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Euclid was a Greek mathematician from Alexandria known as the "Father of Geometry". His influential work Elements laid out the principles of Euclidean geometry through a small set of axioms and deduced many other geometric principles through logical proofs. Elements was used as the main geometry textbook for over 2000 years. Euclid introduced deductive reasoning and the axiomatic method to geometry which established it as the first example of a formal axiomatic system.

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Euclid's axiom

Euclid's axiom

Introduction to euclid`s geometry by Al- Muktadir hussain

Introduction to euclid`s geometry by Al- Muktadir hussain

Euclid’s geometry

Euclid’s geometry

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Euclid's axiom

Maths presentation pls select it . It would be very useful for all.
It is about the axioms and euclid's definitions. its an animated presentation pls download it and see . i got 1st prize for it,.....................

Introduction to euclid`s geometry by Al- Muktadir hussain

Euclid's Geometry defines basic geometric concepts like points, lines, and planes. It describes 23 definitions put forth by the ancient Greek mathematician Euclid, including the definition of a point as having no parts and of a line as having no breadth. It also explains Euclid's five postulates, such as the ability to draw straight lines between points and the property that straight lines extending infinitely will meet on the inside of two angles summing to less than two right angles. The document aims to explain Euclid's geometry clearly for students to better understand its complicated concepts.

Euclid’s geometry

Geometry is a branch of mathematics concerned with questions of shape, size, position, and space. A key figure was the Greek mathematician Euclid, whose book Elements systematized geometry in the 3rd century BC. Euclid defined fundamental terms like point and line, and postulated axioms and rules for reasoning about geometric concepts. Euclid's system of Euclidean geometry reigned for over 2000 years, until non-Euclidean geometries emerged in the 19th century challenging its assumptions about physical space.

"Euclid" - 'The Father Of Geometry'

The Presentation explains 'The Father Of Geometry' - "Euclid" with his life history and some of his most influential and remarkable works which contribute to The Modern Mathematics.

Mathematics Euclid's Geometry - My School PPT Project

The word ‘Geometry’ comes from Greek words ‘geo’ meaning the ‘earth’ and ‘metrein’ meaning to ‘measure’. Geometry appears to have originated from the need for measuring land.
Nearly 5000 years ago geometry originated in Egypt as an art of earth measurement. Egyptian geometry was the statements of results.
The knowledge of geometry passed from Egyptians to the Greeks and many Greek mathematicians worked on geometry. The Greeks developed geometry in a systematic manner..

CLASS 9 MATHS GEOMETRY INTRODUCTION TO EUCLID'S GEOMETRY.pptx

This document provides an introduction to Euclid's geometry. It discusses how geometry originated from the need to measure land and was studied in ancient civilizations. Euclid collected prior geometric works into his famous treatise "Elements", dividing it into 13 books. The document outlines Euclid's definitions of basic geometric terms like points, lines, and surfaces. It also describes Euclid's 5 postulates, or fundamental assumptions, which formed the basis for developing proofs in geometry. The postulates include being able to draw straight lines between points and extend line segments indefinitely.

Euclids geometry class 9 cbse

This document discusses the history and evolution of geometry. It begins by defining geometry as the measurement of earth and outlines its origins in ancient Egypt and the Indus Valley civilization where it was used to measure land and construct buildings. It then covers important early Greek mathematicians like Thales and Pythagoras and their theorems. Most of the document focuses on Euclid's Elements, outlining his definitions, postulates, axioms and use of deductive reasoning to prove 465 theorems. It also discusses criticisms of Euclid's definitions and the development of non-Euclidean geometry on curved surfaces.

introduction to euclid geometry

This document provides an overview of Euclid and geometry. It introduces Euclid and defines some key terms from his work, including definitions of points, lines, and straight lines. It outlines some of Euclid's axioms, such as things equal to the same thing being equal to each other. It also lists Euclid's five postulates, including that a straight line can be drawn between any two points and a circle can be drawn with any center and radius. The document is presented by Shobhit Chaudhary and covers topics like the origins and early developments of geometry as well as key concepts from Euclid's work.

