the manufacturing plane field, enabling all countries to globally stand on equal footing. Dr. Sabrie Soloman, Chairman & CEO 3D Printing & Design Not ever previously consumer has had a technology where we so easily interpret the concepts into a touchable object with little concern to the machinery or talents available. 3D Printing Technology builds up parts by adding materials one layer at a time based on a computerized 3D solid model. It allows design optimization and the producing of customized parts on-demand. Its advantages over conventional manufacturing have captivated the imagination of the public, reflected in recent corporate implementations and in many academic publications that call additive manufacturing the “Fourth Industrial Revolution.” 3D Printing produces 3D solid items from a digital computer file. The printing occurs in an additive process, where a solid object is generated through the consecutive layering of material. The process begins with the generation of a 3D digital file such as CAD file. The 3D digital file is then directed to a 3D Printer for printing using a simple print command. Freed of the constraints of traditional factories, additive manufacturing allows designers to produce parts that were previously considered far too complex to make economically. Engineers and Biologists are finding practical applications to use 3D additive manufacturing. It permits novel designs to become matchless rare-products that were not likely with preceding manufacturing methods. 3D Printing Technology is poised to transform medicine and biology with bio-manufacturing, and traditional manufacturing into 3D Printing. This technology has the possibility to upsurge the well-being of a nation’s citizens. Additive manufacturing may progress the worldwide resources and energy effectiveness in “Ground, Sea and Air.” This 3D Printing & Design book will enable you to develop and 3D Print your own unique object using myriads of available worldwide materials. One-off prototypes can be hideously expensive to produce, but a 3D Printer can bring down the cost by a sizable margin. Many consumers goods, mechanical parts, aerospace, automobiles, robots, shoes, fashions, architects' models, dentures, hearing aids, cell biology, now appear in a 3D-printed form for appraisal by engineers, stylists, biologist, and clients before obtaining the final approval. The 3D Printing Technology provides the additional advantage of removing many overhead manufacturing costs and time-delay. The rewards are substantial, as it permits product development teams effortlessly, rapidly and cost effectively yielding models, prototypes, and patterns to be manufactured in hours or days rather than weeks, or months.

This book is about mathematics teaching and learning in Africa during the Fourth Industrial Revolution. The Fourth Industrial Revolution (4IR) has evolved to utilize new technologies in the teaching and learning of Mathematics. It is characterized by the fusion of the biological, physical and digital worlds and embodies a new era of innovation in mathematics education, leading to the rapid emergence of new technologies for mathematics teaching and learning. Because 4IR in mathematics education is happening differently in various parts of Africa, the authors of the various chapters in this volume have positioned their work in their respective local contexts. The chapters address a wide variety of interests, concerns, and implications regarding 4IR and Mathematics Education in Africa. Additionally, a number of chapters address teaching mathematics in the context of the COVID-19 pandemic that has gripped the world. Other chapters discuss the implications of inequalities in Africa that effect mathematics education during 4IR. Chapters also incorporate arguments, observations, and suggestions to, improve and transform the teaching and learning of mathematics in Africa during the 4IR. This book highlights a new era of innovation in mathematics education in the context of the Fourth Industrial Revolution, leading to the rapid emergence of new technologies in mathematics teaching and learning. It is a valuable resource for graduate students, people with research interests in the fourth industrial revolution and mathematics educators at any level, including all mathematics teachers; mathematics education curriculum designers and policymakers.

This volume provides new insights on creativity while focusing on innovative methodological approaches in research and practice of integrating technological tools and environments in mathematics teaching and learning. This work is being built on the discussions at the mini-symposium on Creativity and Technology at the International Conference on Mathematical Creativity and Giftedness (ICMCG) in Denver, USA (2014), and other contributions to the topic. The book emphasizes a diversity of views, a variety of contexts, angles and cultures of thought, as well as mathematical and educational practices. The authors of each chapter explore the potential of technology to foster creative and divergent mathematical thinking, problem solving and problem posing, creative use of dynamic, multimodal and interactive software by teachers and learners, as well as other digital media and tools while widening and enriching transdisciplinary and interdisciplinary connections in mathematics classroom. Along with ground-breaking innovative approaches, the book aims to provide researchers and practitioners with new paths for diversification of opportunities for all students to become more creative and innovative mathematics learners. A framework for dynamic learning conditions of leveraging mathematical creativity with technology is an outcome of the book as well.

Supporting education through digital technology becomes increasingly important. Especially in the light of the Covid-19 pandemic, online teaching and learning has been increased massively. In these precarious times, multiple approaches have been developed to enable the delivery of online education. But also for the regular classroom setting, more and more technologies are developed and implemented in educational practice. This volume contains the papers presented at the Research On STEM Education in the Digital Age (ROSEDA) Conference, held in Porto, Portugal, in February 2023. The proceedings summarize and link theoretical consi-derations, practical experiences and ideas, and empirical research on the use of technology to enrich students’ learning. Hereby, the papers focus on the STEM subjects of Mathematics, Technology, Engineering and Mathematics. The ROSEDA Conference and its proceedings are part of the Erasmus+ Strategic Partnership ASYMPTOTE which is co-funded by the European Union.

This new volume explores the exciting and diverse applications of three-dimensional printing in a variety of industries, including food processing, environmental sciences, biotechnology, medical devices, energy storage, civil engineering, the textile and fashion industry, and more. It describes the various 3D printing methods, the commonly used materials, and the pros and cons. It also presents an overview of the historical development and modern-day trends in additive manufacturing, as well as an exploration of the prospects of 3D printing technology in promoting academic education.

Education has changed dramatically in recent years as educational technologies evolve and develop at a rapid pace. Teachers and institutions must constantly update their practices and curricula to match this changing landscape to ensure students receive the best education possible. 3D printing has emerged as a new technology that has the potential to enhance student learning and development. Moreover, the availability of makerspaces within schools and libraries allows students to utilize technologies that drive creativity. Further study on the strategies and challenges of implementation is needed for educators to appropriately adopt these learning practices. The Research Anthology on Makerspaces and 3D Printing in Education considers the benefits these technologies provide in relation to education as well as the various ways they can be utilized in the classroom for student learning. The book also provides a review of the difficulties educators face when implementing these technologies into their curricula and ensuring student success. Covering topics such as educational technologies, creativity, and online learning, this major reference work is ideal for administrators, principals, researchers, scholars, practitioners, academicians, instructors, and students.

This sixth volume, in the series of yearbooks by the Association of Mathematics Educators in Singapore, entitled Learning Experiences to Promote Mathematics Learning is unique in that it focuses on a single theme in mathematics education. The objective is for teachers and researchers to advance the learning of mathematics through meaningful experiences.Several renowned international and Singapore scholars have published their work in this volume. The fourteen chapters of the book illustrate evidence-based practices that school teachers and researchers can experiment with in their own classrooms to bring about meaningful learning outcomes. Three broad themes, namely fundamentals for active and motivated learning, learning experiences for developing mathematical processes, and use of ICT tools for learning through visualizations, simulations and representations, shape the ideas in these chapters. The book makes a significant contribution towards the learning of mathematics. It is a good resource for mathematics teachers, educators and research students.