**Creative Mathematics**

By Ruby Kopsiaftis

By Ruby Kopsiaftis

Leonardo Pisano Bigollo

Leonardo pisano bigollo was a famous Italian mathematician. Leonardo was best known as Fibonacci. Fibonacci's first major work was the 'Liber Abbaci' (In English it is known as the book of calculations). Liber abbaci showed the practical importance of the new number system, Hindu-Arabic's. He was the one who spread the Hindu–Arabic number system over Europe and without him doing that European tradesmen and scholars would still be using old Roman numerals. Modern maths would have been impossible to Europeans if they hadn't changed to Hindu-Arabic number system!He is also well known for inventing the Fibonacci sequence. The Fibonacci sequence starts at one and adds the previous two numbers together to make the next number (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233). It was discovered in 1202, the same year that the Liber Abbaci was published! The Fibonacci sequence can be used in many different ways like in mathematics,

science and art!

Blaise Pascal

Blaise Pascal was a French mathematician, inventor, writer and Christian philosopher! In Mathematics he was very well known for inventing the Pascal Triangle. The Pascal Triangle is like a pyramid that starts at the top and works it's way down. It can be found in maths and nature!!!!!!!!!!!!

The two numbers above get added together to make the number below and if it is the first number or one of

the numbers on the side of the triangle there is

nothing to plus it with so it just stays the

same!!!

Sam Loyd

Sam Loyd was raised in New York. He was a

chess player, chess composer, puzzle creator, and

he was also a recreational mathematician. Out of these four things to most people Sam was best known as a puzzle creator and a chess star not so

much as a mathematician. He was also quite well known

for stealing other peoples puzzles and then publishing them under his own name. He did this with a puzzle called the 14–15 Puzzle which was a little box of movable pieces. Sam also used to work with another puzzle creator called Henry Dudeney and soon after they started to work together Henry accused Sam of stealing their puzzles and then going and publishing them under only his (Sam's) name.

Bibliography

http://en.wikipedia.org/wiki/Main_Page

http://kids.net.au

http://britton.disted.camosun.bc.ca/fibslide/jbfibslide.htm

http://library.thinkquest.org/27890/mainIndex.html

https://math.temple.edu/~reich/Fib/fibo.html

google.com

http://ptri1.tripod.com/

http://www.mathsisfun.com/puzzles/sam-loyd-puzzles-index.html

http://www.greatbuildings.com/buildings/Philips_Pavilion.html

http://www.ancientgreece.com/s/People/Archimedes/

http://archimedeshistory.weebly.com/mathematics-and-discoveries.html

http://answers.yahoo.com/question/index?qid=20090409172308AA5Molf

http://www.agnesscott.edu/lriddle/women/noether.htm

**Creative Mathematics**

Fibonacci Sequence in Nature

The Fibonacci sequence can also be found in nature...

Like this flower has one petal...

and this one has two petals...

and this one has three petals...

and this one has 21 petals!

These numbers are all part of the Fibonacci sequence!

Pictures that

relate to

Fibonacci!!!

The Formula

This is the formula for the Fibonacci sequence...

n= 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

x= 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377

x= n-1 + n-2

The Formula

The triangle starts at the top. The row at the

top is 'row 0' and that contains one number, the number one. If all of the numbers outside the triangle are zero then you would do 1 + 0 = 1 so then in row 1 (the second row down) you would put two one's. You would do the same for row 2 and row 3 and all the other rows!

Row 0 = 1+0=1

Row 1 = 1+0=1 1+0=1

Row 2 = 1+0=1 1+1=2 1+0=1

Row 3 = 1+0=1 1+2=3 1+2=3 1+0=1

Row 4 = 1+0=1 1+3=4 3+3=6 1+3=4 1+0=1

Pascal Triangle

The Pascal Triangle is related to the Fibonacci Sequence!!!

Blaise Pascal

Sam was called many

things, good and bad, in his time.

Martin Gardner called him "America's greatest

puzzler" and The Strand called him "the prince of puzzlers". Mel Stover called Sam "an old rascal" and

Matthew Costello called Sam "puzzledom's greatest celebrity...popularizer, genius" but also "fast-talking, snake oil salesman".