Axioms and postulates (Euclidean geometry)

Euclid (325 to 265 B.C.) is known as the Father of Geometry. In his seminal work Elements, he organized all known mathematics into 13 books, defining key geometric concepts like points, lines, planes, and establishing axioms and postulates. Some of the key ideas he defined and established include that a point has no size, a line has length but no width, parallel lines don't intersect, and the interior angles of a triangle add to 180 degrees. Euclid's work was hugely influential and established the foundations of geometry and mathematical thought for centuries.

Euclid ppt final

- The document discusses Euclid's geometry and its origins in ancient Egypt and Greece. It describes how Euclid introduced a new deductive method of proving geometric results using axioms and postulates.
- Some of Euclid's key definitions, axioms, and five postulates are presented, including his fifth postulate regarding parallel lines. Equivalent versions of this controversial fifth postulate, such as Playfair's axiom, are also discussed.

Euclids geometry

it is a ppt on euclid;s geometry. it consists his theories and formulas and some information about him.

EUCLID'S GEOMETRY

FOR THOSE WHO WANT TO LEARN AND GET IDEA ABOUT EUCLID'S GEOMETRY SHOULD SEE THIS PPT THANK U HAVE A GOOD DAY

Euclids five postulates

This document outlines Euclid's five postulates of geometry. The five postulates are: 1) A straight line may be drawn between any two points. 2) A terminated line can be indefinitely produced in both directions. 3) A circle can be drawn with any center and radius. 4) All right angles are equal. 5) If two lines intersect such that the interior angles on the same side sum to less than two right angles, the lines will intersect on that side. The postulates form the basis for Euclidean geometry.

Euclids postulates

Euclid was a Greek mathematician from Alexandria known as the "Father of Geometry". In his influential work Elements, he deduced the principles of Euclidean geometry from 5 postulates (axioms) for plane geometry related to drawing lines and circles. The postulates state that a line can be drawn between any two points, a line can be extended indefinitely, a circle can be drawn with any center and radius, all right angles are equal, and if two lines intersect another such that the interior angles on the same side sum to less than two right angles, the two lines will intersect on that side. Euclid's work was foundational and served as the main geometry textbook for over 2000 years.

Euclidean geometry

Euclid was an ancient Greek mathematician who is considered the founder of geometry. He proposed 23 definitions and 5 postulates to form the basis of Euclidean geometry. The postulates could not be proved, but were considered intuitively true, while the definitions assigned clear meanings to basic geometric elements like points, lines, and planes. Euclid then deduced many other geometric theorems and propositions by applying logical reasoning to these initial definitions and postulates. His textbook, Elements, laid the foundations of geometry as a logical deductive system and influenced mathematics for centuries.

Euclid

Euclid of Alexandria, known as the "Father of Geometry", lived from approximately 325-265 BC in Alexandria, Egypt. He studied at Plato's Academy in Athens and wrote the influential textbook Elements, which systematized geometry and became the most successful mathematics book ever published next to the Bible. The Elements used a logical structure of definitions, postulates, theorems, and proofs without calculations to present geometric concepts and techniques in 13 books, laying the foundations for mathematics for over 2000 years. Euclid's work in rigorously deducing geometric principles from a small set of axioms established the influence of his ideas to this day.

Euclid

Euclid was a Greek mathematician born around 300-330 BC in Alexandria, Egypt. He is considered the "Father of Geometry" and is best known for his work Elements, which was a foundational textbook on geometry and mathematical reasoning used for over 2000 years. Elements defined basic geometric terms like point and line and used logical deductions from a small set of axioms to prove hundreds of propositions about geometry. Euclid made major contributions to mathematics through his use of deductive reasoning and is credited with developing the field of geometry into a formal axiomatic system.

