Mathematics did not just happen, it has evolved. For your first maths homework, you are going to look at one part of the history of mathematics. Choose a period of history from the next page and then select a suitable task(s). This will be an opportunity to impress with the standard of your work. Don’t settle for second best. In the side bar, you will find various web links that can help. Click on the link to access the internet.
Choose your topic by clicking on the picture
THE EGYPTIANS AND MATHEMATICS • The Egyptians are best known for the magnificent pyramids which are still standing in our modern world. The construction of these gigantic buildings needed a high level of mathematical ability which we will look at more closely. • Possible Tasks • The most famous Egyptian is the Pharoah Tutankamen. Find out as much as possible about this man and the pyramid he was buried in. • As said already, the pyramids are interesting buildings. You could make a small pyramid of your own, and look into its many properties. • To illustrate how the Egyptians used mathematics produce an attractive wall display for the classroom. • The Egyptians knew a great deal about triangles and pyramids. For the below triangles they found the rule to find out how many were needed for a given number of levels. Can you?
CHINESE AND MATHEMATICS • The Chinese being separated from Europe continued to be ignored by foreigners until the late Nineteenth Century. It was then found to have a very high level of mathematical treasures among other precious possessions. • Possible Tasks • Produce a sheet of Chinese mathematics questions and answers using this web link to produce Chinese numbers. • The Chinese produced many games, notably ‘Chess’ and ‘Go’. Find out as much as you can about these two games. • The ‘Magic Square’ was used by the Chinese for many decorative purposes. Make up a magic square and use it in a Chinese design of your own. • Produce a wall display showing the Chinese using mathematics. • A Chinese story goes that an Emperor was so fascinated by the game of chess when it was shown to him that he said he would give the inventor any reward he wanted. The crafty inventor said he would like one grain of wheat for the first square of his chessboard, two for the next, four for the next, and so on. Work out how many grains of wheat the inventor would receive. Is this a reasonable price?
GREEKS AND MATHEMATICS • The Greek civilisation was at its height approximately 600 – 300 B.C. and during this time they produced many of the ideas governing our life today. These include such areas as philosophy, medicine and of course mathematics. The most famous Greeks are Pythagoras, Euclid and Aristotle. • Possible Tasks • Find out as much as possible about these three Greeks. (If you become struck try and find out about Pythagoras’ Theorem and Euclid’s Elements). • Using the Greek numbers, write a sheet of Greek mathematics questions. You must also, of course, provide an answer sheet. • Produce a short play starring a Greek mathematician. • Make a wall display showing the Greeks and the mathematics they used. • (A Greek Paradox). Achilles and a tortoise run a race. The tortoise runs a mile of the course before Achilles, running ten times as fast as the tortoise, starts. When Achilles has covered his first mile the tortoise will, therefore, be 0.1of a mile further ahead. When Achilles has completed this distance, the tortoise will be 0.01 of a mile ahead of him… and so on. Are we to conclude that the tortoise will always be a little ahead?
ROMANS AND MATHEMATICS • Much of the development of mathematics stopped after the Roman Empire came to dominate Europe. They were too busy conquering than counting. However, some mathematics continued to be used, especially if of a practical nature. The most famous examples being the aqueducts, bridges and roads which are still standing. • Possible Tasks • Roman numerals are still used today, notably to show when a television programme was made. Make a list of your favourite programmes and find the year they were filmed. • An Abacus was a counting frame used by the Romans. Find out how you use this helpful device. Perhaps write out a set of instructions. • The most famous Roman building is the Colosseum. Collect as much information about this building as possible. • Make up a set of mathematics question using Roman numerals. Remember to include an answer sheet. • Construct an attractive wall display with the theme being ‘Romans using mathematics’.
THE RENAISSANCE AND MATHEMATICS • During the sixteenth century, Europe came out of a dark age to a world of thought and discovery. One of these paths of enthusiasm was in the area of mathematics. Many of our modern ideas about numbers date from this enlightened time. • Possible Tasks • Italy was a leader in this age of new thought. It produced many brilliant thinkers but probably the most famous is Leonardo De Vinci. Find out as much as possible about this great man. • The slide rule was first used during this time and, until the invention of the calculator, was an important piece of equipment for most mathematicians. Possibly you could make one yourself and find out how they work. • Gambling became widespread during this time. Many different games became popular and mathematics was used by a few to ensure victory. Find out how mathematics can help you win money. • Produce a wall display to show how mathematics was used during the Renaissance. • About this time experiments were tried with coordinates. Draw a picture on a coordinate grid, then redraw the picture using a doubled horizontal scale and a halved vertical scale. What has happened?
COMPUTERS AND MATHEMATICS • Electric computers have now become part of our everyday life. Few areas of the modern world have been left unaffected. However, mechanical computers were used in Europe since the 17th Century. Needless to say these mechanical computers did not calculate as fast as their modern equivalents. • Tasks • Charles Babbage is called the father of modern computers. Find as much as possible about him. • The electronic calculator can do many different operations. Choose a suitable example, and find out what the various buttons do. • All major companies now use computers to help in the work that they do. Collect examples of these. • Make an attractive wall display showing how computers are used in our modern world. • The earliest computers were of a mechanical operation. Try to build a computer of your own which can be used for simple arithmetic. • Alan Turing is often linked with code breaking. Find out about what he achieved.
Greek numerals are a bit more complicated than Roman. There are two distinct groups of Greek numerals, and both are given below. First is the Acrophonic - this is type of Greek numerals that were used in ancient Greece up to Roman times (100 BC). It is called acrophonic because of the initial letter of the word designation - for example g (in Greek script as below) stood for five, and five was 'gente'; h stood for 100, and hundred was 'hekaton' and so on. This system is also sometimes called 'Attic' - it also stands for an offspring of Ionic dialect spoken in the city of Athens. This was later replaced by the Alphabetic numerals - where 27 letters and their combinations stood for all numbers. The table is given below too. This system is also sometimes called Ionic. It was not positional, meaning that the place of the letter did not denote its value like we have it in our number system. Acrophobic Alphabetic