Geometry

Brannan, David A.; Esplen, Matthew F.; Gray, Jeremy

doi:10.1017/cbo9781139003001

Cited by 47 publications

(54 citation statements)

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“…Analytic Geometry, a great invention of Descartes and Fermat, is a branch of algebra that is used to model geometric objects -points, (straight) lines, and circles being the most basic of these (Brannan et al, 2002). In the algebraic approach, the main focus of teaching is to explain to the learners a way to determine the relationship between the object and its image in the form of an equation.…”

Section: Teaching Transformationsmentioning

confidence: 99%

The Teaching of Geometric (Isometric) Transformations at Secondary School Level: What Approach to Use and Why?

Mashingaidze¹

2012

ASS

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The topic of Geometric transformation is topic number 10 out of 11 topics on the national ordinary level mathematics syllabus. It involves both analytic and algebraic geometry. Analytic because it can be approached using the graphical perceptive, and algebraic because matrix theory can be applied. It requires learners to have a good grasp of a number of skills, the so called assumed knowledge. Thus Teachers of mathematics before designing, selecting and implementing a lesson, ought to understand the knowledge that their students already have (or do not have). This is because one mathematical topic depends on another, early strengths support later progress while earlier weaknesses compound into greater debility. Such information is extremely useful for planning instruction. Assumed knowledge base covers topics such as vectors, construction of shapes, symmetry, properties of shapes, Cartesian equations and graphs, similarity and congruency, etc. Because of such demands learners are found wanting especially where it involves deciding the type of transformation. It is thus the thrust of this paper to approach transformations first by using graphs. Such an approach may cause understanding and enjoyment amongst teachers and learners in the topic. This approach aims at exposing the student to real practical experiences with transformations. Brief synopses on issues of the subject content are provided.

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Section: Teaching Transformationsmentioning

confidence: 99%

The Teaching of Geometric (Isometric) Transformations at Secondary School Level: What Approach to Use and Why?

Mashingaidze¹

2012

ASS

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“…It may be further proved that (3) always represents a family of curves of "coaxal" circles [8] passing through (1,0) when symmetrical losses occur at the ports. Actually it may be demonstrated that (3) can be written as (5), where F(ω) (5) will be of form a+j*b(ω) or a(ω)+j*b thus S(ω) will have always the form of a Möbius transformation of the extended line a+jb(ω) or a(ω)+j*b ( when symmetrical losses at the ports occur) and will map F(ω) in a family of circles [1,8].…”

Section: The Path Of the Sum Of The Transmission And Reflection Smentioning

confidence: 99%

“…Actually it may be demonstrated that (3) can be written as (5), where F(ω) (5) will be of form a+j*b(ω) or a(ω)+j*b thus S(ω) will have always the form of a Möbius transformation of the extended line a+jb(ω) or a(ω)+j*b ( when symmetrical losses at the ports occur) and will map F(ω) in a family of circles [1,8].…”

Section: The Path Of the Sum Of The Transmission And Reflection Smentioning

confidence: 99%

“…The presence of symmetrical losses at the ports influences its position in the family of circles through one point (unit circle when there is no loss). This family of circles may be converted by the usage of inversive geometry [8] into lines, thus it will be shown that the presence of losses in a circuit or asymmetry may be detected by examining the sum of the reflection and transmission coefficient at a single port.…”

Section: Introductionmentioning

confidence: 99%

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On the sum of the reflection and transmission coefficient on the Smith chart and 3D Smith chart

Müller

Codesal

Moldoveanu

et al. 2015

2015 Asia-Pacific Microwave Conference (APMC)

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IEEEMüller, A.; Sanabria-Codesal, E.; Asavei, V.; Favennec, J. (2015). On the sum of the transmission and reflection coefficient on the Smith chart and 3D Smith chart. Asia-Pacific Microwave Conference (APMC 2015 Abstract-The paper presents in premiere a simple mapping property of the sum of the reflection and transmission parameters of reciprocal two port networks. It is proved that although the reflection and transmission parameter may have very complicated paths on the Smith chart, their sum will be always moving on the unit circle if the circuit is symmetric and lossless. Further once symmetrical losses at the ports occur their sum path will switch on a family of circles through one point. Using inversive geometry we construct a new function which maps this family of circles in lines on the extended Smith chart. The proposed method for checking the symmetry uses just two parameters and avoids testing the phase of the corresponding input and output parameters. By means of the 3D Smith chart we propose in the end an alternative approach to visualize the parameters.

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“…The modern Cartesian coordinate system for a three-dimensional Euclidean space (denoted ℝ 3 ) can be described using an triplet of pair-wise perpendicular axes [140]. The three axes are typically defined as x, y, and z with different conventions describing the orientation of the axes [141]- [143].…”

Section: Cartesian and Spherical Coordinate Systems And Reference Framesmentioning

confidence: 99%

A Custom GPS Recording System for Improving Operational Performance of Aerially-Deployed Herbicide Ballistic Technology

Rodríguez¹

2014

2014 ASABE Annual International Meeting

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ACKNOWLEDGEMENTSI would like to express my sincere gratitude to those who helped me complete this thesis:To my advisor Dr. Daniel Jenkins for his support and guidance on my studies and research. I am grateful for his immense patience through my successes and failures.To Dr. James Leary for his advice and criticisms and providing me with a challenging and enjoyable research project.To Dr. Soojin Jun for his review and suggestions over the course of the project.To Dr. James Foster and the Pacific GPS Facility for providing resources and facilities for portions of this project.To Ryan Kurasaki for assistance and advice in the mechanical design and machining of early prototypes. In an effort to improve operations, GPS and other sensors were integrated directly into the electro-pneumatic device for instantaneously recording time, origin, and trajectory of each projectile discharged. These data are transmitted wirelessly to a custom android application that displays target information in real-time both textually and on a map. The application also records data into a comma delimited file so that it can easily be recalled for map display, or exported to other software such as for conducting additional GIS analysis. The logger makes data collection a seamless part of the operation, facilitates logistics of applying airborne HBT, and improves our interpretations of operational HBT performance with more statistically robust measures of herbicide use rate and time-on-target. This provides enhanced capabilities for building operational intelligence relevant to landscape scale invasive species management.

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Geometry

Cited by 47 publications

References 0 publications

The Teaching of Geometric (Isometric) Transformations at Secondary School Level: What Approach to Use and Why?

The Teaching of Geometric (Isometric) Transformations at Secondary School Level: What Approach to Use and Why?

On the sum of the reflection and transmission coefficient on the Smith chart and 3D Smith chart

A Custom GPS Recording System for Improving Operational Performance of Aerially-Deployed Herbicide Ballistic Technology

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