math+as+AOK!

**Math as an Area of Knowing**

 * 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.**


 * Copy the following onto your Math page and add your thinking:**


 * A. Record here 3 Math Questions raised in class that interest you. Then under each write your answer/s and reflect on your process for expanding your knowledge in that area.**

about 50 moons would fit into the earth. there are about 2000 craters that can be seen from a normal telescope and countless other craters can be spotted with a more professional telescope. Q3. which is laregest crater on the moon? aitken basin is the pargest crater found on the moon it is about 2240 kilometers in diameter.
 * Q1.**
 * Q1.** Ho many moons would fill the earth? ( in terms of liquid volume? Spherical volume?)
 * Q2.** How many craters are there in the moon? (Define crater – by shape, size, …..)

What is the velocity of the moon? The moon travels at 1.022 km/s

What is the diameter of the largest crater on the moon that can be seen by the naked eye? South Pole Aitken it is 1,300 miles in diameter and stretches from the south pole of the moon to the Aitken crater.

Does the distance between the earth and the moon ever change? It never changes because its orbit stays equilivant to the earth all the time.

What is the velocity of the moon? - orbit

Fully orbits in 27.3 days, and its speed is 1.023 km/s. This is pretty slow and that is why it is visible to see the many changes and stages of the moon cycle with the naked eye.

I knew that the Moon fully orbited within a month, but I had no idea about to speed to I searched up some websites off the Internet.

What is the size of the moon compared to other moons?

Fifth largest satellite in the Solar System. List of moon sizes: Satellite of Jupiter Satellite of Saturn Satellite of Jupiter Satellite of Jupiter

On the moon, there are too many craters too count. But we can approximate how much there is by assuming there is 300,000 craters with diameters down to 1km. We are unable to count them all because there different sized craters that hard to observe. From what we know, the moon travels at approximately 1.023 km/s. A moon is a natural satellite that orbits something much smaller then itself. It is know that there about 140 moons in our solar system and our moon compared to those is at a average. There are four other moons that are larger than our Moon in our solar system. They are Ganymede, which orbits around Jupiter, Titan, Callisto and Io. The moons named Callisto and Io orbit around Jupiter, while the moon Titan orbits around the planet Saturn. There is one moon that is known by the name of Europa, which is a moon of Jupiter. This last moon is one of the four largest moons in our solar system including those moons mentioned previously, yet Europa is known to be smaller than our Moon. Just using their volumes and not taking shape into consideration, roughly 49 moons can be put into Earth It cannot be seen with the naked eye. None, it reflects light form the sun it does not produce light. "Impact craters are the remains of collisions between an asteroid, comet, or meteorite and the Moon."[]. There are said to be indefinite amount of craters on the Moon and that it is impossible to count how many there are, because if we keep looking closer and closer at the Moon we will notice even more craters, even craters that are invisible to the naked eye! Also every now and again there are objects in space hitting the Moon causing more craters, and therefore leaves us with no definite answer! In the moon, there are holes caused by the meteors that hit the surface of the moon due to the lack of the air hemisphere. On the moons' surface, the craters that have a diameter more than 1 km are approximately 300,000. Other craters that are smaller cannot really be counted, they are millions. The count for the 300 craters was approximated, by the scopes from the earth and by the satellites. 2.38 km/s
 * Q1.How many craters are there on the moon? **
 * Q2.What is the velocity of the moon as it orbits the Earth? **
 * Q3.What is the size of the moon compared to other moons? **
 * Q4. How many moons can you fit into the earth? **
 * Q5. What is the diameter of the largest crater on the moon that can be from Earth with the naked eye? **
 * Q6. How much light does the moon produce? **
 * Q7. How many craters are there in the moon? **
 * Q8. What is the Escape Velocity of the moon? **


 * Q1. What is the velocity of the Moon's Orbit?**

roughly 1km/s

Average Center to Center distance is 384.403 km
 * Q2. What is the average distance of the moon from the Earth?**

Just using their volumes and not taking shape into consideration, roughly 49 moons can be put into Earth
 * Q3. How many moons can you fit into the earth?**

**Q3. What is the diameter of the largest crater on the moon that can be from Earth with the naked eye? **
 * It cannot be seen with the naked eye. **

**Q2. How much light does the moon produce? **
 * None, it reflects light form the sun it does not produce light. **

What is the escape velocity of the moon? 2.38 km/s

Does the distance between the moon and the earth change over time? Yes, The distance of the moon from the earth increases by 38 mm per year.

What is the size of the moon compared to other moons? What is the diameter of the largest crater on the moon that can be seen on Earth by the naked eye? Tycho It is located in the southern lunar highlands. At its closest point, known as the perihelion, the Moon is only 363,104 km (225,622 miles). And at its most distant point, called aphelion, the Moon gets to a distance of 406,696 km (252,088 miles).
 * Q1.Does the distance of the moon and earth change overtime? **


 * Q2.How many moons would fit inside of earth? **
 * The moon could fit in our Earth approximately 30 times! **


 *  As many things as I have read so far, ideally, up to 49 moons could fit if divided mathematically. However, due to the spherical shape, we have to allow for empty space between the spheres inside the Earth. So the number would be considerably lower. This is the only answer I can find that says approximately 30 times. It's rather misleading. **

The largest crater Tycho is 85 km's in diameter, named after the Danish astronomer Tycho Brahe (1546-1601)
 * Q3.What is the diameter of the largest crater on the moon that can be seen on earth by the naked eye? **

 " Short answer: too many to count. Approximately 300,000 craters (with diameters down to 1 km) are visible from ground based telescopes; high-definition photographs from lunar probes reveal millions of craters; extreme close-ups show countless microscopic craters.  There are estimated to be roughly 300,000 craters wider than 1 km on the Moon's near side alone.  Well, that no-one will ever know my friend. But a good estimate would be around 5000-10,000!"
 * Q4**. How many craters are there in the moon?

