A transformation maps an initial figure onto a final image and can be a reflection, rotation, translation, or composition of those transformations. An isometry is a transformation that preserves shape, size, angle measure, betweenness of points, collinearity, and parallel lines. A preimage is the original figure and its image is the transformed final figure, with primed notation like Δ X'Y'Z' used to denote the image of triangle XYZ.
The slide show was developed by me and my student Snehasis on account of Mathematics day and presented in National Meet at NCERT,New Delhi
Pratima Nayak (pnpratima@gmail.com)
The slide show was developed by me and my student Snehasis on account of Mathematics day and presented in National Meet at NCERT,New Delhi
Pratima Nayak (pnpratima@gmail.com)
Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement")[1] in everyday language refers to a sense of harmonious and beautiful proportion and balance.[2][3][a] In mathematics, "symmetry" has a more precise definition, that an object is invariant to any of various transformations; including reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart, they are related, so they are here discussed together.
Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, theoretic models, language, music and even knowledge itself.[4][b]
This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and nature; and in the arts, covering architecture, art and music.
The opposite of symmetry is asymmetry.
In geometry[edit]
Main article: Symmetry (geometry)
The triskelion has 3-fold rotational symmetry.
A geometric shape or object is symmetric if it can be divided into two or more identical pieces that are arranged in an organized fashion.[5] This means that an object is symmetric if there is a transformation that moves individual pieces of the object but doesn't change the overall shape. The type of symmetry is determined by the way the pieces are organized, or by the type of transformation:
An object has reflectional symmetry (line or mirror symmetry) if there is a line going through it which divides it into two pieces which are mirror images of each other.[6]
An object has rotational symmetry if the object can be rotated about a fixed point without changing the overall shape.[7]
An object has translational symmetry if it can be translated without changing its overall shape.[8]
An object has helical symmetry if it can be simultaneously translated and rotated in three-dimensional space along a line known as a screw axis.[9]
An object has scale symmetry if it does not change shape when it is expanded or contracted.[10] Fractals also exhibit a form of scale symmetry, where small portions of the fractal are similar in shape to large portions.[11]
Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement")[1] in everyday language refers to a sense of harmonious and beautiful proportion and balance.[2][3][a] In mathematics, "symmetry" has a more precise definition, that an object is invariant to any of various transformations; including reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart, they are related, so they are here discussed together.
Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, theoretic models, language, music and even knowledge itself.[4][b]
This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and nature; and in the arts, covering architecture, art and music.
The opposite of symmetry is asymmetry.
In geometry[edit]
Main article: Symmetry (geometry)
The triskelion has 3-fold rotational symmetry.
A geometric shape or object is symmetric if it can be divided into two or more identical pieces that are arranged in an organized fashion.[5] This means that an object is symmetric if there is a transformation that moves individual pieces of the object but doesn't change the overall shape. The type of symmetry is determined by the way the pieces are organized, or by the type of transformation:
An object has reflectional symmetry (line or mirror symmetry) if there is a line going through it which divides it into two pieces which are mirror images of each other.[6]
An object has rotational symmetry if the object can be rotated about a fixed point without changing the overall shape.[7]
An object has translational symmetry if it can be translated without changing its overall shape.[8]
An object has helical symmetry if it can be simultaneously translated and rotated in three-dimensional space along a line known as a screw axis.[9]
An object has scale symmetry if it does not change shape when it is expanded or contracted.[10] Fractals also exhibit a form of scale symmetry, where small portions of the fractal are similar in shape to large portions.[11]
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
This presentation provides an introduction to quantitative trait loci (QTL) analysis and marker-assisted selection (MAS) in plant breeding. The presentation begins by explaining the type of quantitative traits. The process of QTL analysis, including the use of molecular genetic markers and statistical methods, is discussed. Practical examples demonstrating the power of MAS are provided, such as its use in improving crop traits in plant breeding programs. Overall, this presentation offers a comprehensive overview of these important genomics-based approaches that are transforming modern agriculture.
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Solid waste management & Types of Basic civil Engineering notes by DJ Sir.pptxDenish Jangid
Solid waste management & Types of Basic civil Engineering notes by DJ Sir
Types of SWM
Liquid wastes
Gaseous wastes
Solid wastes.
CLASSIFICATION OF SOLID WASTE:
Based on their sources of origin
Based on physical nature
SYSTEMS FOR SOLID WASTE MANAGEMENT:
METHODS FOR DISPOSAL OF THE SOLID WASTE:
OPEN DUMPS:
LANDFILLS:
Sanitary landfills
COMPOSTING
Different stages of composting
VERMICOMPOSTING:
Vermicomposting process:
Encapsulation:
Incineration
MANAGEMENT OF SOLID WASTE:
Refuse
Reuse
Recycle
Reduce
FACTORS AFFECTING SOLID WASTE MANAGEMENT:
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
For more information, visit-www.vavaclasses.com
![Rigid Motion in a Plane ,[object Object],Start looking for logos that illustrate this. You will have to bring one in very soon!](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)