Introduction to euclid’s geometry

Euclid (325-265 BCE) is considered the father of geometry. He organized geometry into a logical system using definitions, axioms, and postulates in his work Elements. Some key ideas are:
- Euclid defined basic geometric terms like points, lines, and planes. He also stated basic axioms about equality and properties of wholes and parts.
- Euclid proposed five postulates, including ones about drawing straight lines and circles. The fifth postulate about parallel lines was controversial and spurred development of non-Euclidean geometries.
- Euclid proved 465 theorems in Elements through deductive reasoning based on the definitions, axioms, and postulates

Euclid powerpoint

Euclid was a Greek mathematician from ancient Greece who is often referred to as "The Father of Geometry". He is renowned for writing the influential textbook "The Thirteen Books of Elements", which covered fundamental geometric concepts such as triangles, parallels, area, circles, constructions, proportions, number theory, and solid geometry. The textbook was widely used as the core text for teaching geometry and mathematics for over 2000 years.

7 euclidean&non euclidean geometry

Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these.

Euclid's axiom

Euclid's axiom

Introduction to euclid`s geometry by Al- Muktadir hussain

Introduction to euclid`s geometry by Al- Muktadir hussain

Euclid’s geometry

Euclid’s geometry

"Euclid" - 'The Father Of Geometry'

"Euclid" - 'The Father Of Geometry'

Mathematics Euclid's Geometry - My School PPT Project

Mathematics Euclid's Geometry - My School PPT Project

CLASS 9 MATHS GEOMETRY INTRODUCTION TO EUCLID'S GEOMETRY.pptx

CLASS 9 MATHS GEOMETRY INTRODUCTION TO EUCLID'S GEOMETRY.pptx

Euclids geometry class 9 cbse

Euclids geometry class 9 cbse

introduction to euclid geometry

introduction to euclid geometry

Axioms and postulates (Euclidean geometry)

Axioms and postulates (Euclidean geometry)

Euclid ppt final

Euclid ppt final

Euclids geometry

Euclids geometry

EUCLID'S GEOMETRY

EUCLID'S GEOMETRY

Euclids five postulates

Euclids five postulates

Euclids postulates

Euclids postulates

Euclidean geometry

Euclidean geometry

Euclid

Euclid

Euclid

Euclid

Introduction to euclid’s geometry

Introduction to euclid’s geometry

Euclid powerpoint

Euclid powerpoint

7 euclidean&non euclidean geometry

7 euclidean&non euclidean geometry

Introductiontoeuclidsgeometryby 131215081330-phpapp02

Euclid's geometry is a system of geometry developed by the ancient Greek mathematician Euclid. It consists of definitions, common notions, postulates, and theorems. The document summarizes Euclid's definitions, which define basic geometric objects like points, lines, and angles. It also discusses Euclid's axioms and postulates, which state properties like things equal to the same thing are equal to each other and that a straight line can be drawn between any two points. The document aims to introduce students to Euclid's foundational work in geometry.

ANECDOTAL RECORDS.pptx

This document provides an overview of Euclid's Elements and developments in geometry from Euclid. It discusses Euclid's geometric structure and postulates, including his parallel postulate. It also examines attempts to prove or replace the parallel postulate, such as Playfair's postulate and the works of Proclus and Saccheri. Figures were important in developing Euclid's geometry and understanding problems like the parallel postulate.

euclid's life and achievements

Euclid was an ancient Greek mathematician born around 325 BC in Greece. He received education from Plato's school and later taught in Alexandria, Egypt. There he wrote his famous book "The Elements" which established the foundations of geometry and is still used today. The book defined basic geometric terms like points, lines, and angles and established fundamental principles through a series of definitions, axioms, and postulates. These included being able to draw straight lines between points and extend lines indefinitely, as well as the parallel postulate which helped define parallel lines. Euclid's work established geometry as the first deductive system and has influenced mathematics for centuries.

euclid geometry

Euclid was a Greek mathematician from Alexandria known as the "Father of Geometry". His influential work Elements laid out the principles of geometry and served as the main geometry textbook from its publication until the 19th century. Elements deduced geometric principles from a small set of axioms and also covered number theory. Euclid wrote extensively on geometry, including dimensions, angles, curves, and shapes in two and three dimensions. He also wrote works on optics, perspective, and conic sections that investigated the apparent sizes of objects at different distances and angles.

