From Pure Geomatics for Algebraic Procedures with a View to Obtaining Equations from Ellipse from the Perspective of René Descartes
Ezequias Adolfo Domingas Cassela,
Amado Leonardo André
Issue:
Volume 10, Issue 4, August 2021
Pages:
89-95
Received:
19 July 2021
Accepted:
28 July 2021
Published:
4 August 2021
Abstract: This article aims to study the ellipse from the perspective of pure or synthetic geometry to the representation of points on a plane through the use of real numbers, as well as the representation and classification of this conic curve through the use of equations. The perspective developed in this article is based on the view of René Descartes, in considering that “the algebraic steps in a demonstration should really correspond to a geometric representation.” The relevance of this article is to bring a reflection that eliminates the study of Analytical Geometry through ready-made and finished formulas, without satisfactory justification and without a logical chain that gives a greater meaning to the studied concepts. In general, the study developed in this article emphasizes the demonstration of results based on propositions adapted a priori, whose ability to be developed is aimed at establishing an "if...then" type of reasoning, making conjectures involving various knowledge already acquired and confirming such truths from a logical system, using definitions and propositions. Therefore, the demonstrations made in the scope of Synthetic Geometry will help to establish a connection with the equations obtained from the perspective of Analytical Geometry, serving as a consultation for students and professors of Analytical Geometry, thus avoiding sudden transitions between contents of degrees of distinct difficulties.
Abstract: This article aims to study the ellipse from the perspective of pure or synthetic geometry to the representation of points on a plane through the use of real numbers, as well as the representation and classification of this conic curve through the use of equations. The perspective developed in this article is based on the view of René Descartes, in ...
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Modelling Tourism in Australia Based on Periodic Autoregressive Time Series Models
Ezra Precious Ndidiamaka,
Okonta Charles Arinze,
Okoro Udu Ukpai
Issue:
Volume 10, Issue 4, August 2021
Pages:
96-103
Received:
27 July 2021
Accepted:
9 August 2021
Published:
19 August 2021
Abstract: Tourism has become very important in international commerce and also represents one of the main sources of income for some developing countries in the world. It is the act of people travelling and staying in a place outside their usual environment for leisure, business or other purposes, and this may include sightseeing, camping, retreats, etc Tourism is one of the key economic growth contributors and has contributed towards complete growth and development of Australia by bringing numerous economic value and benefits to her, and also building her brand value, image and identity. This paper seeks to generate a periodic autoregressive PAR model that could be used to make reliable forecast for tourism in Australia. Periodic autoregressive models are for seasonally observed data, particularly quarterly and monthly. Its’ parameters take different values across the seasons. The data used in this work was extracted from the official website of the Australian Bureau of Statistics (ABS), (www.abs.gov.au). It consists of monthly historical data of the number of short term visitors in Australia from January 1998 to December 2017 and was analysed using R- statistical software. The result revealed the order of the PAR model, and also verified that there is periodic variation (periodicity) in the tourism data. It was also verified that there is existence of single unit root and periodic integration which led to the fitting of periodic integrated autoregressive (PIAR(2)) model as the suitable model for the Australian tourism data. Finally, the residual generated from the model was subjected to statistical test and it showed a white noise behavior. Based on these findings, it is concluded that periodic autoregressive time series model can be used to generate reliable forecast for Australian tourism data. Further research on the stochastic nature and seasonality of Australian tourism data was recommended.
Abstract: Tourism has become very important in international commerce and also represents one of the main sources of income for some developing countries in the world. It is the act of people travelling and staying in a place outside their usual environment for leisure, business or other purposes, and this may include sightseeing, camping, retreats, etc Tour...
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