Methodology
First, the value of n is identified, where in, n is the number of points to be connected. Then the equation formulated will applied.
L=[n+(n-1)+(n-2)+......+4+3]-[n-3], wherein n is not equal to 1
then, after the value is gathered the number of lines that can be produced over the given number of points.
Thursday, March 19, 2009
Set-up
The researcher did many researches that has relation on the investigation, she conducted. She did many experimentations and investigation until she come up with the data. From the data gahtered, an equation is formulated, wherein:
L= [n+(n-1)+(n-2)+.........+4+3]-[n-3]
The researcher did many trials to assure that the equation will satisfy the data gathered.
Experimentations:
n=10
=[10+9+8+7+6+5+4+3]-[10-3]
=[52]-[7]
=45
n=9
=[9+8+7+6+5+4+3]-[9-3]
=42-6
=36
n=8
=[8+7+6+5+4+3]-[8-3]
=33-5
n=7
=[7+6+5+4+3]-[7-3]
=25-4
=21
n=6
=[6+5+4+3]-[6-3]
=18-3
=15
n=5
=[5+4+3]-[5-3]
=12-2
=10
n=4
=[4+3]-[4-3]
=7-1
=6
n=3
=3
n=2
=[0]-[2-3]
=0-(-1)
=1
But the equation has exemption, the given nshould not be equal to 1.
n=1
=0-[1-3]
=2
The researcher did many researches that has relation on the investigation, she conducted. She did many experimentations and investigation until she come up with the data. From the data gahtered, an equation is formulated, wherein:
L= [n+(n-1)+(n-2)+.........+4+3]-[n-3]
The researcher did many trials to assure that the equation will satisfy the data gathered.
Experimentations:
n=10
=[10+9+8+7+6+5+4+3]-[10-3]
=[52]-[7]
=45
n=9
=[9+8+7+6+5+4+3]-[9-3]
=42-6
=36
n=8
=[8+7+6+5+4+3]-[8-3]
=33-5
n=7
=[7+6+5+4+3]-[7-3]
=25-4
=21
n=6
=[6+5+4+3]-[6-3]
=18-3
=15
n=5
=[5+4+3]-[5-3]
=12-2
=10
n=4
=[4+3]-[4-3]
=7-1
=6
n=3
=3
n=2
=[0]-[2-3]
=0-(-1)
=1
But the equation has exemption, the given nshould not be equal to 1.
n=1
=0-[1-3]
=2
Review of Related Literature
In geometry, line segment is a part of a line that is bounded by two distinct end points and contains every point on the line between its end points. Two or more line segments may have some of the same relationships as lines, such as being parallel, intersecting, or skew. Line segment is different from line, it is because line has unlimited length while line segment has distinct length for it was stopped by its two endpoints. Examples of line segments include the sides of a triangle or square. More generally, when the end points are both vertices of a polygon, the line segment is either an edge if they are adjacent vertices, or otherwise a diagonal.
Line segments have specific properties to be differentiated to others. First, it is a connected, non-empty set. Secondly, If V is a topographical vector scale, then a closed line segment is a closed set in V. However, an open line segment is an open set in V if and only if V is one-dimensional. And more generally than above, the concept of a line segment can be defined in an ordered geometry.
One of the fundamental objects within the framework of Eucledian geometry is the point. Euclidoriginally defined the point vaguely, as "that which has no part". In two dimensional Euclidean space, a point is represented by an ordered pair of numbers, where the first number conventionally represents the horizontal and is often denoted by x, and the second number conventionally represents the vertical and is often denoted by y. This idea is easily generalized to three dimensional Euclidean.
In the recent times the only known relation of line segments to points is that, points are a part of a line segment. There are also some relations about points and lines but then it doesn’t says anything about the number of line segments obtained in connecting the given points.
