Virtual-Field-Trips
Mathematics
Site Overview:
Have you ever wondered where the concept of mathematics came from? Well, this site explains the origins of math from the Ancient Egyptians and Mayans to the Greeks and Arabians to modern-day concepts. The site offers over 1550 biographies of mathematicians, a Top 100 list, and pictures of famous curves that we use in everyday life. Whether you’re just learning to add, or already love math, this site is very informative and comprehensive.
Goals and objectives:
The Goals and Objectives of this field trip are to 1) Read at least one biography of a famous mathematician, 2) Learn more about the history of mathematics, and 3) look at mathematical principles such as circles, curves, and lines.
Further Research:
Every culture on earth has developed some mathematics. In some cases, this mathematics has spread from one culture to another. Now there is one predominant international mathematics, and this mathematics has quite a history. It has roots in ancient Egypt and Babylonia, and then grew rapidly in ancient Greece. Mathematics written in ancient Greek was translated into Arabic. About the same time some mathematics of India was translated into Arabic. Later some of this mathematics was translated into Latin and became the mathematics of Western Europe. Over a period of several hundred years, it became the mathematics of the world. There are other places in the world that developed significant mathematics, such as China, southern India, and Japan, and they are interesting to study, but the mathematics of the other regions have not had much influence on current international mathematics. There is, of course, much mathematics being done these and other regions, but it is not the traditional math of the regions, but international mathematics. By far, the most significant development in mathematics was giving it firm logical foundations. This took place in ancient Greece in the centuries preceding Euclid. Logical foundations give mathematics more than just certainty-they are a tool to investigate the unknown. By the 20th century the edge of that unknown had receded to where only a few could see. One was David Hilbert, a leading mathematician of the turn of the century. In 1900 he addressed the International Congress of Mathematicians in Paris, and described 23 important mathematical problems. Mathematics continues to grow at a phenomenal rate. There is no end in sight, and the application of mathematics to science becomes greater all the time.
Lesson Plans and Site Navigation:
1. The website for this field trip is http://www-history.mcs.st-andrews.ac.uk/history/index.html. From time to time, the links on a website do not work. Either skip the questions below or go to the page you have been directed to and go on. When navigating this site, please use your forward and back arrows to go back to the original page. This tour is easy to navigate. If you get lost, click on “Main Index” form any page to get to the homepage. On the left sidebar, Go to Biographies Index. The biographies are listed alphabetically and chronologically. If you don’t have a favorite mathematician, some interesting ones are: Nash, Einstein, Newton, Galileo, Aristotle, Euler, Pascal, Nightingale, and Descartes. At the bottom of each biography page, there are links to more references about the mathematician, to others born in the same country, honors the mathematician received, and sometimes a quotation.
2. Go to the History Topics page. Under Mathematics in various cultures, Select a people you would like to learn about and read the information. The overviews for each topic provide the most information. There is also a list of some of the concepts the people came up with. Go back onto the History Topics page. Under Mathematical topics, there are links to the different branches of Math.
3. From the bottom of any page, you can go to Birthplace Maps. Choose a region or country and go to the map. Wherever there are little black dots, a mathematician was born there. To see who it was, click on the dot and his/her name and where she/he was born will appear in the right sidebar. Click on the link to read their biography.
4. Go to the Famous Curves Index. Some of the curves are very advanced, but others are easier, such as: circle, eight curve, straight line, involute of a circle, and parabola. Click on any of the curves to see a drawing of one, its equation, and who invented and studied the curve (note: the drawings may take a second or two to load).
5. Click on Mathematicians of the Day. This site shows which mathematicians were born and who died on the day that you view the website. It also usually includes a quotation of one of the mathematicians.
6. The TimeLine of mathematicians gives a timeline of each period in history. Choose a period. The horizontal lines show the mathematicians’ lifespan, the vertical lines indicate the year. From the Timeline page, click on the link that says ‘A list of Mathematicians alive on a particular date”. When you type in a year, it will show you all the mathematicians who were alive and died during that year.
7. If you wish to search the MacTutor Archives, go to the Search Form and type in what you are looking for. Check the boxes to the left if you think it might be found under any of those categories.
8. Just for fun, if you would like to find out any mathematicians who were born and died on your birthday, go to Mathematicians Anniversaries. It will bring up a calendar, so you can pick the month and date.
Scavenger Hunt Questions
Grades K-3:
1. Why is math important to us?
2. Where was John Nash born?
3. Why did Albert Einstein move to America?
4. Isaac Newton discovered the concept of gravity. How does gravity work?
5. Florence Nightingale was a nurse in the Crimean War, which is one of the reasons she was famous. Why else was she famous?
6. Can you draw any of the famous curves from the website? If you can, draw them and label them.
7. Were any mathematicians born where you were? If so, who were they?
8. Where did the Mayan civilization come from?
Grades 4-8:
1. Name some of the uses of math in your life.
2. Why did John Nash never go to his lectures at Princeton University?
3. The book Newton wrote is said to be the greatest Science book ever written. What was it called?
4. Newton came up with a few theories as well as inventions. Name some of them.
5. What were Hieroglyphics and who used them?
6. What was the base of the Mayans’ number system and why?
7. When the Mayans built the Caracol Building, they positioned windows of the building to line up with significant lines of sight such as that of the setting sun on the spring equinox of 21 March and also certain lines of sight relating to the moon. How did they do this?
8. What would you use Pi for?
9. Many of the ideas, which were previously thought to have been brilliant new conceptions due to European mathematicians of the sixteenth, seventeenth, and eighteenth centuries are now known to have been developed by whom?
10. What was the Peruvians’ Abacus, or counting board, known as? How do we know it existed?
Grades 9-12:
1. There are many different branches of math. Name some of them.
2. What is written on the Rhind Papyrus, who wrote it and when was it written?
3. Where did the concept of Zero come from?
4. How was the Babylonians’ number system similar to ours?
5. The Mayans’ Haab calendar was similar to our calendar. Explain how theirs worked.
6. What is the numerical value of Pi? Give the modern value, as well as some from mathematicians from the past.
7. Which Arabic scribes wrote a numeral system that looks a lot like the one we use today?
8. How did Garcilaso de la Vega describe the Peruvians’ quipus?
9. What did Einstein’s’ formula E = mc2 express? When did he formulate it and why did he win the Nobel Prize in 1921?
Additional Activities:
• Instead of using a calculator to solve a math problem, use an abacus (if you have one) like the Arabians did.
• Use a compass to draw perfect circles. Make small and big ones. Color them in if you like.
• What do you want to do when you grow up? Research your profession and find out if you will need to use math or not. If you will need math, write a one-page report on why you need math.
• Look for examples of math and it’s applications around you and write them down. For example, patchwork quilts incorporate geometry, as do buildings. Ice crystals are made by fractals.
• For children 13 and older, watch the movie ‘A Beautiful Mind’. It is a very good movie and a biography of the mathematician John Nash’s life.
• For Younger children, play store. Put prices on household items, use real change, and calculate cost and change. Practice being the shopkeeper and being the customer by giving the right amount of money to pay and the right amount of change. Take turns!
• Probability is a branch of mathematics. One way of demonstrating probability is flipping a coin. Flip a coin and use one side as heads, one as tails. Flip the coin 10 times and write down the results. What is the probability that out of 10 coin flips, only 3 will be heads?
• Play a game of dominoes.