how to plot into the multidimensional cartesian ...

HOW TO PLOT INTO THE MULTIDIMENSIONAL CARTESIAN COORDIANTE SYSTEM? BY Mario Arturo Ruiz Estrada Faculty of Economics and Administration, University of Malaya, 50603 Kuala Lumpur, MALAYSIA Email: [email protected] Website: www.econonographication.com Tel: +006012-6850293

Abstract This paper is interested to show HOW to plot into the multidimensional Cartesian coordinate system. It is based on a general explanation about the multidimensional Cartesian coordinate system theoretical framework and some few examples. The idea is to learn and understand better how multidimensional graphs works in the process to optimize the visualization of a large database behavior into the same graphical space. Keywords: Econographicology, Mathematical Modeling, Calculus, Mathematical Economics, Multi-Dimensional graphs and Multi-Dimensional Physical Spaces JEL: C02 1. Introduction Initially, we like to explain how the multidimensional Cartesian coordinate system works. Basically, the multidimensional Cartesian coordinate system follows a basic coordinate system structure according to expression 1. The basic coordinate system structure is formed by three levels of analysis: the level of general-space (i), the level of sub-space (j) and level of microspace (k) respectively. In the case of plotting into the multidimensional Cartesian coordinate system start with define our specific general-space (i), sub-space, micro-space (j), alpha-space (α) and beta-space (β) respectively. (1.)

(α , β)

The plotting into the multidimensional Cartesian coordinate system can show clearly a major power in the moment to visualize information in multi-data level into the same graphical space than the classic 2-Dimensional (X,Y) and 3-Dimensional (X,Y,Z) Cartesian coordinate plane. We assume that the 2-Dimensional and 3-Dimensional Cartesian coordinate systems are subcoordinate system into the multidimensional Cartesian coordinate system. We like to remain that into the structure of the multidimensional Cartesian coordinate system is build by infinity

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general-spaces (i), sub-spaces (j) and micro-spaces (k) distributed into different places along a cylinder. Therefore, the multidimensional Cartesian coordinate system starts from the general space zero (i0) until the general space infinity (i∞). And each sub-space starts from sub-space zero (j0) until the sub-space infinity (j∞). Finally, the micro-space starts from micro-space zero (K0) until the micro-space infinity (K∞) (See Expression 2). An important issue to mention is that the multidimensional Cartesian coordinate system is available to generate the waves data effect by join a large number of micro-spaces (k) distributed into the same sub-space (j) and general space (i) by strait lines, it is possible through the application of inter-linkage (╦) under sub-space level. We like to remain that each micro-space (k) is independent from another micro-spaces (k) into the same sub-space (j) and general space (i). The idea to join each point(s) located into a specific micro-space with the next neighbor micro-space (k) into the same sub-space (j) and general space (i) level in analysis, it is to observe the waves data effect (Ruiz Estrada, 2008). Additionally, we also suggest the application of the inter-linkage (╬) under general-space (i) level. The waves data effect can be defined as imaginary single line that start from micro-space zero (k0) until arrive to the micro-space infinity (k∞). The idea is to observe the information domino effect into the same database behavior simultaneously.

2. Steps to plot into the Multidimensional Cartesian Coordinate System Basically, the plotting into the multidimensional Cartesian coordinate system is follow by five basic steps follow by:

1. We need to find the general-space (i) into the multidimensional Cartesian coordinate system (See Figure 1). 2. Secondly, we proceed to search the sub-general space (j) into its general space (i) (See Figure 1) respectively. 3. Thirdly, if we select any sub-general space (j) into its general-space (i), then we are available to find any micro-space (k) into its sub-general space (k) (See Figure 1). 4. Finally, we can start to join all micro-spaces (k) into the same general-space (i) and subspace (j) under the application of the inter-linkage (╦) under sub-space (j) level.

Electronic copy available at: http://ssrn.com/abstract=1517179

5. Fifth, it is possible observe into each different sub-space in different levels the data waves effect under the application of the inter-linkage (╬) under general-space (i) level.

(2.)

(α , β) ╦ (α , β) ╦ . . . ╦ (α , β) ╬

(α , β) ╦ (α , β) ╦ . . . ╦ (α , β) ╬

(α , β) ╦ (α , β) ╦ . . . ╦ (α , β) ╬

. . . ╬

(α , β) ╦ (α , β) ╦ . . . ╦ (α , β) ╬

(α , β) ╦ (α , β) ╦ . . . ╦ (α , β) ╬

(α , β) ╦ (α , β) ╦ . . . ╦ (α , β) ╬

(α , β) ╦ (α , β) ╦ . . . ╦ (α , β) ╬

. . . ╬

(α , β) ╦ (α , β) ╦ . . . ╦ (α , β)

FIGURE 1 THE MULTIDIMENSIONAL CARTESIAN COORDINATE SYSTEM

3. Example to How Plot into the Multidimensional Cartesian Coordinate System We like to show some basic examples to HOW plot into the multidimensional Cartesian coordinate system. First, we request to plot the next coordinate systems into the multidimensional Cartesian coordinate system follow by (3, 5) and (7, 3) (See Figure 2.a.). Secondly, we request to build the waves data effect follow by the coordinate systems (7, 5) ╦ (2, 1) ╦ (4, 5). Subsequently, we also suggest to

plot the waves data effect follow by the next coordinate system (3, 2) ╦ (5, 6) ╦ (7, 2) (See Figure 2.b.). FIGURE 2 THE MULTIDIMENSIONAL CARTESIAN COORDINATE SYSTEM: EXAMPLES 2.a.

2.b.

4. Conclusion It is possible to observe that the uses of multidimensional Cartesian coordinate system can facilitate the visualization of large database into the same graphical space. Basically, we also are available to visualize the performance, monitoring and alerting of possible failures of large database into the same graphical space.

5. References Ruiz Estrada, Mario Arturo (2008). The Economic Waves Effect of the U.S. Economy on the World Economy. Available at SSRN: http://ssrn.com/abstract=1304585