Introduction

Introduction
The mathematics you're studying has a long history. Ideas behind geometry and trigonometry go back to thousands of years before even the ancient Greeks, all the way to one of the oldest civilizations: ancient Egypt. The annual flooding of the Nile river valley forced the ancient Egyptians to become adept at re-creating farming land boundaries within the fertile flooding zones, making Egyptians the first surveyors, and thus the first people to apply principles of geometry and trigonometry.
Thousands of years later, but still over two thousand years before the present day, Greeks improved upon the Egyptian methods with formal logical geometric proofs, and were the first to consider rational and irrational numbers, including powers and roots and other features of numeration and numbering. It was another thousand years later, during the European "Dark Ages", before algebra was created in Islamic Baghdad, and over 800 years after algebra (or about 300 years before now) before calculus was formulated in both Germany and Britain during the "Age of Enlightenment".
These days we use lots of symbols and notations in mathematics without thinking about their history or original meaning. In fact, knowing the history of mathematics can help in understanding it, like the fact that the Greek letter "π" is our letter "p", the first letter in the word "periphery", which brings to mind the circumference of a circle, which helps define π mathematically. That is why your "quest" on the "web" will be to investigate the origin of many of the mathemtical symbols we use today, as well as other aspects of mathematics history.
Task
Task
You will be provided a set of questions which need to be investigated and answered in the context of mathemetical history. The question sets are divided among several areas of mathemetics (algebra, geometry, trigonometry, etc), and your teacher will let you know which areas you will need to work on. You will need to research each answer, and produce a brief one-paragraph report of your answer referencing your research. Pay attention to the rubric in the Evaluation section of this WebQuest when developing your answers.
Process
ProcessResearch and provide a one-paragraph answer to the following questions from mathematics history in the area(s) defined by your teacher.
Area 1) Arithmetic and Numeration(a) Pick a symbol from arithmetic (+, -, =, etc). Who first used it, and why?(b) What does the infinity symbol (∞) have to do with roman numerals?(c) Why is the decimal number system we use called "Hindu-Arabic"?
Area 2) Algebra
(a) What does the word "algebra" have to do with the phrase "completing the square"?(b) Algebra could also have been called "almucabola". Why?(c) Why do we use the letter "x" to represent an unknown variable?
Area 3) Geometry and Trigonometry(a) Why should Christopher Columbus have listened to Eratosthenes?(b) What does the the word "sine" have to do with a bow and arrow?(c) What do bridges in Kaliningrad have to do with graphs?
Area 4) Calculus(a) Why does the integral symbol (∫) look like it does? (b) Why are there so many notations for the derivative (dx/dt, x', ẋ, etc)?(c) Why don't we call derivatives "fluxions"?
Evaluation
Evaluation
The one-paragraph answer to each question from the Process section will be evaluated according to the following rubric. (Sample question: "Who first used pi to represent the circular ratio?")
|
Beginning 1 |
Developing 2 |
Very Good 3 |
Exemplary 4 |
|---|---|---|---|
|
The answer is provided without elaboration of historical or functional context. ("William Jones first used the symbol pi for the circular ratio.") |
The answer is provided with some elaboration of historical or functional context. ("Jones used pi to represent the (p)eriphery of the circle, pi meaning "p" in Greek.") |
The answer is provided with some elaboration of both historical and functional context. ("While Jones first used pi in 1706, it was Euler who popularized its use by 1748, due to his standing among mathematicians in Europe.") |
The answer is provided with ample elaboration of historical and functional context. ("Pi as a concept goes back to the ancient Egyptians, with approximations recorded over 3500 years ago, and possible use in the Great Pyramid 1000 years earlier.") |
Conclusion
Conclusion
Mathematics is not the only subject area that benefits from a historical context. Students should consider their journey through education as being similar to the process society went through to establish the truths students are learning now, just on a much smaller time scale. Familiarizing yourself with society's historical journey developing knowledge can only make your own similar journey easier.
There's a phrase from developmental biology ("ontogeny recapitulates phylogeny") which suggests that there are parallels between embryonic development and evolutionary development. Learning the historical context of a subject area is a "recapitulation theory" for your education. Always keep it in mind.
Credits
CreditsThank you to the people at Google who developed a simple means of searching for all sorts of information, the administrators and contributors of Wikipedia (especially the mathematics-based articles) for putting an encyclopedia in everyone's hands, all the other contributors to the production and maintenance of the World Wide Web, and to the people at CreateWebQuest.com for making a great place to build and host a WebQuest.