http://beshapiro.com/math370/origins-project.html
The goal of this project is to learn that Geometry is an ancient and widely utilized subject that has been studied thoughout the history of the world by a variety of cultures and civilizations. It was not invented in Greece and most especially not by Euclid. Euclid's great contribution was his codifcation: he gave the world a method for deducing a large body of knowledge from a small number of assumptions. Much of what he wrote was actually discovered centuries earlier, and a great deal of it was discovered independently in many different parts of the world (e.g., what we call the Pythagorean Theorem). Even many of the great "discoveries" of the last 300 years were actually European rediscoveries or results that had been already found elsewhere. While the contributions of the Greek philosophers such as the Pythagoreans, Thales, Euclid, Archimedes, and others, is not disputed, there is more to history than what is written in Eurocentric textbooks.
Each group will
- Write a short paper (app. 5 pages double spaced);
- Prepare a one-page handount for the class (timeline or summary); and
- Make a 5-minute presentation to the class.
Each group will be assigned a specific topic. The collection of topics is given below. If your group has a strong preference for or against a particular topic you should let me know as soon as possible. Note that Euclid is specifically excluded from the list of topics!
This written parts of the project counts for 10% of your final grade
Oral presentations over the course of the semester count for another 10% of your grade. There will be one oral presentation by each group. The group will decide whether to select a single speaker or let each student speak. Each student is expected to participate in either the history presentation or the lesson plan presentation later in the semester but is not required to make oral presentations for both projects.
The written paper should be approximately 5 pages, double spaced, 12 point roman-family font. The roman family of fonts is the default in a Latex document (usually it will be some version of a font that looks like Times or Times-Roman in MS Word) and you do not have to specify the font. The five pages excludes title page, any figures you want to include, references and bibliography. Include material in the following order:
- Title page, listing all group members. Do not put your group members' names anywhere else in the paper.
- The (min 5 pages of) text of the paper.
- Any figures you want to include, on separate pages.
- A bibliography listing important original publications of your time period, such as The Nine Chapters of the Mathematical Art, or Euclid's Elements.
- A list of the references you used, including any web pages or books you used. There is no minimum number of references.
Important Note: The text of the paper should discuss contributions to the origins and development of Mathematics. I don't want to see any biographical specifics. The following is UNACCEPTABLE:
Giovanni Girolamo Saccheri was born in 1667, ordained as a priest in 1694, and taught at the University of Turin (1694-1697) and Pavia (1699-1733). He was a protoge of Tommaso Ceva and studied philosophy, theology and mathematics at the Jesuit College of Brera. Very little is known about his early life, although he was born on Sept. 5, 1667, the son of a lawyer, in the village of San Remo, Genoa.The following would be better:
Giovanni Saccheri (1667-1733) most significant work, Euclides ab omni naevo vindicatus (Euclid Freed of Every Flaw) is widely cited as one of the earliest texts on Non-Euclidean Geometry, although many of the significant results had already been presented some 700 years earlier by Ghiyāth ad-Dīn Abul-Fat'h Umar ibn Ibrāhīm Khayyām Neyshābūri (commonly known as Omar Khayyam) in his seminal Risâla fî sharh mâ ashkala min musâdarât Kitâb 'Uglîdis (Discussion of the Difficulties in Euclid). Ironically, Saccheri's work was largely ignored by the European community until it was rediscovered by Beltrami in the 1800's. His major contributions included an attempt to prove Euclid's parallel postulate by assuming the existence of multiple parallels and finding a contradiction. This assumption is now known as the hyperbolic parallel postulate and is one foundation of Non-Euclidean geometry.Finally, feel free to include any mathematical content, figures, and equations you feel are appropriate,e.g.,
A Saccheri quadralateral is a quadrilateral with two equal sides perpendicular to the base, as shown below:and most important, have fun!
The presentation should be approximately 5 minutes and include no more than 5 slides. You can prepare your slides in Powerpoint, Impress, Keynote, Latex, or any presentation software that you have available, and then then convert them to pdf format before mailing them to me. This way all of the presentations will be on a single computer and we will not have to spend time switching between computers. Do not send me powerpoint or other originals, only the pdf file. This way the fonts, formats, and figures will all be included in your presentations - otherwise it is quite likely that they will be garbled in the translation between operating systems or email.
A note about presentations: don't put up a long bulleted list and then read it to the class. In fact, the fewer words you have on your slides, the better. The best slides have nothing but a picture or diagram and in your presentation you explain to people what the picture means. You don't have to memorize your presentation; you can use notes, but by all means, don't read from the slides!
You are only going to have a small number of slides, so don't take the advice of those presentation websites that say you need an introduction and conclusion slide, and all that: each of you slides should have some significant content, and be labeled in the header with you topic and the footer with the names of your group members. We all know the goals of your talk: to tell us about X in geometry. Just make sure we know what X is.
In this slide, you would not read the paragraph out loud: you should assume your audience is capable of doing that themselves. Instead, you would explain that the lines h and k meet at a point S on the side of g such that alpha + beta < 180 degrees.
The handout should be a one-page summary of what you have learned and want your audience to remember. You can put anything you want on it.
Schedule:
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Jan 22: Assignment into groups and topic assignment
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Jan 22 - Feb 22: Groups meet to discuss and prepare project deliverables.
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Sunday Feb 22 at Midnight (email): Papers and Handouts due in both pdf and latex format; Presentation slides in pdf format only.
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Week of Feb 24 and Feb 26: In-class presentations. Each group must bring enough copies of their handouts to make sure everyone in the class gets one.
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March 1 at Midnight (email): Each individual turns in peer evaluation of other group members. This will help me assess whether all group members made a reasonable contribution to the project.
Tentative List of Topics; additional topics may be added. Projects on Greek geometry will only be allowed if there are not a sufficient number of topics for all groups.
Click here for the list of topics