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The Story of Mathematics

Name:___________________________________ No:__________

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The Language Of The Universe & The Origins Of Mathematics

Professor Marcus Du Sautoy describes himself as a ___________________. He believes that this is what Mathematicians are really trying to do. What was the main reason that Mathematics began? _____________________________________________________________________ What did the Egyptians first use to calculate measurement? _____________________________________________________________________ The Egyptians were responsible for creating the ________________ system in Maths. About 2700 BC Egyptians introduced the earliest fully developed base 10 numeration system. What was the main problem with this number system? _____________________________________________________________________ The Rhind papyrus was recorded by a scribe named Achmez around ____________. The Horus Eye was the first hint at a ________________ series. Mathematicians from which continent discovered the concept of an infinite series? _____________________________________________________________________ Name the famous ratio used by the Egyptians when they built the pyramids. _____________________________________________________________________

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Describe how the Egyptians perfected right angles of pyramids. _____________________________________________________________________ Name the famous Greek Mathematician who developed this concept and how long after the Egyptians.______________________________________________________ The Great Sphinx of Giza,

with the Pyramid of Khafre in the background Where did the next huge development of Maths (after the Egyptian era) take place? _____________________________________________________________________ These people were commonly known as the _______________________________. Today, our number system uses powers of ten for counting, but their number system used powers of _________________________________________________________ The Babylonian calendar was based on the cycles of the ________________________ Farmers were always interested in calculating the area of their land. This is what lead to the creation of _______________________________________________________ In modern Mathematics, what application would we use to solve such a problem? _____________________________________________________________________

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Why did the Babylonian era of Mathematics end? _____________________________________________________________________ Who gave us the power of proof in Mathematics? _____________________________________________________________________ When Professor Du Sautoy describes about Greek Mathematics, he says that it has always been ____________________ and __________________________. Pythagoras founded a school in ___________________ in the 6th Century BC. Very little is known about Pythagoras

because none of his writings have survived. Many of the accomplishments credited to Pythagoras mayactually have been accomplishments of his colleagues and

successors

Explain briefly what Pythagoras’ theorem states. _____________________________________________________________________ Pythagoras also made a significant discovery in the field of music. What was it? _____________________________________________________________________ The problem of the diagonal on the triangle was one which frustrated the Greeks. Why could they not express it as a fraction? _____________________________________________________________________ Name the famous Philosopher and mathematician who founded the Academy School in Athens in 387 B.C. _____________________________________________________________________ What did he describe as being the key to unlocking the universe? _____________________________________________________________________

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A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids What did the tetrahedron and the cube represent? _____________________________________________________________________ What city in Egypt became the heart of mathematics after the Greek era? _____________________________________________________________________ The narrator describes one famous mathematician as his hero. What is his name? _____________________________________________________________________ What is the name of his most famous textbook and what does it describe? _____________________________________________________________________ Name the famous mathematician who joined Euclid’s school. _____________________________________________________________________

Archimedes’ contributions to Mathematics were so great that he was even represented on postage stamps in Italy. Some of his inventions are seen in the picture.

Give his main area of interest and how he used these items? _____________________________________________________________________ Archimedes described a circle as being what? _____________________________________________________________________ His approximation gave him the first accurate value for what important symbol? _____________________________________________________________________

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The Genius Of The East The Great Wall of China is approximately 6,400 km long. Almost 3 million people died during its construction

When did the building of the Great Wall of China begin? _________________________________________________________ Give two reasons why the Chinese needed mathematics to build the Great Wall. _____________________________________________________________________ The Chinese did not have a symbol for the number ___________. They believed that odd numbers were male and that even numbers were _______________________________________ Chinese artwork showing some of the symbols used in ancient Chinese mathematics The Chinese people also developed the first version of the popular number game we know today as ____________________________. They called it the _________________________________ Draw the magic square in the box. Name the famous mathematics textbook written by the Chinese and give its central theme. _____________________________________________________________________

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Today we know these equations to be called ____________________________ equations. Quadratic equations involve numbers which are _______________________________________ was interested in ________________________ . This method was not discovered in the West until ___________________ by __________________________________________ What was the main problem with Ch’ins technique? _____________________________________________________________________ The narrator describes mathematics as being an ________________________ science. What country changed the face of mathematics after China? _____________________________________________________________________ Indian mathematics used trigonometry to make calculations about the planets and the world around us.

