http://hdl.handle.net/1813/2711 2013-06-20T06:55:41Z 2013-06-20T06:55:41Z Taimina, Daina http://hdl.handle.net/1813/2718 2006-03-21T08:22:49Z 2004-04-21T00:00:00Z

Title: Historical Mechanisms for Drawing Curves Authors: Taimina, Daina Abstract: Mechanical devices such as linkages for drawing curves are known already from Ancient Greece. Later linkages found use in different mechanical devices and machines like we can see it in 13th century drawings by Honnecourt or in 16th century machine drawings by Agricola. In 17th century Descartes accepted only those curves that had a mechanical device to draw them. Mechanical curve drawing devices later became incorporated into different machine design. In this paper examples from Reuleaux kinematic model collection in Cornell University are given and some history of linkages discussed.

2004-04-21T00:00:00Z Pan, Bing Gay, Geri Saylor, John Hembrooke, Helene Henderson, David http://hdl.handle.net/1813/2717 2006-03-21T08:10:50Z 2004-02-27T00:00:00Z

Title: Usability, Learning, and Subjective Experience: User Evaluation of Authors: Pan, Bing; Gay, Geri; Saylor, John; Hembrooke, Helene; Henderson, David Abstract: This paper describes an evaluation effort of the use of the Kinematic Model for Design Digital Library (K-MODDL) in an undergraduate mathematics class. Based on CIAO! framework, the research revealed usability problems and users? subjective experience when using K-MODDL, confirmed the usefulness of various physical and digital models in facilitating learning, and revealed interesting relationships among usability, learning, and subjective experience.

2004-02-27T00:00:00Z Taimina, Daina Henderson, David W. http://hdl.handle.net/1813/2716 2006-03-21T08:22:39Z 2003-05-15T00:00:00Z

Title: How to Use History to Clarify Common Confusions in Geometry Authors: Taimina, Daina; Henderson, David W. Abstract: We have found that students and even mathematicians are often confused about the history of geometry. Many expository descriptions of geometry (especially non-Euclidean geometry) contain confusing and sometimes-incorrect statements. Therefore, we found it very important to give some historical perspective of the development of geometry, clearing up many common misconceptions. In this paper we use history to clarify the following questions, which often have confusing or misleading (or incorrect) answers: 1. What is the first non-Euclidean geometry? 2. Does Euclid's parallel postulate distinguish the non-Euclidean geometries from Euclidean geometry? 3. Is there a potentially infinite surface in 3-space whose intrinsic geometry is hyperbolic? 4. In what sense are the Models of Hyperbolic Geometry 'models'? 5. What does 'straight' mean in geometry? How can we draw a straight line? We noticed that most confusions related to the above questions come from not recognizing certain strands in the history of geometry. The main aspects of geometry today emerged from four strands of early human activity that seem to have occurred in most cultures: art/patterns, building structures, motion in machines, and navigation/stargazing. These strands developed more or less independently into varying studies and practices that eventually from the 19th century on were woven into what we now call geometry. In this paper we describe how these strands can be used to clarify issues surrounding these questions.

2003-05-15T00:00:00Z Lipson, Hod Moon, Francis C. Hai, Jimmy Paventi, Carlo http://hdl.handle.net/1813/2715 2006-03-21T08:22:57Z 2003-07-31T00:00:00Z

Title: 3D-Printing the History of Mechanisms Authors: Lipson, Hod; Moon, Francis C.; Hai, Jimmy; Paventi, Carlo Abstract: Physical models of machines have played an important role in the history of engineering for teaching, analyzing, and exploring mechanical concepts. Many of these models have been replaced today by computational representations, but new rapid-prototyping technology allows reintroduction of physical models as an intuitive way to demonstrate mechanical concepts. This paper reports on the use of computer-aided modeling tools and rapid prototyping technology to document, preserve, and reproduce in three dimensions, historic machines and mechanisms. We have reproduced several pre-assembled, fully-functional historic mechanisms such as early straight line mechanisms, ratchets, pumps, and clock escapements, including various kinematic components such as links, joints, gears, worms, nuts, bolts, and springs. The historic mechanisms come from the Cornell Collection of Reuleaux Kinematic Models as well as models based on the work of Leonardo da Vinci. The models are available as part of a new online museum of mechanism, which allows visitors not only to read descriptions and view pictures and videos, but now also download, 3D-print and interact with their own physical replicas. Our aim in this paper is to demonstrate the ability of this technology to reproduce accurate historical kinematic models and machines as a tool for both artifact conservancy as well as for teaching, and to demonstrate this for a wide range of mechanism types. We expect that this new form of ?physical? preservation will become prevalent in future archives. We describe the background and history of the collection as well as aspects of modeling and printing such functional replicas.

