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Sincerely,
Mariam Fayad
and Danya (Group work)
a) a statement of your thoughts in response to the question:
The word Discovered means,Most people could argue that math was in fact an invention of humankind that continues to develop everyday. Yet the actionopposing point of finding something by searching for it. becoming awareview states that math was not a mere invention of its existence. andmortals, but it was a discovery that these humans have learned over time. Siding with the word invented means, the actionsecond point of creating something, by creating something from non- existing. By all means,view, Math is and was there,there since the dawn of time, humans discovered what they see,saw, but never invented it. Because after all inReligions are beliefs that reinforces this idea. In most religions,religions it it
b) examples that back up your thinking:
One can argue that
inventing a machine is a form of invention of mathematics to use on this object. Yet it is evident that in most cases, the maths used is not invented but it is only discovered that this mathematic rule can be applied onto this innovation.
An example of how math is discovered and not created is newton's law of gravity. Gravity had always existed,People cannot just invent mathematics, for example, one cannot say a thing such as 2 + 2 = 5 because it was not invented by newton.
Pascal'salready discovered that two and two make four.
Pascal's triangle is because the pattrenpattern was there not invented.
In biology, the life theory, states that life started by the merging of two cells. 1+1=2=life. Math was right there at the beginning of life. Which proves that humans did not invent math.
Therefore it can be concluded from these examples that math is not invented but discovered over time.
? Mariam ( Individual work)
a) a statement of your thoughts in response to the question:
Most people could argue that math was in fact an invention of humankind that continues to develop everyday. Yet the opposing point of view states that math was not a mere invention of mortals, but it was a discovery that these humans have learned over time, and I would have to agree with this point of view because all of these rules and theorems that mathematicians claim they had discovered.

MathMath and The
With the Moon as our starting point to link the Ways of Knowing (WOK's - Think PERL) and the Areas of Knowing (AOK's - Think IB Hexogram - Math / Natural Sciences / Human Sciences / Arts / History) we will a) make sense of some of the Math questions raised in our Moon Perception exercise and b) have fun interpreting some quotations about Math as an AOK.
A. Record here 3 Math Questions raised in class that interest you. Then under each write your answer/s.
Mariam Fayad
Is Math invented or discovered ? Mariam and Danya
the question: The
The word Discovered
b) examples that back up your thinking:
argue that inventing
inventing a machine this innovation. Another
An example of by newton. Pascal's
Pascal's triangle is did not invent, Thereforeinvented.
Therefore it can over time.
Is Math invented or discovered ? Mariam
a) a statement of your thoughts in response to the question:
Most people could argue that math was in fact an invention of humankind that continues to develop everyday. Yet the opposing point of view states that math was not a mere invention of mortals, but it was a discovery that these humans have learned over time, and I would have to agree with this point of view because all of these rules and theorems that mathematicians claim they had discovered.
b) examples that back up your thinking:
People cannot just invent mathematics, for example, one cannot say a thing such as 2 + 2 = 5 because it was already discovered that two and two make four.
Pascal's triangle is a triangle that is an array of number set in a triangular shape, in which those at the ends of the rows are 1 and each of the others is the sum of the nearest two numbers in the row above. A mathematician called Blaise Pascal claimed to invent this series, yet the truth is, such a connection between numbers but Pascal was the first to discover it and states it as his own.
Multiplication has always been there in this world that we life.

Sincerely,
Mariam Fayad
and Danya a)
a) a statement by Humans. b)
b) examples that your thinking: One
One can argue

The Moon
With the Moon as our starting point to link the Ways of Knowing (WOK's - Think PERL) and the Areas of Knowing (AOK's - Think IB Hexogram - Math / Natural Sciences / Human Sciences / Arts / History) we will a) make sense of some of the Math questions raised in our Moon Perception exercise and b) have fun interpreting some quotations about Math as an AOK.
A. Record here 3 Math Questions raised in class that interest you. Then under each write your answer/s.
http://www.crystalinks.com/galileo.html
Sincerely,
Mariam Fayad
Is Math invented or discovered ? Mariam and Danya a) a statement of your thoughts in response to the question: The word Discovered means, the action of finding something by searching for it. becoming aware of its existence. and the word invented means, the action of creating something, by creating something from non- existing. By all means, Math is and was there, humans discovered the existence, and developed what they see, but never truly invented it. Because after all in most religions, it it believed that God had created everything from the smallest spec of dust to the largest phenomenon's in the world, therefore I must believe that Math was always there, not invented but discovered by Humans. b) examples that back up your thinking: One can argue that inventing a machine is a form of invention of mathematics to use on this object. Yet it is evident that in most cases, the maths used is not invented but it is only discovered that this mathematic rule can be applied onto this innovation. Another example of how math is discovered and not created is newton's law of gravity. Gravity had always existed, it was not invented by newton. Pascal's triangle is a triangle in which according to the dictionary is a triangular array of numbers in which those at the ends of the rows are 1 and each of the others is the sum of the nearest two numbers in the row above, Blaise Pascal discovered how the pattern went, because the pattren was there all along, which mean did not invent, Therefore it can be concluded from these examples that math is not invented but discovered over time.