Sam's Many Names

Sam Loyds Puzzles

The Pony Puzzle - Trick Mules - Trick Donkeys

A Question of Time

Covent Garden Problem

Great Picnic Puzzle

Guess the Boy's Age

Marther's Vineyard

Juggler Puzzle

Keys Puzzle

There are many, many more puzzles and just after Sam died his son published a book with over 5000 of his puzzles in it!!!

Le Corbusier was born on the 6th of

October 1887 and was born in Switzerland. He

then became a French citizen. He was an architect, designer, painter, urban planner, writer and one of the pioneers of what is now called modern architecture. He designed many buildings all over Europe, India, and America. Le Corbusier was the architect of all these buildings.

Philips Pavilion

Stotzer House

Immeuble Clarté

Villa Schwob

There are also many more buildings

he designed.

Le Corbusier

A Timeline of Le Corbusier's Life

1887, He was

born.

1906, He

made his first trip outside of

Switzerland.

1907, He traveled

to Paris and found

work.

1908, He studied architecture in Vienna with Josef Hoffmann.

1910 - 1911, He worked for the architect Peter Behrens near Berlin.

1918, He met a Cubist painter named Amédée Ozenfant.

1922, He opened a studio in Paris with his cousin Pierre Jeanneret.

1957, His wife died.

1965, He died.

Philips Pavilion

The Philips Pavilion was designed by Le Corbusier and was built in Brussels, Belgium, 1958. He designed it so it uses 9 hyperbolic paraboloids (that is the shape of a pringle). It is a building that is very modern and was designed to be an exposition site.

1958, He designed Philips Pavilion.

Archimedes

Archimedes is a Greek mathematician. He

was born in Syracuse. Archimedes is one of the

greatest mathematicians of all time. He became very well known for helping defend Syracuse from the Roman's. Using his mathematical knowledge Archimedes invented many weapons that were used to help defend Syracuse. He invented something called the death ray which is used on ships that are sailing in and trying to invade. You get about 100 mirrors and focus them at a certain point on the ship and if you have the right amount of sunlight reflecting off the mirrors then the ship will start burning and it will sink. Another one of his inventions was the Archimedes' claw. It is like a long metal hand. It has a hook at the end and it would hook onto the front of all the attacking ships and then lower the ship

into the water so it would sink. Another name for

the Archimedes claw is the 'ship-shaker'.

Mathematical

Discoveries & Inventions

Archimedes made many mathematical discoveries.

He discovered the relationship between the surface area of a cylinder and a sphere. He also played a big part in the discovery of buoyancy by getting into a tub and displacing water. Some of his inventions were...

The Archimedes Claw

The Death Ray - Burning Mirrors

The Archimedes' Screw

The Gold Crown

He invented many other things as well.

Amalie Noether

Amalie Noether was born in Erlangen,

Germany on March 23, 1882. She was named

Amalie but she was always called Emmy. Emmy was the eldest

of four children and out of the four only two of them survived

childhood. Luckily Emmy was one of those two. You could almost predict that she would go into mathematics when she was older because her dad, Max Noether, was quite a well known mathematician and her brother, Fritz Noether, also had a career in mathematics. As a child Emmy didn't really enjoy maths. In school she payed more attention to learning French and English and at home she was learning to cook, clean, and play the clavier. When Emmy finished high school she passed a test that allowed her to teach both French and English at schools for young women. When she turned 18 she decided to take classes in mathematics at the University of Erlangen. Her dad was a professor and her brother Fritz was a student there. Since she was a girl Emmy was only allowed to sit in on the

classes and not participate in them but she didn't mind. After

two years of sitting in on classes, Emmy went and helped her

dad in teaching students mathematics and shortly

after that she started to publish papers

on mathematics.

Emmy's Contributions

to Mathematis

Emmy contributed in three main mathematical things. Abstract algebra, mathematical physics, and the representation theory. Abstract algebra is algebraic structures in their own right. Such structures include groups, rings, fields, modules, vector spaces, and algebras. The main one Emmy worked with was rings.