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Geometry is the branch of mathematics dealing with shapes and sizes. Euclid was a Greek mathematician from around 300 BC who is best known for his influential textbook 'Elements', which laid out the foundations of geometry and logical deductive reasoning. The 'Elements' begins with plane geometry and uses just five axioms or postulates to prove many other geometric theorems. While some of Euclid's work built upon earlier mathematicians, he was the first to organize geometry into a comprehensive deductive system based on a small set of axioms.

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Geometry is the branch of mathematics dealing with shapes and sizes. Euclid was a Greek mathematician from around 300 BC who is best known for his influential textbook 'Elements', which laid out the foundations of geometry and introduced logical reasoning and mathematical proofs. The 'Elements' begins with plane geometry and is based on five postulates from which many other geometric properties can be deduced. Euclid was the first to show how geometric propositions could fit into a comprehensive deductive system.

Geometry

1. Euclid's Elements/Postulates - Euclid wrote a text titled 'Elements' in 300 BC which presented geometry through a small set of statements called postulates that are accepted as true. He was able to derive much of planar geometry from just five postulates, including the parallel postulate which caused much debate.
2. Euclid's Contribution to Geometry - Euclid is considered the "Father of Geometry" for his work Elements, which introduced deductive reasoning to mathematics. Elements influenced the development of the subject through its logical presentation of geometry from definitions and postulates.
3. Similar Triangles - Triangles are similar if they have the same shape but not necessarily the same

PO WER - XX LO Gdańsk - Euclid - father of geometry

Euclid was an influential Greek mathematician from Alexandria known as the "Father of Geometry". He wrote the Elements, one of the most important works in mathematics, which deduced the principles of geometry from a small set of axioms and became the main textbook for teaching mathematics until the 19th century. Euclid based his deductive system upon 10 axioms or postulates and used them to prove hundreds of theorems. His work covered topics in arithmetic, geometry, and number theory and helped establish geometry as a formal logical system.

Ppt on triangles class x made my jatin jangid

The document discusses learning objectives related to similarity of triangles. Students will understand the concept of similarity, prove and apply the Basic Proportionality Theorem, learn similarity rules like SAS, SSS, and AA, and learn and apply Pythagoras' Theorem and its converse. It also defines similar figures as those with the same shape but not necessarily the same size, and discusses how similarity can be used to indirectly measure distances like the height of Mount Everest.

Euclid's geometry

This document discusses Euclid and the foundations of geometry. It explains that Euclid was the first to take a deductive approach to geometry based on definitions, axioms, and postulates. Some of Euclid's key definitions included points, lines, planes, and relationships between them. His axioms stated basic logical truths like "equals added to equals are equal." Euclid also introduced five postulates, such as being able to draw straight lines between points and produce lines indefinitely. Overall, the document outlines Euclid's foundational work in clearly defining terms and establishing logical principles, making him the father of geometry.

9019. Kavyaa Ghosh (Class 9th) Presentation.pptx

This presentation by Kavyaa Ghosh provides an overview of Euclid's geometry. It defines key terms like geometry, axiom, postulate, and theorem. It introduces Euclid as the "Father of Geometry" and discusses his work collecting earlier geometric knowledge into his famous text Elements. The presentation outlines Euclid's five postulates, including the controversial fifth postulate. It also briefly explains Euclid's axioms and how theorems are proved using the definitions, axioms, and previously proved statements in his system.

