First Semester = Over

Well, it's like days had only passed. As I read my latest post aside from this, I realize that I haven't posted since the start of the semester. That's a remembrance, though.

Anyway, second semester is nearly approaching, and I am somehow excited for the new subjects we'll be taking as well the new professors we'll be meeting. I just hope that they're as good and as awesome as the professors we've had last semester. Oops! the grades were released already, and I'm happy with the result. I was one of the Dean's Listers for last semester, and I'm hoping to be on the top of the list as well. Well, that's just a wish. =))

Hi guys! I should be active here already. :)

Ghantt Chart

*The clearer one and the better one will be printed the same as this.

Methodology

The conjecture of the research will be presented through the information given at the research paper. Hypotheses may be one that can also help in showing the conjecture of the research. The conjecture is presented through the example and proofs given at the mathematical investigation.

A formula is formed with the proofs that also served as basis in this mathematical investigation. The formula is c=n(p-1)/n where c is the symbol for carousel number, n is for the integer that will be used and p is for the number of periods the integer has if divided to 1. Though the formula can be simplified, it is stated in that way in order to show the relation between the number of points and the integer together with the answer to the formula to be used.

Internet sites and periodicals are said to be the basis of the conjecture of the mathematical investigation the researcher pursued. These materials are used that can prove regarding the presentation of the researcher on the conjecture. These materials are also used for the betterment of the research and for additional information regarding the research proposal which is conducted.

Few applications are under this topic and one of the major applications is for educational purposes. Teachers worldwide are now ready to introduce new topic under Mathematics at either Elementary or Secondary Level. Additional information are gotten in the field of Mathematics that the students’ ability in Mathematics is enhanced much than before. Some minor applications are introducing this to other people in the way that the person knew much about this topic. Also, people who knew more about Mathematics are said to teach other people with more information since those people knew more about other people who knew much other fields like Science and English. Few applications are mentioned about the research topic due to its popularity which seems to be as not popular as the other mathematical investigation and the concepts which was confusing at the first part but will understand at the latter part as the researcher and the readers read it again as long as they understand it.

Review of Related Literature (part 1)

All people know what numbers are. Numbers are what people called as an object used in counting and measuring. Numbers can be written in words but mostly, people are mostly using the symbols since it is easier for the people to write symbols than the words itself. In can also be used as in label for telephone numbers, serial numbers for barcode reading and for codes also. Numbers are very broad though people can say that numbers are just numbers, wherein it is 1,2,3 and so on. It can be zero, rational, irrational, negative, and complex numbers. But carousel numbers are included as irrational for the researcher will determine the possible numbers that will be belonged to it.

Introduction to Numbers

Since the problem is about carousel numbers, first will be the introduction about irrational numbers. First, irrational numbers are numbers which are not rational. It means that they are numbers that cannot be expressed in an expression m/n or fraction. They are also non-terminating decimals when they are divided which means that the numbers are not repeating but after some time, it will be repeated also. As a consequence of Cantor’s proof that real numbers are uncountable, it follows that almost all real numbers are irrational. Most of the examples as irrational numbers are pi, e, and square root of 2.

Pi is an irrational number since the value of pie is 3.1415926535897932384626433832795 and more. Also, the value of e or Euler’s number is 2.7182818284590452353602874713527 and so on. Well, Golden Ratio is also included here which has a value of 1.61803398874989484820 and so on. Also, other numbers which was squared will be included in this category. Finally, carousel numbers are included here since we all know that carousel numbers are the numbers which we will find the possible numbers which has repeating values as you multiplied to other numbers.

(to be continued)

Background of the Study (\m/)

This research problem wherein the topic is about Carousel Numbers is under the field of Number Theory and Algebra. Number Theory is a branch of pure Mathematics wherein it deals about properties of numbers and particularly of integers. This has specific subareas which leads to what course does the topic really belong and here, it is under the Algebraic Number Theory. The Number Theory is also called arithmetic or higher arithmetic but because of some people just used these terms, so others considered now to use Number Theory. This is the oldest branch from mathematics and the widest one also for it has many branches else that can make your topic more specific from where it belongs.

Algebra is also a branch of Mathematics that talks about structure, relation and quantity. This is also one of the main branches of Mathematics for it has many subareas that talks about relationship of numbers to each other. Since this research is not for elementary students, then we can tell that this is under secondary algebra which according to the word, it is for secondary or high school students. It also talks about set elements, symbols and variables. In the case of Carousel Numbers, it may talk about elements for we need much trials in order to classify or set them in one group, which are the numbers rotating of their products if any n is multiplied on it.