In geometry, line segment is a part of a line that is bounded by two distinct end points and contains every point on the line between its end points. Two or more line segments may have some of the same relationships as lines, such as being parallel, intersecting, or skew. Line segment is different from line, it is because line has unlimited length while line segment has distinct length for it was stopped by its two endpoints. Examples of line segments include the sides of a triangle or square. More generally, when the end points are both vertices of a polygon, the line segment is either an edge if they are adjacent vertices, or otherwise a diagonal.
Line segments have specific properties to be differentiated to others. First, it is a connected, non-empty set. Secondly, If V is a topographical vector scale, then a closed line segment is a closed set in V. However, an open line segment is an open set in V if and only if V is one-dimensional. And more generally than above, the concept of a line segment can be defined in an ordered geometry.
One of the fundamental objects within the framework of Eucledian geometry is the point. Euclidoriginally defined the point vaguely, as "that which has no part". In two dimensional Euclidean space, a point is represented by an ordered pair of numbers, where the first number conventionally represents the horizontal and is often denoted by x, and the second number conventionally represents the vertical and is often denoted by y. This idea is easily generalized to three dimensional Euclidean.
In the recent times the only known relation of line segments to points is that, points are a part of a line segment. There are also some relations about points and lines but then it doesn’t says anything about the number of line segments obtained in connecting the given points.
Sunday, February 8, 2009
A. Background of the Study
Simple studies in Mathematics can develop simple equations or simple answers. But then, with the use of these, new eminent genres of products are produced. Mathematics investigation also contributes in the production of new concepts or to make complicated equations, a simpler one to relief the burden of the students. The researcher believes that Mathematics has not been widely used in research studies, and there are still many hidden patterns or equations that are not yet discovered. She also believes that her research about the relation of points and line segments may be a great help in constructions or to other fields. Because of these reasons, the researcher conducted this study entitled, “The Number of Line Segments Formed in Connecting Given Numbers of Points.”
In this study, the researcher gives different sets of points which are of different numbers. These points are arranged in a form of polygon to avoid confusions. And then, the points are connected by lines. After the investigation had done, the researcher was able to find the pattern and formulated an equation.
Simple studies in Mathematics can develop simple equations or simple answers. But then, with the use of these, new eminent genres of products are produced. Mathematics investigation also contributes in the production of new concepts or to make complicated equations, a simpler one to relief the burden of the students. The researcher believes that Mathematics has not been widely used in research studies, and there are still many hidden patterns or equations that are not yet discovered. She also believes that her research about the relation of points and line segments may be a great help in constructions or to other fields. Because of these reasons, the researcher conducted this study entitled, “The Number of Line Segments Formed in Connecting Given Numbers of Points.”
In this study, the researcher gives different sets of points which are of different numbers. These points are arranged in a form of polygon to avoid confusions. And then, the points are connected by lines. After the investigation had done, the researcher was able to find the pattern and formulated an equation.
Saturday, January 10, 2009
Research Problem
Mathematics Research
First Research Problem
1. Problem:
Determining the number of line segments formed in connecting given numbers of points
Purpose:
To identify the number of lines produced in connecting the given points in a shorter way. To produce an easy equation for counting these lines.
2. Information available
A point is a position in space. Imagine touching a piece of paper with a sharp pencil or pen, without making any sideways movement. It has no size, but has a position. This means it has no volume, lenght and area. It is represented by a small 'X' or by a small dot (a small, round shape). In geometry, points are always labelled by capital letters (A,B,C...X,Y,Z).
A line segment is one of the basic terms in geometry. We may think of a line segment as a "straight" line that we might draw with a ruler on a piece of paper. A line segment does not extend forever, but has two distinct endpoints. We write the name of a line segment with endpoints A and B as "line segment AB" or as . Note how there are no arrow heads on the line over AB such as when we denote a line or a ray.
A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others.
3. Data to be generated
Number of points: 1,2,3,4,5,6,7,8,9,10
Number of lines : 0,1,3,6,10,15,21,28,36,45
4. Availability of equipment
Mostly in Mathematics investigation materials or equipment are not necessary.
First Research Problem
1. Problem:
Determining the number of line segments formed in connecting given numbers of points
Purpose:
To identify the number of lines produced in connecting the given points in a shorter way. To produce an easy equation for counting these lines.