**Q5**. What is the Escape Velocity of the moon?  Escape velocity is the speed of zero (addition of kinetic energy and gravitational potential energy)

2.38 km/s

Approximately 1km/s
 * Q6**. What is the velocity of the moon?

Mars is nearly 500 times smaller looking than the Moon! Although the Moon is actually about half the diameter of Mars, the Moon appears a lot bigger because the Moon is much closer to us than Mars
 * Q7**. What is the size of the moon compare to other moons?

http://tok-2012-krutheeka.wikispaces.com/math+as+AOK%21 it is not mental because mathematics of independent of what you or i think. it is not even physical because the circles and triangles that mathematics do not deal with physical triangles and circles but with something ideal. and it is social because some authors are working to give a humanistic answer mathematics. it has the abitily to influence emotions.it is useful combinations they add to special sensibility which is worth our fixing our attention and useful in teaching us a new mathematical theory.
 * 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-**
 * "The useful combinations (in mathematics) are precisely the most beautiful." Henri Poincare, 1854-1912**
 * "Mathematics is the abstract key with turns the lock of the physical universe." John Polkinghorne, 1930 -**


 * "Everything that can be counted does not count. Everything that counts cannot be counted." Albert Einstein, 1879-1955**


 * "The mark of a civilized man is the ability to look at a column of numbers and weep." Berterand Russell, 1872-1970**


 * "A mathematician is a machine for turning coffee into theorems." Paul Erdos, 1913-96**


 * "Mathematics began when it was discovered that a barce of pheasants, and a couple of days have something in common: the number two." Bertrand Russell, 1872-1970**


 * To speak freely, I am convinced that it (mathematics) is a more powerful instrument of knowledge than any other..." Rene Descaret, 1596-1650**

Math helps me misunderstand the world:
 * "Instead of having "answers" on a math test, they should just call them 'impressions", and if you got a different "impression", so what, cant' we all be brothers?| Jack Handy 1949-**

Math is an abstract form of science involving numbers and digits, but what makes it different from other sciences (physics chemistry and biology) is the practicality. The argument is that the math we learn now, helps to put us in a more confused position, mostly because we haven’t seen any of it practically used. But at the same time at the same time the argument does not suggest that math helps us to completely misunderstand the world, because a part of it is used in our day-to-day lives for example, it is like saying I am hungry all I need to know is how to eat, and where to get my food from or the recipes or the ingredients I need, I do not have to know how the wheat was reaped or how much water was supplied to all my raw ingredients. But the math we learn about trigonometry and functions, none of it is actually proved, the word proof has a different meaning in math, it is defined as when equation A is equal to equation B. I don’t know how many people are out there who can not provide actual evidence (including me), for example when there is a question that asks me to prove something, ones first instinct would be to link all possible formulas, even thought most of the times they may not know how the basic formula is derived, and my evidence would be, due to so and so statement ,this equation thus proved. But then again a person with more insight into the subject would be able to provide keener explanations. For example if someone asked me the definition of asymptote, a math teacher would be able to explain better than me for the simple reason that she has more insight into the subject, there by concluding that people are different in their own perspectives towards math.

Mathematics starts with counting. It is not reasonable, however, to suggest that early counting was mathematics. Only when some record of the counting was kept and, therefore, some representation of numbers occurred can mathematics be said to have started. ” Dear Sir O’Connor and Sir Robertson, Early man were basically farmers, and they need something or some medium to keep tabs on their cattle or their land or their food stuff. At this juncture the idea of counting stepped in, enabling them to keep track of all their accountable property. According to the statement, if the counting was not recorded somewhere then it was not math, but that is not true, for example when we eat food, we do not actually account for the steps that we take in eating our food, but that does not mean we did not eat it. It is in a similar way, there must have been a necessity to measure days, years, or time, for this a system must have been created like counting, it is also possible that at the beginning there weren’t any characters to represent the idea of number, and that it might have come along a few years later. I agree with the statement in one aspect that, the evidence of counting can be accepted as the beginning of math, but then again there is no evidence to prove that math did not exist before that, thus not letting us draw any conclusions. For example this is just like saying that a baby before getting his birth certificate was not born at all until he got the certificate, the universal truth here remains that the baby has born, but officially the baby is not yet born.

Yours truly, Krutheeka Rajkumar

a ) A statement of your thoughts in response to the question

b ) Examples that back up your thinking c ) Any other questions or ways of looking at the question that occur to you

Can a mathematical statement be true before it has been proven ?

No, I do not think a math statement can be ture without proving, the whole basis of math is on proving, showing that one statement leads to another, and math unlike the other sciences cannot be experimented on, and therefore the only was to know if a statement or true or not, is by supporting your statement with sufficient proof.

For example we all know fire is hot, but how did we know that? We touched it and got burnt, there was proof to support that when a body of lower temperature comes in contact with a body of higher temprature, the heat starts to flow form the body of higher temperature to that of the lower temperature. But this is an experimental setup, math is does not support this kind of experimental knowledge, therefore moving to a non-experimental example would be any math sum, trigonometry for example, one would not know that a particular statement is true or false, the only way of finding out is by equating the right hand side (RHS) to the left hand side (LHS) and by doing so we are providing proof. it is arguable that all numbers that end with a 2 are even, today all students know this is true. but how did it become true? it was proved. this example shows us, that all these theories that we hold true now was proved one time or another, and thats how we know it is true!

Another question that occurs is, and then would all the statements not proved be false? For example we have not proved what is infinity, or what is a number divided by zero, why is it called undefined? Is it because we cannot prove what is a number divided by zero it is called undefined.