2003-07-31T00:00:00Z Henderson, David W. Taimina, Daina http://hdl.handle.net/1813/2714 2006-03-21T08:11:54Z 2003-05-15T00:00:00Z

Title: Experiencing Meanings in Geometry Authors: Henderson, David W.; Taimina, Daina Abstract: It is deep experience of meanings in geometry (and indeed in all of mathematics and well as art and engineering) that we believe deserve to be called aesthetic experiences. We believe that mathematics is a natural and deep part of human experience and that experiences of meaning in mathematics should be accessible to everyone. Much of mathematics is not accessible through formal approaches except to those with specialized learning. However, through the use of non-formal experience and geometric imagery, many levels of meaning in mathematics can be opened up in a way that most people can experience and find intellectually challenging and stimulating. Many formal aspects of mathematics have now been mechanized and this mechanization is widely available on personal computers or even handheld calculators, but the experience of meaning in mathematics is still a human enterprise. Experiencing meanings is vital for anyone who wishes to understand mathematics, or anyone wishing to understand something in their experience through the vehicle of mathematics. We observe in ourselves and in our students that these are, at their core, aesthetic experiences. In this paper we will tell some stories of our experience of meanings in geometry and art. David's story starts with art and ends with geometry, while Daina's story starts with geometry and ends with art. However we both share the bulk in the middle, including experiences of non-Euclidean geometries and kinematics models.

2003-05-15T00:00:00Z Taimina, Daina http://hdl.handle.net/1813/2713 2006-03-21T08:21:19Z 2003-05-01T00:00:00Z

Title: How it was to study and to teach mathematics in Cornell at the end of Authors: Taimina, Daina Abstract: Cornell University's Kroch Library Rare Book and Manuscript Division has a collection called "Department of Mathematics records 1877-1976". It was used already as case studies of the emergence of mathematical research at Cornell University in several publications; but I will talk about my experience going through these records and trying to imagine what mathematics students had learned before entering Cornell University (looking at entrance exams they were given). The earlier publications reported that mathematics entrance requirements to Cornell "were minimal by today's standards" but I found that this was not the case. Many of the students taking the entrance exams were engineering students. At that time the Reuleaux kinematic models collection was used to bring mathematical ideas into engineering curriculum. Preliminary report partially supported by National Science Foundation's National Science, Technology, Engineering, and Mathematics Education Digital Library (NSDL) Program under grant DUE-0226238. (Based on a talk given at AMS- MAA Joint Conference Special Session in History of Mathematics, January 18, 2003, Baltimore.)

2003-05-01T00:00:00Z Moon, Francis C. http://hdl.handle.net/1813/2712 2006-03-21T08:10:45Z 2002-10-17T00:00:00Z

Title: Franz Reuleaux: Contributions to 19th C. Kinematics and Theory of Authors: Moon, Francis C. Abstract: This review surveys late 19th century kinematics and the theory of machines as seen through the contributions of the German engineering scientist, Franz Reuleaux (1829-1905), often called the "father of kinematics". Extremely famous in his time and one of the first honorary members of ASME, Reuleaux was largely forgotten in much of modern mechanics literature in English until the recent rediscovery of some of his work. In addition to his contributions to kinematics, we review Reuleaux's ideas about design synthesis, optimization and aesthetics in design, engineering education as well as his early contributions to biomechanics. A unique aspect of this review has been the use of Reuleaux's kinematic models at Cornell University and in the Deutsches Museum as a tool to rediscover lost engineering and kinematic knowledge of 19th century history of machine.

2002-10-17T00:00:00Z