2. Information available
A point is a position in space. Imagine touching a piece of paper with a sharp pencil or pen, without making any sideways movement. It has no size, but has a position. This means it has no volume, lenght and area. It is represented by a small 'X' or by a small dot (a small, round shape). In geometry, points are always labelled by capital letters (A,B,C...X,Y,Z).
A line segment is one of the basic terms in geometry. We may think of a line segment as a "straight" line that we might draw with a ruler on a piece of paper. A line segment does not extend forever, but has two distinct endpoints. We write the name of a line segment with endpoints A and B as "line segment AB" or as . Note how there are no arrow heads on the line over AB such as when we denote a line or a ray.
A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others.
3. Data to be generated
Number of points: 1,2,3,4,5,6,7,8,9,10
Number of lines : 0,1,3,6,10,15,21,28,36,45
4. Availability of equipment
Mostly in Mathematics investigation materials or equipment are not necessary.
Sunday, October 12, 2008
Sample Abstracts
Oral Research Sample
Real-Time Quantitative PCR and Culture Analyses of Enterococcus Faecalis in Primary and Refractory Endodontic Infections
J.M. Williams*, M. Trope, M. Heffernan, D.C. Shugars, University of North Carolina, Chapel Hill, NC
Enterococcus faecalis is frequently implicated in endodontic treatment failures. Limited genotype-based quantitative data exist on E. faecalis in primary (PI) and refractory infections (RI). This study sought to develop a real-time quantitative PCR (qPCR) assay to measure E.f. and total bacteria loads in RI and PI, compare qPCR and culture in bacterial quantification and detection, and evaluate endodontic treatment effectiveness on E.f. clearance. Duplicate intracanal samples were collected preinstrumentation (S1), postinstrumentation/irrigation (S2) and post-Ca(OH)2 treatment (S3) from 15 PI and 14 RI, totaling 29 single-rooted teeth. Samples were cultured on selective and nonselective media in aerobic and anaerobic conditions or analyzed by qPCR using ubiquitous and E.f.-specific primers and fluorogenic probes. qPCR detection range was 101–108 copies/DNA. qPCR was more sensitive than culture in detecting E. faecalis and total bacteria at all time points (McNemar, p<0.05).>E.f. detection was greater using qPCR than culture (time-qPCR/culture: S1-42.8%/14.2%, S2-57%/7.1%, S3-50%/0%; Wilcoxon, p<0.05).>E.f. was detected by qPCR/culture in S1-13%/6.7%, S2-20%/0% and S3-20%/0%. E. faecalis comprised 4% (qPCR)-14% (culture) RI median total bacterial levels at S1 versus 0.03%(qPCR)-3.8% (culture) of PI. Treatment reduced median S1-S3 E.f. counts 10-fold by qPCR and culture in RI; in PI, reduction was detected by culture but not qPCR. E. faecalis detection by qPCR was up to 6-fold more sensitive than culture. E. faecalis was found more frequently and comprised a larger proportion of total bacteria in RI than PI. Following endodontic therapy, E. faecalis and total bacteria were detected in both infection types. Supported b
Saturday, July 12, 2008
The Making of a scientist
Comment
I was really very amazed of the three scientist, Cristina Binag, Gina Dedeles, Maricor Soriano, and Elaine Tolentino. They said their parents have a big role in the chosen of their career. Though they have different ways on how they got interested in science, all of them have determination to achieve thair goal and have passion on what they are doing. After reading the information about the four scientist, I am becoming interested about science though my favorite subject is Mathematics.
Comment
I was really very amazed of the three scientist, Cristina Binag, Gina Dedeles, Maricor Soriano, and Elaine Tolentino. They said their parents have a big role in the chosen of their career. Though they have different ways on how they got interested in science, all of them have determination to achieve thair goal and have passion on what they are doing. After reading the information about the four scientist, I am becoming interested about science though my favorite subject is Mathematics.
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