Since Algebraic Number Theory falls in this research, then that means that numbers here are falling under integers. The Galois theory, group cohomology, class field theory, group representations and L-functions. Those theories that falls under Algebraic Number Theory is also an area which is open for the Carousel Numbers. Carousel numbers are not that significant in other people but for those who knows how to analyze everything in this world and with the each person’s patience, then people can also do this kind of work. In terms of applications, this can be used as topics in all secondary schools in the world for this may be a confusing and hard-time topic for each students which will explore their knowledge about numbers.

Carousel numbers are those numbers in such that if n is divided to 1, as in 1/n, then the number of periods or the numbers where it will repeat at the other time is n-1. Many already tried to do this but maybe they can’t finish too many numbers to try. Some of their reasons is that it is too difficult to use long hand division as the numbers increasing. If a researcher has a program that will make computations easier, it will not be difficult for him to pursue this but since only few can do this and others are not continuing it anymore, then this researcher may be done by me. Limitations, of course, are included for it will take much time to the researcher to do this in a rush. It can be done for a long time that will make for him easier to analyze with the numbers.

Carousel numbers maybe partial or not depending on the products that will appear if the process is done. It is not partial if all of the periods, when multiplied to any number will just rotate and rotate. It is partial if not all of the products in the carousel numbers are rotating and only chosen numbers that will be divided to the period will make it carousel numbers. Furthermore, the researcher analyzes of the numbers that will be belonging to carousel numbers. Either partial or not, at least the definition was proven already that it is rotating.

Carousel Numbers

Purpose:

The purpose of this research is to determine all the possible numbers that can be used as carousel numbers or numbers wherein the products are just rotating their numbers.

Field:
It is in the field of Algebra or Number Theory.

Date Started:
January 8, 2008

What is it all about:
This is group of numbers wherein the product if multiplied to a certain number is just rotating the numbers at a limited part. In this, we will talk about period of decimals. In the quotient as 1/n, we will look the numbers which belongs to this group. It is not about a limitation of the quotient but the point where the quotient, as terminating, will go back to the starting number. I will still research more things about this for I just have few times for this.

Target:

n=? still under thinking?? but is it okay if i'll use first 50 numbers per trial?

The Last Day for Intramurals; The Championship for Basketball Girls Also!

This is the last day of Intramurals and this day was the most exciting day and funny for me again because of the Championship for girls between Red Macintosh and Blue Vaio. Even before, our team heard that our team was good in Basketball for girls and though we were proud of it, we were still nervous for they were Seniors. The players for Red Macintosh were Jamare Rose Resus, Terrence Joyce Avilla, Ann Rojini Bersamina, Sharika Claire Mirandilla, Marie Roxanne Afonso, Katrina Anne Marc Riman, Jessica Niña Cuapiaco, Katrianne Luz Obillo, Charmaine Dela Paz, Ria Marcelle Vivo, Jia Andrei Telmo, Maria Loriza Miranda, Lerina Permentilla and to others who were not mentioned. On the other side, their players were Alyssa Shane Piol, Serene Ezra Bondad, Bethsaida Laurino, Neil Amery Fabi, Roublle King, Ate Judian Camille, ... Elegores and to others who were not mentioned.

At first part of the game, we, Juniors, were very nervous because their was a tie of 2 points between the two teams but we were still full of happiness if ever a player from us got a shoot and it was sang with a cheer. On the other side, Vaio people were like that also. When the game is getting more exciting, our team is getting more points and it stop with 16-8 in favor of Red Macintosh.

After few minutes for rest of the players, the game started already and now, the Vaio players were getting aggressive that they have consecutive shots but sometimes, our team could block them and get the ball from their opponent. At the funny side, we could see that sometimes, when they were passing the ball, it was passed on the other team that's why it was funny. Back to the game, the players of Juniors still didn't let them to shot with points higher than them so it stopped at 18-15 in favor of Red Macintosh. At overall for Basketball Girls, our team were the Champion and we were all happy and cheering after the game. A nice game and honest as well. Go for Blue Vaio and RED MACINTOSH!!! M-A-C...I-N-T...O-S-H... MACINTOSH!!!