Euclidean geometry

Euclidean geometry is based on the work of the ancient Greek mathematician Euclid and involves studying geometry on a flat plane using axioms like lines being straight and triangles having 180 degree internal angles. In the 19th century, non-Euclidean geometries emerged which don't follow these axioms, like Riemannian geometry describing a spherical space where triangles have greater than 180 degree angles and hyperbolic geometry describing a saddle-shaped space where lines can be parallel and triangles have less than 180 degree angles.

Euclids geometry for class IX by G R Ahmed

This document summarizes key concepts from Euclid's Geometry, including:
1. It discusses Euclid and his introduction of logical reasoning and proof to geometry. He is known for his work on plane figures called "Euclidean Geometry".
2. It defines basic geometric terms like points, lines, planes, and provides Euclid's original definitions and postulates.
3. It covers Euclid's influential axioms and 23 definitions that formed the basis for logic and proof in geometry. The definitions cover concepts like circles, triangles, parallelograms.

ANALYTIC-GEOMETRY(4).pptx

This document provides information about various concepts in analytic geometry including:
- Points, lines, planes, line segments, circles, angles, polygons, and their definitions.
- Finding midpoints, distances between points, slopes and inclinations of lines.
- Calculating slopes, tangents of angles, and the angle between two lines.
- Examples are provided to demonstrate finding midpoints, distances, slopes, angles, and solving geometric problems using coordinate systems.

Math ppt by parikshit

This document provides an introduction to Euclid's geometry. It defines key terms like point, line, and plane used in Euclid's work. It explains that Euclid was the first to take a systematic deductive approach to geometry, establishing definitions, axioms, and proving theorems. It lists some of Euclid's definitions, five axioms, and provides an example of a proof from his work in "The Elements" establishing that two distinct lines cannot share more than one point.

Presentation on the Euclid

Euclid of Alexandria lived around 300 BCE and wrote The Elements, the most influential and widely used mathematics textbook in history. The Elements collected, organized, and proved many geometric ideas and theorems that were known at the time. Euclid began with definitions, common notions, and postulates as foundations for geometry. He then used deductive reasoning to prove hundreds of theorems, establishing geometry as a logical science. While little is known about Euclid's life, his work The Elements has had an immense impact and remains highly influential to this day.

Euclid’ s geometry

Euclid was an ancient Greek mathematician who is considered the founder of geometry. He developed a systematic framework for geometry based on definitions, postulates, and logically derived theorems. Some of Euclid's key contributions included defining basic geometric elements like points, lines, planes, and figures. He also established fundamental postulates about the properties of and relationships between these elements, such as how to construct geometric figures and the fact that parallel lines do not intersect. This framework formed the basis for geometry as a logical mathematical system.

Euclid's geometry

This document provides an introduction to Euclid's fifth postulate of geometry. It discusses how Euclid was a famous Greek mathematician who wrote influential works on geometry. The document then defines a postulate as a statement assumed to be true without proof, and provides Euclid's fifth postulate which states that if two lines intersect such that the interior angles on the same side sum to less than two right angles, the lines will intersect on that side. It provides an example illustration and discusses how geometers have tried to prove the fifth postulate from the other postulates.

Term Paper Coordinate Geometry

The document provides a summary of coordinate geometry. It begins with definitions of key terms like the coordinate plane, axes, quadrants, and coordinates. It then discusses finding the midpoint, distance, and section formula between two points. Methods for finding the coordinates of the centroid and area of a triangle are presented. The document outlines different forms of equations for straight lines, including their slopes and the general equation of a line. It concludes with some uses of coordinate geometry, such as determining if lines are parallel/perpendicular.

Amstext 21-prev

- Euclid was a Greek mathematician from Alexandria, Egypt around 300 BCE who wrote the Elements, organizing all known geometry and number theory knowledge at the time into a single logical system.
- The Elements began with definitions, postulates, and previously proved results, building new proofs through deductive reasoning. This provided a model for mathematical logic still used today.
- While some portions may have been added later, Euclid established the framework of organizing mathematics through logical definitions, accepted truths as postulates, and building new knowledge through deduction from initial definitions and postulates.

