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.
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