Math+in+All+Ways+of+Knowing+and+Areas+of+Knowing

Math in all Ways and Areas of Knowing 1. List how the ways of knowing are a part of Math Knowledge 2. Describe how Math may or may not be found in all other ways of knowing:

Rubic's Cube is composed of mathematical formulas and different patterns grouping and techniques in solving it. It also has a certain beauty in it as one observes the way the different colors are combined and how are they placed together perfectly in perfect alignment.



In looking at the Rubic's cube, there's a lot of areas of Ways of Knowing and Areas of Knowing:

Math and Perception Perception is evident in this example of relationship between Math and Perception. It is because that the use of your sense of sight in solving the Rubic's cube, which involves putting all the right colors together in order to solve the cube. And perception is also used in viewing and perceiving that there are different combinations of colors and patterns to follow in order to solve the cube by grouping them correctly. Math and Emotion In solving the Rubic's cube, people usually get excited and pumped up in a sense that they have accomplished solving the cube. For example, the first time I have completed one side of the cube and that gave way for emotions to come in to the solving the problem. And I was so excited that I had attempted to solve the whole cube and although it took me over almost a month but it paid off as that feeling of achieving something greater than just solving one side of the cube. And in looking at the Rubic's cube that is completely solved, one could stare and be simply fascinated by the simplicity of the appearance and at the same time the complexity of the integration of math with the cube.

Math and Reason Solving the Rubic's cube requires a lot of reasoning skill because it requires for one to know where to twist and turn all the colors in putting them in the right places at the right order in order to solve the cube. The cube is also composed of different patterns that are distinct to each other and either of those can be chosen in order to solve the cube as people have their own preferences in the way they solve the problem.

Math and Language Language is also an important factor in solving the cube as not all people can solve the cube on their own and they sometimes seek help from other people. Another important relationship between Math and Language is that the visual language it presents to the person solving the cube and probably other people observing how the cube is solved. People also learn how to speak the so-called "Rubic" language because it transforms into a informal and universal language that is used by probable users of the Rubic cube.

Math in: Natural Sciences Natural Sciences and Mathematics have a great deal of relationship with each other and in general in creating the basic concepts of Natural Sciences that is the basis of studying the complexity of a specific natural science. For example in Chemistry, when looking for the number of moles in a substance, one can't just assume a number as the value of it is only existent with a given valuable and reliable proof with it. It does not only provide result but also let's us see through the similarity of the language of chemistry and math as one unit of language. Human Sciences Human Sciences with Mathematics also has a great deal of work to deal with each other in terms of using either more complex or even basic Math like dates. In History, being classified as a Human Science, the History Art Music Ethics

ToK 1. What is a torus?is a surface of revolution generated by revolving a circle in three dimensional space about an axis coplanar with the circle. 2. Why was Riemann an important figure in mathematics?Discovered Riemann geometry, which had greatly improved Analytical and Differential Geometry and had become the main basis of the general theory of relativity by Albert Einstein 3. What does the author state about the importance of Riemann's work with regards to changing our view of the world?Riemann's extensive study of geometry had further advanced the importance of the role of geometry in how we humans now perceive the world as it is. It had completely challenged the Euclidian geometry as a whole new concept of perceiving the things around us. 4. Describe the changing political structure of Europe at that time, and explain the increasing role of the university as an institution of significance.It was the time of the great political turmoil in the European continent as the countries are dissolved and some are formed. It is was the ear of great European battles that would give way to World War I. 5.Write down any questions you have about the reading. 6.Write down any points of interest you would like to share:HistoricalSocial PersonalThe effects of what happened during that era to Riemann's work had a lot to do on Riemann's study. Before, he always had nervous breakdowns in speaking in large crowds but as he became older, he had learned to speak more confident;y of his work and thus had improved the way he had done his work although he had died before even completely finishing bis work as a whole. Math Related Thought Processes
 * How did Riemann has suddenly been much involved in the field of geometry despite different factors that was holding him back?
 * What is the main motivator that made him more interested in the field of mathematics?
 * What is the major role of Riemann's geometry in the modern world today in any fields of perspectives?
 * What concept of Riemann's geometry had convinced the mathematical world to accept the new field? Was it accepted as a whole or some concepts of it only?
 * How did Riemann's ideologies influence the works of Einstein's Theory of Relativity? What key concepts of theory of relativity had a major role in establishing RIemann's geometry?

Read first four points in on page 59 (Page 6 of PDF) -Summarize the first four ideas Riemann argues that mathematical reality must be differentiated fro physical reality as Riemann was basing his ideas into mathematical terms. By investigating different mathematical spaces provide possible images of the universe that prevents us men in being stuck with narrow concepts and in studying mathematical spaces, Riemann determined that continous spaces can have any dimension andeven the possibility of infinite dimensiomal spaces. Riemann also states that space and space with geometry are way different to each other and that same space can have different types of geometry having geometry defined as another structure in the space and Riemann is trying to teach all of us that we can distinguish topology from geomtery and vice versa. -What does it mean? What has Riemann done with Math? Riemann defines that the dimensions of these spaces that exists in our world are based on mathematical concepts that turns ordinary physical spaces into mathematical spaces that people misconceptualize the difference of both realities, which are totally different conceptualities where mathematical reality is a far more complex dimension than the narrow concept of physical reality. Riemann also wants to differentiae space and space with geometry with geomtery being another sort of formation confined within a mathematical space and having its complete distinction from it unlike having a space only.

Think Math, Creating Knowledge, Truth, Validity c,

"Questions of Math creating realities."

Read first four points in on page 59 (Page 6 of PDF)

-Summarize the first four ideas

Riemann argues that mathematical reality must be differentiated fro physical reality as Riemann was basing his ideas into mathematical terms. By investigating different mathematical spaces provide possible images of the universe that prevents us men in being stuck with narrow concepts and in studying mathematical spaces, Riemann determined that continous spaces can have any dimension and even the possibility of infinite dimensional spaces. Riemann also states that space and space with geometry are way different to each other and that same space can have different types of geometry having geometry defined as another structure in the space and Riemann is trying to teach all of us that we can distinguish topology from geometry and vice versa.

-What does it mean? What has Riemann done with Math?

Riemann defines that the dimensions of these spaces that exists in our world are based on mathematical concepts that turns ordinary physical spaces into mathematical spaces that people have wrong preconceptions of the difference of both realities, which are totally different concepts where mathematical reality is a far more complex dimension than the narrow concept of physical reality. Riemann also wants to differentiate space and space with geometry with geometry being another sort of formation confined within a mathematical space and having its complete distinction from it unlike having a space only. It directly implies in all of these that in mathematical spaces, which have infinite dimensions, isn't affected by anything in it like the solar system in our universe because our solar system is a completely different structure that even if it occupies a space in our universe, it won't alter the shape of our universe if it ever has one.

"Questions of Math creating realities."