Extended Essay
Knowing the Moon
Math As an AOK

Math Math and The Moon
With the Moon as our starting point to link the Ways of Knowing (WOK's - Think PERL) and the Areas of Knowing (AOK's - Think IB Hexogram - Math / Natural Sciences / Human Sciences / Arts / History) we will a) make sense of some of the Math questions raised in our Moon Perception exercise and b) have fun interpreting some quotations about Math as an AOK.
A. Record here 3 Math Questions raised in class that interest you. Then under each write your answer/s.
{Math helps me understand the world.docx}
Math helps me understand the world
of substance.
This science that is being discovered day by day is what links many cultures together, because for example language is not uniform between them all, yet math and math rules are uniform between everyone in the world.
Essay #2:
I would like to share with you knowledge that I have found using a few resources online under the instruction of my ToK teacher. We were instructed to choose a famous mathematician and research about him. The mathematician that I chose was Galileo Galilei since I have always had an interest in him due to the parody of a song that he was mentioned in. We were instructed to so this in order to be familiar with one of the many areas of knowing recognized by the International Baccalaureate Organization. I was able to find most of my information through a “Google” search which provided me with resources like “Wikipedia”, “LucidCafe” and “Crystalinks” which you would find links for in the bottom of this message. I have found out that Galileo was a an Italian physicist, mathematician, astronomer and philosopher who was born in 1564 and died in 1542. He was the first to use a telescope in which he made great astronomical discoveries with. His astronomical observations made him a supporter of the heliocentric view, which was the discovery that the Earth revolved around the sun that caused him trouble with the Catholic Church. Galileo went blind at age 72, which was rumored that it was due to his frequent observations of the Sun. I hope that you have benefited and enjoyed this quick overview of Galileo.
Resources:
http://en.wikipedia.org/wiki/Galileo_Galilei
http://www.lucidcafe.com/library/96feb/galileo.html
http://www.lucidcafe.com/library/96feb/galileo.html
http://www.crystalinks.com/galileo.html
Sincerely,
Mariam
Mariam Fayad

Math and The Moon
With the Moon as our starting point to link the Ways of Knowing (WOK's - Think PERL) and the Areas of Knowing (AOK's - Think IB Hexogram - Math / Natural Sciences / Human Sciences / Arts / History) we will a) make sense of some of the Math questions raised in our Moon Perception exercise and b) have fun interpreting some quotations about Math as an AOK.
A. Record here 3 Math Questions raised in class that interest you. Then under each write your answer/s.
Q1.How many moons would fill the earth? ( in terms of liquid volume? Spherical volume?)
Approximately 49 to 50.
Q2.What is the velocity of the moon? (Relative to what other object/s?)
About 4.627 m/s
Q3.How many craters are there in the moon? (Define crater – by shape, size, …..)
Approximately 300,000 craters (with diameters down to 1 km) are visible from ground based telescopes.
B. Read the following Math quotations (some you may have heard before) and below three of them, write your interpretation of what you believe the author is trying to say.
"Mathematics is neither physical nor mental, it's social." Reuben Hersh, 1927-
He says so because mathematics can go beyond science and it could even become part of the culture.
"Mathematics is the abstract key which turns the lock of the physical universe." John Polkinghorne, 1930 -
Polkinghorne is trying to convey that through mathematics, anything can be calculated from how many apples are in a basket to how big the universe is.
To speak freely, I am convinced that it (mathematics) is a more powerful instrument of knowledge than any other..." Rene Descaret, 1596-1650
He says so because it is possible to prove mathematics while not being able to prove other AOKs like language for example you can prove the 1+1=2 yet you can't prove that any word actually means what people or the dictionary say it means.
Essay #1:
Math Helps me Understand the World
{Math helps me understand the world.docx}
Math helps me understand the world
Its is believed that the most commonly asked question in grade school’s math classes is “Are we ever going to use this in real life?” or “Why do we have to learn this if we have computers and calculators nowadays?” And the answer received is usually yes for this reason or that. I believe that Math helps us understand the world in general more efficiently. Mathematics are used in daily lives from the moment one awakens to the moment they fall asleep. Galileo, one of the notable scientists in history said, "Mathematics is the alphabet with which God has created the universe." For example, when one wakes up, they look at the alarm clock and calculate how long they have to get ready for work or school, or calculating how many people you can invite to dinner and where depending on your budget. Math also helps us imagine great numbers like Avogadro’s number, which can be used to calculate how many moles are in a certain amount of substance.
This science that is being discovered day by day is what links many cultures together, because for example language is not uniform between them all, yet math and math rules are uniform between everyone in the world.
Essay #2:
Write a 200 word letter to a friend describing your search for understanding about a famous mathematician listed on the University of St. Andrews math web site.
{understanding about Galileo letter.docx}
Dear friend,
I would like to share with you knowledge that I have found using a few resources online under the instruction of my ToK teacher. We were instructed to choose a famous mathematician and research about him. The mathematician that I chose was Galileo Galilei since I have always had an interest in him due to the parody of a song that he was mentioned in. We were instructed to so this in order to be familiar with one of the many areas of knowing recognized by the International Baccalaureate Organization. I was able to find most of my information through a “Google” search which provided me with resources like “Wikipedia”, “LucidCafe” and “Crystalinks” which you would find links for in the bottom of this message. I have found out that Galileo was a an Italian physicist, mathematician, astronomer and philosopher who was born in 1564 and died in 1542. He was the first to use a telescope in which he made great astronomical discoveries with. His astronomical observations made him a supporter of the heliocentric view, which was the discovery that the Earth revolved around the sun that caused him trouble with the Catholic Church. Galileo went blind at age 72, which was rumored that it was due to his frequent observations of the Sun. I hope that you have benefited and enjoyed this quick overview of Galileo.
Resources:
http://en.wikipedia.org/wiki/Galileo_Galilei
http://www.lucidcafe.com/library/96feb/galileo.html
http://www.crystalinks.com/galileo.html
Sincerely,
Mariam Fayad