These were the first major steps in linking mathematics with astronomy.

The Indians were known to be using a decimal system by the middle of the ________ century. They also discovered the number ___________________ in the ________________ century. They believed that one divided by zero is equal to ______________________________________ The Indian mathematicians also discovered ___________________________ numbers.

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Quadratic equations always have _____________ solutions, one which can be _______________ This was later discovered in the West in ___________by French mathematician ______________ The Indian mathematicians also made major developments in ____________________________ Name two areas where the sine function is commonly used today. _____________________________________________________________________ How much further from the earth is the sun than the moon? _____________________________________________________________________ Madhava, a famous Indian Mathematician, made huge progress on what topic? _____________________________________________________________________ The symbol is the ratio of ______________________________________________________ Madhava’s approximation of was more accurate than anyone who had attempted it before him. He

used the concept of infinite series to get an exact value.

Mathematics of Ancient Babylonia (now Iraq), once the centre of the Mesopotamian Empire

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The Frontiers of Space

An artistic technique known as ____________________ became popular with artists in Italy. It was used to change objects from ________________________ to _________________________ Rene Descarte was one of the greatest mathematicians

of all time. He made huge contributions to many areas and led the way for the beginning of calculus.

Rene Descarte was a famous __________________ mathematician who was also interested in ____________________________________. What was the name of his famous textbook and what connection did it make? _____________________________________________________________________ Who became Descarte’s main rival during his time as a scholar? _____________________________________________________________________ Name one of Fermat’s famous theorems. _____________________________________________________________________ What is Sir Isaac Newton most famous for discovering? _____________________________________________________________________ Newton developed a very important concept in mathematics. What was it? _____________________________________________________________________ Isaac Newton discovered gravity when an apple fell

on his head as he sat under a tree. “If I have seen further than others, it is by standing upon the shoulders of giants.” (Sir Isaac Newton).

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Newton’s main rival was another great mathematician from Germany. What was his name? _____________________________________________________________________

At what age did his developments in differential and integral calculus take place? _____________________________________________________________________ What credit did the Royal Society give to both Newton and Leibniz? _____________________________________________________________________ In which years did Newton and Leibniz die? _____________________________________________________________________ Name the great dynasty (family) of mathematicians who studied in Basel. _____________________________________________________________________ Give one use of the calculus of variation in the world today. _____________________________________________________________________ The narrator describes a Swiss mathematician as being the most famous name in mathematics. What is his name? _____________________________________________________________________ Euler got a job as a university lecturer in which Russian city? _____________________________________________________________________

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Leonhard Euler (1707-1783) was arguably the greatest mathematician of the 18th century and one of the most

prolific of all time. He published a massive total of 886 books and papers throughout his life.

Euler made huge contributions in every field of mathematics at the time, and also developed a new theory of ___________________________________________________________________ Who does the narrator say is his favorite mathematician of all time? _____________________________________________________________________ Gauss developed a new set of numbers perpendicular to those on the number line. These numbers are known as ___________________________________________________________________ What problem did Euclid discover with Euclid’s geometry? _____________________________________________________________________ The Romanian mathematician Bolyai developed geometry known today as _____________________________________________________________________ The famous picture of ‘Janos Bolyai’ which in fact is actually a picture of his brother. By the age of 13, he had mastered

calculus and other forms of analytical mechanics, receiving instruction from his father. He studied at the Royal Engineering College in Vienna from 1818 to 1822.

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To Infinity and Beyond – 20th Century Mathematics

Name two of the great unsolved problems that confronted mathematicians in the 20th century _______________________________________________________________

How many problems did Hilbert pose which he believed were crucially important? ___________

David Hilbert - German mathematician who was regarded as one of the most influential of the 20th century

Name one major contribution to 20th century mathematics by Georg Cantor. _____________________________________________________________________ By the age of 20, Évariste Galois was making major contributions to mathematics and was being described as a true genius. What stopped him from making further progress in the 20th century? ______________________________________________ ______________________________________________ Name one famous female mathematician of the 20th century _____________________________________________________________________ The Riemann Hypothesis, still unsolved as of today, deals with distribution of ___________ numbers. Name one idea or topic or problem which you found interesting over the course of this class, and describe how it has helped you understand mathematics a little better. Does it have any applications in the real world? What are they? ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________