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Microcontroller Software
Published in Syed R. Rizvi, Microcontroller Programming, 2016
René Descartes (1596–1650) was a French philosopher, mathematician, physicist, and writer, one of the key figures in the Scientific Revolution. One of Descartes’ influences in mathematics was the Cartesian coordinate system, which is named after him. Descartes published a philosophical and mathematical treatise titled Discourse on the Method in 1637. (Its full name is Discourse on the Method of Rightly Conducting One’s Reason and of Seeking Truth in the Sciences.) Descartes notes down in the Discourse on the Method the quote that begins this chapter. In today’s software engineering world, the best practice of decomposing a problem is what Descartes was talking about. Best practices in software engineering employ the divide-and-conquer strategy in order to decompose the problem or the customer requirements into smaller and easy-to-handle problems or product requirements. At another place in the same thesis, Descartes points to the importance of enumeration as “In every case to make enumerations so complete, and reviews so general that I might be assured that nothing was omitted.” In software engineering’s state of the art practices, enumeration holds the key to problem-solving methodologies. It is essential since it not only helps in project planning but also aids in keeping track of the completeness of the proposed solution.
Trigonometry and geometry
Published in C.W. Evans, Engineering Mathematics, 2019
If that went well, then move ahead to step 4. Otherwise, try the next exercise. Remember that to transform from polar coordinates to cartesian coordinates we must use x = r cos θ and y = r sin θ. Once r and θ have been eliminated it is then just a question of identifying the curve.
Orthogonal Coordinate Systems
Published in Sivaji Chakravorti, Electric Field Analysis, 2017
The invention of Cartesian coordinates in the seventeenth century by the French mathematician René Descartes revolutionized mathematics by providing the first systematic link between Euclidean geometry and algebra. In this coordinate system, the three constant coordinate surfaces are defined by Equation 3.3
Using artificial neural network-self-organising map for data clustering of marine engine condition monitoring applications
Published in Ships and Offshore Structures, 2018
Yiannis Raptodimos, Iraklis Lazakis
Clustering strategies generally follow two fundamentally different strategies namely hierarchical or agglomerative clustering and point assignment clustering, respectively. In hierarchical or agglomerative clustering, clusters can be combined based on their ‘closeness’, using a distance measure/metric (Vesanto and Alhoniemi 2000). As such, after obtaining the initial clusters from the SOM, the SOM clusters are interclustered based on the Euclidean distance metric in order to divide them into groups providing useful insight and information regarding the data. The centre of each SOM cluster is calculated and based on the hierarchical clustering principle, can be used in a Euclidean space for finding similar clusters. A Euclidean space allows the representation of a cluster by its centroid or average of the points in the cluster. Interclustering distances are defined by calculating the Euclidean distance (square roots of the sums of the squares of the differences between the coordinates of the points in each dimension) between the SOM clusters and selecting the clusters with the shortest distance. Cluster centres with small Euclidean distances between them could possibly contain similar data and could be confined under one cluster group. Stopping can be achieved by considering the number of clusters that should be in the data or when the best combination of existing clusters produces a cluster that is inadequate, pre-defined by the user or when the Euclidean distances exceed a threshold (Jung et al. 2003). The Euclidean distance between two points p and q is the length of the line segment connecting them. In Cartesian coordinates, if p = (p1,p2,…,pn) and q = (q1,q2,…,qn) are two points in Euclidean n-space, then the distance d from p to q or vice versa is given by the Pythagorean formula (Pascual 2015): Figure 3 demonstrates the Euclidean distance d12 of two points A1 and A2.