Appendix A

Event	Start	end
Notched wolf bone in groups of 5	30000B.C.
Egyptian had a fully developed number system that could be used to continue counting indefinitely	3500 B.C.
Sumerians Succumbed to the Akkadians	2500 B.C.
Beginning of Babylonian times	2000 B.C.
Babylonian-Symbol for a Place holder-represents "nothing"	600 B.C.	200 B.C.
Greeks had an extensive alphabetic numeral system	500 B.C.
Zeno was born/ little actually known about him	450 B.C.
Zeno's Paradox lay unsolved, Very rough estimation	450 B.C.	1754A.D.
Ptolemy used the omicron for doing calculations of astronomy	150 A.D.
Darius Vase	300 A.D.	400 A.D.
Indian culture adopted a Babylonian type numeration system	400 A.D.	500 A.D.
Dark ages	400 A.D.	1100 A.D.
Rome fell\ Place holder "re-discovered"	476 A.D.
King Charlemagne	742 A.D.	814 A.D.
Indian culture was using a base 10 system with a zero type "place holder"	800 A.D.	900 A.D.
Al-Khowarizmi	1040 A.D.	1123 A.D.
Scientific work of Aristotle forbidden at the University of Paris under pain of excommunication	1210 A.D.
Nicolas Copernicus	1473 A.D.	1543 A.D.
Germon monk Luther Nails list of complaints to the Church's door	1517 A.D.
Copernican Universe	1543 A.D.
Copernicus died/ 'De Revolutionibus Orbium colestium' was published	1543 A.D.
Pope Paul II issud the index of forbidden books	1543 A.D.
Galileo of Galilei	1564 A.D.	1642 A.D.
Appr. Date-Giordano Bruno published 'On the Infinite Universe and Worlds'	1580 A.D.
Giordano Bruno was burned at the stake	1600 A.D.
Church ordered Galileo to cease his "scientific investigations"	1616 A.D.
Copernicus's 'De RevolutionibusOrbium Colestium' was placed on the Index of forbidden books	1616 A.D.
Galileo's manuscript 'the Dalogue'	1632 A.D.
Galileo stood trial for 'the Dialogue'/it was placed on the Index of forbidden books	1635 A.D.
Isaac Newton	1642 A.D.	1727 A.D.
Galileo's assistant, Evangelista Torricelli, prooved that a vacume in space exists(Seife,2000, pp. 97-98)	1643 A.D.
Gottfried Leibniz	1646 A.D.	1716 A.D.
Newton's years of leasure in Woolsthrope	1664 A.D.	1666 A.D.
Newton's De Analysi per Aequationes Numero Terminorum Infinitas	1669 A.D.
Leibniz developed his Calculus	1672 A.D.	1676 A.D.
Jean D'Alembert	1717 A.D.	1783 A.D.
D'Alembert's Encyclopédie-volume 4 suggests the idea of limits	1754 A.D.
Augusstin Louis Cauchy	1789 A.D.	1857 A.D.
Cauchy's treatise 'Course d' analyse de I' Ecole Royale Polytechnizue'	1821 A.D.
Midnight, December 31, 1999, we celebrated the New millennium on the wrong day	1999 A.D.	2000 A.D.

Appendix B

(1) The theme of this webpage is the concept of zero. I chose this topic after being introduced to the idea that zero could be considered one of the greatest inventions of mankind, but was not very easily accepted, by a trade book by Charles Seife entitled Zero:The Biography of a Dangerous Idea. I had previously only read a chapter or two from the book, but it really captured my attention and this project presented me with an opportunity to learn more.

(2) I have constructed this website in order to broaden the user's scope of view so that they will be able to see zero transcend through time. I would like users to understand what zero is, how it behaves, and make historical connections in mathematics, and the world. Zero provides a seat that can take you through almost every aspect of modern mathematics, and part of this website is designed to help make a few of those connections. More specific objectives include:

· Users observe zero in the scope of time from nonexistence to now.

· Users comprehend some of the basic properties of zero and discover how they lead to unacceptable mathematical consequences.

· Users discover the connection between zero and its religious consequences.

· Users discover proof that zero was avoided, discouraged, and fought against through time.

· Users comprehend and distinguishes between zero: an Idea of nothing, a symbol for nothing, a place holder, and a number.

· Users understand the connection zero has to infinity, calculus, and limits.

· Users visualize the historical atmosphere surrounding each step of the development of zero.

(3) One of the most important technological enhancements that will help achieve my objectives is the image mapping of the timeline, where the events on the timeline are linked to the material in the other web pages. Being able to use image mapping has allowed me to connect the material throughout the website in an accessible way; it has essentially tied everything together. Particularly, the timeline broadens the users point of view to see zero throughout time. As much information, and in many cases, background information that is included in the webpage, the timeline will help users move through the website and focus on points that interest them. Much of the background information will be navigated around, unless the user decides to read it. This is a major component that I used to "condense" the material.

The audio is a technological enhancement that will help users be relaxed and entertained In the Explanation of Mathematics page. Receiving some feedback on the webpage, I was lead to understand that this page did not have very much of a natural appeal that would drive readers to read it. The audio recording allows me to add drama, emphasis, and enthusiasm for the subtle but very important aspects of zero on this page. I will also be able to clarify some of the subtle connections and more complex connections that aren't as easy to make in writing. A huge benefit of using the audio will be that users be able to consider the main points of each section and consider a condense version of the written material. This will help the concept of zero remain in full view where else it could be lost in some of the more detailed descriptions.

I chose to incorporate a technology enhanced activity about Zeno's paradox. The realm of a limit is a little out of the scope of the intent of this website but I wanted to do something to help users understand a bit of what it is and how zero is connected to it. Where this concept can be very difficult to grasp, by including the applet, I was able to provide an interactive and entertaining approach to accomplish this objective.

I incorporated a link to http://nrich.maths.org/2671 which is about the legend of Hippasus of Metapontum, in order to provide some historical background to the severity of the atmosphere surrounding numbers. This legend is very interesting but to go into it too far would distract from the main point of the paper, and well, I’m already pushing that boundary quite a bit. I also included a variety of links in the applications page to provide visuals of the applications of zero that we used today. I am using these links to finish up the goal of showing the entire life of zero, by ending on Zero today.

(4) I have learned a lot through this project. I learned about the different components of zero (an Idea of nothing, a place holder, a symbol, and a number), and how they developed in a chain of events that lead to zero as we know it today. To me, one of the more interesting parts of what I learned was how the world resisted zero. It was compelling to learn how zero was tied to religion, which accounted for much of the resistance. I had no idea that zero caused so many problems for so many famous historical mathematicians, and their discomfort of zero (along with their religious ties) even prevented them from making huge strides in mathematics. It was also very interesting to see the properties of zero in a different light. I was able to learn how it would feel to be in the shoes of someone trying to accept zero when its properties defy everything I would know about numbers. I learned how big of a role zero plays in, pretty much, every aspect of mathematics. It was fun to see the artifacts left form mankind's avoidance of zero, including issues in the calendar.

For my presentation, I would like to first introduce my classmates to zero as an Idea of nothing, a place holder, a symbol, and a number. Following that I would like to have them consider some of the evidence suggesting the avoidance of zero and the repercussions of accepting zero as a number. I also want my class to observe how zero is tied to pretty much everything in mathematics. I want my classmates to see where these events are happening in time and consider how long it took for some of the steps in the development of zero to happen.