Envelope Curves Unify Sinusoidal Graphing

2020 ◽  
Vol 113 (4) ◽  
pp. 301-308
Author(s):  
Christopher Harrow ◽  
Nurfatimah Merchant
Keyword(s):  
Conceptual Understanding ◽  
Coordinate Systems ◽  
Envelope Curve ◽  
Polar Coordinate ◽  
Sinusoidal Function

Transferring fundamental concepts across contexts is difficult, even when deep similarities exist. This article leverages Desmos-enhanced visualizations to unify conceptual understanding of the behavior of sinusoidal function graphs through envelope curve analogies across Cartesian and polar coordinate systems.

Polar Coordinate Systems

2011 ◽  
pp. 191-216
Author(s):  
Fletcher Dunn ◽  
Ian Parberry
Keyword(s):  
Coordinate Systems ◽  
Polar Coordinate

scholarly journals Relating simple harmonic motion and uniform circular motion with Tracker

2020 ◽  
Vol 17 (2 Jul-Dec) ◽  
pp. 141
Author(s):  
E. Pratidhina ◽  
F. Rizky Yuliani ◽  
W. Sunu Brams Dwandaru
Keyword(s):  
Conceptual Understanding ◽  
Low Cost ◽  
Angular Speed ◽  
Circular Motion ◽  
Simple Experiment ◽  
Pendulum Motion ◽  
Harmonic Motion ◽  
Simple Harmonic Motion ◽  
Physics Course ◽  
Sinusoidal Function

In this study, we demonstrate an interesting relationship between simple harmonic motion and uniform circular motion trough a simple experiment. The experiment requires a low cost-easily found materials and free software, Tracker. To represent uniform circular motion, we use a tape that is stick on a fan moving with the constant angular speed. Meanwhile, spring and pendulum motion are used to represent simple harmonic motion. Through Video Tracker analysis, we have shown that the positions (x and y coordinates) of an object undergoes uniform circular motion fit to the sinusoidal function of time, as same as shown in simple harmonic motion. This simple experiment can be used in high school physics course to lead students in developing a conceptual understanding of uniform circular motion with a less mathematical approach.

Polar coordinate systems

2013 ◽  
pp. 921-942
Author(s):  
K.A. Stroud ◽  
Dexter Booth
Keyword(s):  
Coordinate Systems ◽  
Polar Coordinate

scholarly journals Method for Training Convolutional Neural Networks for In Situ Plankton Image Recognition and Classification Based on the Mechanisms of the Human Eye

Sensors ◽  
2020 ◽  
Vol 20 (9) ◽  
pp. 2592
Author(s):  
Xuemin Cheng ◽  
Yong Ren ◽  
Kaichang Cheng ◽  
Jie Cao ◽  
Qun Hao
Keyword(s):  
Neural Networks ◽  
Convolutional Neural Networks ◽  
Classification Accuracy ◽  
Image Data ◽  
Recall Rate ◽  
Classification Performance ◽  
Support Vector ◽  
Coordinate Systems ◽  
Polar Coordinate

In this study, we propose a method for training convolutional neural networks to make them identify and classify images with higher classification accuracy. By combining the Cartesian and polar coordinate systems when describing the images, the method of recognition and classification for plankton images is discussed. The optimized classification and recognition networks are constructed. They are available for in situ plankton images, exploiting the advantages of both coordinate systems in the network training process. Fusing the two types of vectors and using them as the input for conventional machine learning models for classification, support vector machines (SVMs) are selected as the classifiers to combine these two features of vectors, coming from different image coordinate descriptions. The accuracy of the proposed model was markedly higher than those of the initial classical convolutional neural networks when using the in situ plankton image data, with the increases in classification accuracy and recall rate being 5.3% and 5.1% respectively. In addition, the proposed training method can improve the classification performance considerably when used on the public CIFAR-10 dataset.

scholarly journals The shape of space: Evidence for spontaneous but flexible use of polar coordinates in visuospatial representations

2021 ◽  
Author(s):  
Sami Ryan Yousif ◽  
Frank Keil
Keyword(s):  
Spatial Representation ◽  
Dimensional Space ◽  
Spatial Scales ◽  
Human Mind ◽  
Polar Coordinates ◽  
Polar Coordinate System ◽  
Coordinate Systems ◽  
Spatial Tasks ◽  
Polar Coordinate ◽  
Visual Matching

What is the format of spatial representation? In mathematics, we often conceive of two primary ways of representing two-dimensional space, Cartesian coordinates, which capture horizontal and vertical relations, and polar coordinates, which captures angle and distance relations. Do either of these two coordinate systems play a representational role in the human mind? Six experiments utilizing a simple ‘visual matching’ paradigm show that (1) representational format is recoverable from the errors observers make in simple spatial tasks; (2) human-made errors spontaneously favor a polar coordinate system of representation; and (3) observers are capable of using other coordinate systems when acting in highly structured spaces (e.g., grids). We discuss these findings in relation to classic work on dimension independence, as well as work on spatial representation at other spatial scales.

The Assembly Variation Modeling for the Rear Casing Wax Part Based on Polar Coordinate

2015 ◽  
Author(s):  
Changhui Liu ◽  
Sun Jin ◽  
Xinmin Lai ◽  
Jie Luo ◽  
Bo He ◽  
...  
Keyword(s):  
Variation Analysis ◽  
Practical Application ◽  
Coordinate Systems ◽  
Computational Accuracy ◽  
Dimensional Precision ◽  
Shaped Part ◽  
Polar Coordinate ◽  
Cartesian Coordinate ◽  
Assembly Variation Modeling

Rear casing is a key part of the aeroplane engine. Its dimensional precision is significant to the quality of the aeroplane engine. In the rear casing manufacturing process, the assembly variation of its corresponding wax dramatically affects the final dimensions. In this paper, a polar-coordinate based model is proposed to calculate the assembly variation of ring-shaped rear casing wax part. It avoids the variation caused by the coupling relationship between Cartesian coordinate systems and locating position. We also compare the polar-coordinate based model with the ordinary one in practical application. The results show that the polar-coordinate based model can simplify the calculating process and improve the computational accuracy for the assembly variation analysis of the ring-shaped part.

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