Introductiontoeuclidsgeometryby 131215081330-phpapp02

Introductiontoeuclidsgeometryby 131215081330-phpapp02

ANECDOTAL RECORDS.pptx

ANECDOTAL RECORDS.pptx

euclid's life and achievements

euclid's life and achievements

euclid geometry

euclid geometry

New microsoft power point presentation

New microsoft power point presentation

New microsoft power point presentation

New microsoft power point presentation

Geometry

Geometry

PO WER - XX LO Gdańsk - Euclid - father of geometry

PO WER - XX LO Gdańsk - Euclid - father of geometry

Ppt on triangles class x made my jatin jangid

Ppt on triangles class x made my jatin jangid

Euclid's geometry

Euclid's geometry

9019. Kavyaa Ghosh (Class 9th) Presentation.pptx

9019. Kavyaa Ghosh (Class 9th) Presentation.pptx

Euclidean geometry

Euclidean geometry

Euclids geometry for class IX by G R Ahmed

Euclids geometry for class IX by G R Ahmed

ANALYTIC-GEOMETRY(4).pptx

ANALYTIC-GEOMETRY(4).pptx

Math ppt by parikshit

Math ppt by parikshit

Presentation on the Euclid

Presentation on the Euclid

Euclid’ s geometry

Euclid’ s geometry

Euclid's geometry

Euclid's geometry

Term Paper Coordinate Geometry

Term Paper Coordinate Geometry

Amstext 21-prev

Amstext 21-prev

Dot NET Interview Questions PDF By ScholarHat

Dot NET Interview Questions PDF By ScholarHat

RDBMS Lecture Notes Unit4 chapter12 VIEW

Description:
Welcome to the comprehensive guide on Relational Database Management System (RDBMS) concepts, tailored for final year B.Sc. Computer Science students affiliated with Alagappa University. This document covers fundamental principles and advanced topics in RDBMS, offering a structured approach to understanding databases in the context of modern computing. PDF content is prepared from the text book Learn Oracle 8I by JOSE A RAMALHO.
Key Topics Covered:
Main Topic : VIEW
Sub-Topic :
View Definition, Advantages and disadvantages, View Creation Syntax, View creation based on single table, view creation based on multiple table, Deleting View and View the definition of view
Target Audience:
Final year B.Sc. Computer Science students at Alagappa University seeking a solid foundation in RDBMS principles for academic and practical applications.
Previous Slides Link:
1. Data Integrity, Index, TAble Creation and maintenance https://www.slideshare.net/slideshow/lecture_notes_unit4_chapter_8_9_10_rdbms-for-the-students-affiliated-by-alagappa-university/270123800
2. Sequences : https://www.slideshare.net/slideshow/sequnces-lecture_notes_unit4_chapter11_sequence/270134792
About the Author:
Dr. S. Murugan is Associate Professor at Alagappa Government Arts College, Karaikudi. With 23 years of teaching experience in the field of Computer Science, Dr. S. Murugan has a passion for simplifying complex concepts in database management.
Disclaimer:
This document is intended for educational purposes only. The content presented here reflects the author’s understanding in the field of RDBMS as of 2024.

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Description:
Welcome to the comprehensive guide on Relational Database Management System (RDBMS) concepts, tailored for final year B.Sc. Computer Science students affiliated with Alagappa University. This document covers fundamental principles and advanced topics in RDBMS, offering a structured approach to understanding databases in the context of modern computing. PDF content is prepared from the text book Learn Oracle 8I by JOSE A RAMALHO.
Key Topics Covered:
Main Topic : USERS, Roles and Privileges
In Oracle databases, users are individuals or applications that interact with the database. Each user is assigned specific roles, which are collections of privileges that define their access levels and capabilities. Privileges are permissions granted to users or roles, allowing actions like creating tables, executing procedures, or querying data. Properly managing users, roles, and privileges is essential for maintaining security and ensuring that users have appropriate access to database resources, thus supporting effective data management and integrity within the Oracle environment.
Sub-Topic :
Definition of User, User Creation Commands, Grant Command, Deleting a user, Privileges, System privileges and object privileges, Grant Object Privileges, Viewing a users, Revoke Object Privileges, Creation of Role, Granting privileges and roles to role, View the roles of a user , Deleting a role
Target Audience:
Final year B.Sc. Computer Science students at Alagappa University seeking a solid foundation in RDBMS principles for academic and practical applications.
URL for previous slides
chapter 8,9 and 10 : https://www.slideshare.net/slideshow/lecture_notes_unit4_chapter_8_9_10_rdbms-for-the-students-affiliated-by-alagappa-university/270123800
Chapter 11 Sequence: https://www.slideshare.net/slideshow/sequnces-lecture_notes_unit4_chapter11_sequence/270134792
Chapter 12 View : https://www.slideshare.net/slideshow/rdbms-lecture-notes-unit4-chapter12-view/270199683
About the Author:
Dr. S. Murugan is Associate Professor at Alagappa Government Arts College, Karaikudi. With 23 years of teaching experience in the field of Computer Science, Dr. S. Murugan has a passion for simplifying complex concepts in database management.
Disclaimer:
This document is intended for educational purposes only. The content presented here reflects the author’s understanding in the field of RDBMS as of 2024.

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Open and Critical Perspectives on AI in Education

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Codeavour 5.0 International Impact Report - The Biggest International AI, Cod...

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Unlocking potential across borders! 🌍✨ Discover the transformative journey of Codeavour 5.0 International, where young innovators from over 60 countries converged to pioneer solutions in AI, Coding, Robotics, and AR-VR. Through hands-on learning and mentorship, 57 teams emerged victorious, showcasing projects aligned with UN SDGs. 🚀
Codeavour 5.0 International empowered students from 800 schools worldwide to tackle pressing global challenges, from bustling cities to remote villages. With participation exceeding 5,000 students, this year's competition fostered creativity and critical thinking among the next generation of changemakers. Projects ranged from AI-driven healthcare innovations to sustainable agriculture solutions, each addressing local and global issues with technological prowess.
The journey began with a collective vision to harness technology for social good, as students collaborated across continents, guided by mentors and educators dedicated to nurturing their potential. Witnessing the impact firsthand, teams hailing from diverse backgrounds united to code for a better future, demonstrating the power of innovation in driving positive change.
As Codeavour continues to expand its global footprint, it not only celebrates technological innovation but also cultivates a spirit of collaboration and compassion. These young minds are not just coding; they are reshaping our world with creativity and resilience, laying the groundwork for a sustainable and inclusive future. Together, they inspire us to believe in the limitless possibilities of innovation and the profound impact of young voices united by a common goal.
Read the full impact report to learn more about the Codeavour 5.0 International.BÀI TẬP BỔ TRỢ 4 KỸ NĂNG TIẾNG ANH LỚP 12 - GLOBAL SUCCESS - FORM MỚI 2025 - ...

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RDBMS Lecture Notes Unit4 chapter12 VIEW

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- 1. EUCLID GEOMETRY MADE BY :- PRATIKSHA MANWATKAR CLASS – IX/M
- 2. Who Was Euclid Euclid, sometimes called Euclid of Alexandria to distinguish him from Euclid of Megara, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I (323–283 BC). His Elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometr y) from the time of its publication until the late 19th or early 20th century. In the Elements, Euclid deduced the principles of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory and rigor
- 3. Why Was He Famous • Euclid was the first Greek mathematician who initiated a new way of thinking the study of geometry. • He introduced the method of proving a geometrical result by deductive reasoning based upon previously proved result and some self evident specific assumptions called axioms .
- 4. Euclidean Geometry • Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated by earlier mathematicians,[1] Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system. TheElements begins with plane geometry, still taught in secondary school as the first axiomatic system and the first examples of formal proof. It goes on to the solid geometry of three dimensions. Much of the Elements states results of what are now called algebra and number theory, explained in geometrical language. •
- 5. AXIOMS OF EUCLID • AXIOMS • Things which are equal to the same thing are also equal to one another. • If equals be added to equals, the wholes are equal. • If equals be subtracted from equals, the remainders are equal. • Things which coincide with one another are equal to one another. • The whole is greater than the part.
- 6. POSTULATES OF EUCLID • POSTULATES • Let the following be postulated: • To draw a straight line from any point to any point. • To produce a finite straight line continuously in a straight line. • To describe a circle with any centre and distance. • That all right angles are equal to one another. • That if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the straight lines, if produced indefinitely, will meet on that side on which the angles are less that two right angles. •
- 7. EXAMPLES OF AXIOMS • Suppose the area of a rectangle is equal to the area of a triangle and the area of that triangle is equal to the area of a square. By applying Euclid’s first axiom, we can say that the areas of the rectangle and the square are equal. Similarly, if a = b and b = c, then we can also say that a = c
- 8. EXAMPLES OF AXIOMS • Let us now discuss the second axiom. Let us consider a line segment AD in which, AB = CD. • If we add BC to both sides of this relation (equals are added), then according to Euclid’s second axiom, we can say that, AB + BC = CD + BC i.e., AC = BD. •
- 9. EXAMPLES OF AXIOMS • Consider the rectangles ABCD and PQRS drawn in the given figure. Suppose that the areas of the rectangles ABCD and PQRS are equal. If we remove triangle XYZ from each of the two rectangles as shown in the figure, then we can say that the areas of remaining portions of the two triangles are equal. We derived this from Euclid’s third axiom.
- 10. EXAMPLES OF AXIOMS • Euclid’s fourth axiom is sometimes used in geometrical proofs. Let us consider a point Q that lies between points P and R of a line segment PR as shown in the figure. • From this figure, we can notice that (PQ + QR) coincides with the line segment PR. Thus, by using Euclid’s fourth axiom, which states that “things which coincide with one another are equal to one another”, we can write, PQ + QR = PR. • Using the same figure that we used in the fourth axiom, we can see that PQ is a part of line segment PR. By using Euclid’s fifth axiom, we can say that the whole i.e., line segment PR is greater than the part i.e., PQ. Mathematically, we can write it as PR > PQ •
- 11. EXAMPLES OF POSTULATES Postulate one suggests that if we have two points P and Q on a plane, then we can draw at least one line that can simultaneously pass through these two points. Euclid does not mention that only one line can pass through two points, but he assumes the same. The fact that there can be only one line passing through two given points is illustrated in the following figure.
- 12. EXAMPLES OF POSTULATES • Postulate 2: A terminated line can be produced indefinitely. • This postulate can be considered as an extension of postulate 1. According to this postulate, we can make a different straight line from a given line by extending its points on either sides of the plane. • In the following figure, MN is the original line, while M′N′ is the new line formed by extending the original line in either direction. •
- 13. EXAMPLES OF POSTULATES • Postulate 3: It is possible to describe a circle with any centre and radius. • According to Euclid, a circle is a plane figure consisting of a set of points that are equidistant from a reference point. It can be drawn with the knowledge of its centre and radius. • The shapes of circles do not change when different radii are considered. Only their sizes change. •
- 14. EXAMPLES OF POSTULATES • Postulate 4: All right angles are equal to one another. • A right angle is unique in the sense that it measures exactly 90°. Hence, all right angles are of the measure 90° irrespective of the lengths of their arms. Hence, all right angles are equal to each other. • Remark: Unlike right angles, acute and obtuse angles are not unique in the sense that their measures lie between 0° to 89° and 91° to 179° respectively. Hence, the measure of one acute angle is not the same as the measure of another acute angle. Similarly, each obtuse angle has a different measure.