Geometry powerpoint
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Geometry is the study of angles, triangles, perimeter, area and volume. It has applications in fields like building, navigation, surveying and astronomy. Geometry has a long history dating back to ancient societies in Greece and other cultures. It continues to be vital in fields like architecture, art and engineering today.
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History of geometry
Geometry originated in response to practical problems like surveying land. It developed techniques for measuring spatial relationships and properties of space. Geometry was revolutionized by Euclid, who introduced mathematical rigor and axiomatic methods still used today. In modern times, geometric concepts have become highly abstract and complex, connected to calculus and algebra.
Historical events in geometry
This document provides an overview of the history and development of geometry. It discusses how geometry originated with early peoples discovering principles like the Pythagorean theorem thousands of years before Pythagoras. It then covers the major developments of geometry in ancient cultures like Egypt, Babylon, Greece, China, Islamic caliphates, and the modern era. Key figures discussed include Euclid, who introduced rigorous logic and axioms still used today, and Archimedes, considered one of the greatest mathematicians for his approximations of pi and work on limits.
"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.
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.
History Of Mathematics
All about how Number s were developed, Geometry, Arithematic Operations. DO NOT UNDER ESTIMATE WITH THE FRIEND COVER.
Euclid
Euclid was a Greek mathematician from Alexandria known as the "Father of Geometry". His influential work Elements deduced the principles of Euclidean geometry from a small set of axioms. It served as the main textbook for teaching mathematics for over 2000 years. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory, and rigor. He established an innovative deductive system in geometry based on definitions, axioms, and theorems and used it to prove various geometric results, such as how to construct a regular dodecahedron.
PPT on Geometry in our Daily life .....
The earliest recorded beginnings of geometry can be traced to ancient Mesopotamia and Egypt in the 2nd millennium BC. Early geometry was a collection of empirically discovered principles used for practical applications like surveying, construction, and astronomy. Some of the earliest known texts include the Egyptian Rhind Papyrus from 2000-1800 BC and the Moscow Papyrus from around 1890 BC, as well as Babylonian clay tablets such as Plimpton 322 from around 1900 BC. For example, the Moscow Papyrus contains a formula for calculating the volume of a truncated pyramid.
Euclids geometry
Euclid's Geometry is considered one of the most influential textbooks of all time. It introduced the axiomatic method and is the earliest example of the format still used in mathematics today. The document provides background on Euclid and the key aspects of his influential work Elements, including:
- Euclid organized geometry into a deductive system based on definitions, common notions, postulates, and propositions/theorems proved from these foundations.
- The Elements covers 13 books on topics like plane geometry, number theory, and solid geometry, containing over 450 theorems deduced from the initial assumptions.
- It established geometry as a logical science and had a major impact on mathematics and science for over 2000
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History of geometry
Geometry originated in response to practical problems like surveying land. It developed techniques for measuring spatial relationships and properties of space. Geometry was revolutionized by Euclid, who introduced mathematical rigor and axiomatic methods still used today. In modern times, geometric concepts have become highly abstract and complex, connected to calculus and algebra.
Historical events in geometry
This document provides an overview of the history and development of geometry. It discusses how geometry originated with early peoples discovering principles like the Pythagorean theorem thousands of years before Pythagoras. It then covers the major developments of geometry in ancient cultures like Egypt, Babylon, Greece, China, Islamic caliphates, and the modern era. Key figures discussed include Euclid, who introduced rigorous logic and axioms still used today, and Archimedes, considered one of the greatest mathematicians for his approximations of pi and work on limits.
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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.
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.
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All about how Number s were developed, Geometry, Arithematic Operations. DO NOT UNDER ESTIMATE WITH THE FRIEND COVER.
Euclid
Euclid was a Greek mathematician from Alexandria known as the "Father of Geometry". His influential work Elements deduced the principles of Euclidean geometry from a small set of axioms. It served as the main textbook for teaching mathematics for over 2000 years. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory, and rigor. He established an innovative deductive system in geometry based on definitions, axioms, and theorems and used it to prove various geometric results, such as how to construct a regular dodecahedron.
PPT on Geometry in our Daily life .....
The earliest recorded beginnings of geometry can be traced to ancient Mesopotamia and Egypt in the 2nd millennium BC. Early geometry was a collection of empirically discovered principles used for practical applications like surveying, construction, and astronomy. Some of the earliest known texts include the Egyptian Rhind Papyrus from 2000-1800 BC and the Moscow Papyrus from around 1890 BC, as well as Babylonian clay tablets such as Plimpton 322 from around 1900 BC. For example, the Moscow Papyrus contains a formula for calculating the volume of a truncated pyramid.
Euclids geometry
Euclid's Geometry is considered one of the most influential textbooks of all time. It introduced the axiomatic method and is the earliest example of the format still used in mathematics today. The document provides background on Euclid and the key aspects of his influential work Elements, including:
- Euclid organized geometry into a deductive system based on definitions, common notions, postulates, and propositions/theorems proved from these foundations.
- The Elements covers 13 books on topics like plane geometry, number theory, and solid geometry, containing over 450 theorems deduced from the initial assumptions.
- It established geometry as a logical science and had a major impact on mathematics and science for over 2000
Euclid ppt about him and his inventions
Euclid of Alexandria, known as the "Father of Geometry", wrote his influential treatise Elements around 300 BC. In it, he defined fundamental geometric terms like points, lines, and planes and established basic principles called axioms and postulates that could be used to prove other geometric results without needing further proof. Some of Euclid's key definitions included that a point has no size, a line has length but no width, and a plane surface has length and width. His axioms and postulates laid the groundwork for deductive reasoning in geometry.
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History of Math is a project in which students worked together in learning about historical development of mathematical ideas and theories. They were exploring about mathematical development from Sumer and Babylon till Modern age, and from Ancient Greek mathematicians till mathematicians of Modern age, and they wrote documents about their explorations. Also they had some activities in which they could work "together" (like writing a dictionary, taking part in the Eratosthenes experiment, measuring and calculating the height of each other schools, cooperating in given tasks) and activities that brought out their creativity and Math knowledge (making Christmas cards with mathematical details and motives and celebrating the PI day). Also they were able to visit Museum, exhibition "Volim matematiku" and to prepare (and lead) workshops for the Evening of mathematics (Večer matematike). At the end they have presented their work to other students and teachers.
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.
Introduction to euclid’s geometry
This document provides an overview of geometry and Euclidean geometry. It discusses that geometry is the branch of mathematics concerned with shape, size, position, and space. Euclidean geometry is based on Euclid's work in the Elements and uses undefined terms like point and line, along with definitions, axioms, and postulates to develop theorems about flat space. Some of Euclid's key definitions, axioms, and postulates are presented, including the parallel postulate which caused debate as it did not seem as obvious as the others. Alternative versions of the parallel postulate are also mentioned.
Geometry in real life
Geometry is a branch of mathematics that deals with measurement and spatial relationships. It is used to calculate areas, perimeters, volumes, and other properties of shapes and spaces. Geometry is applied in many fields like carpentry, painting, gardening, engineering, surveying, astronomy, graphic design, and medical imaging. It allows people in these occupations to perform measurements and calculations essential to their work.
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The document provides an overview of mathematics in ancient Greece, covering important Greek mathematicians and their contributions. It discusses Thales of Miletus, who made early advances in geometry. It also covers Pythagoras and the Pythagorean school, whose discoveries included relationships between musical intervals and ratios. Euclid is discussed for writing the influential Elements, compiling earlier work. Archimedes made advances in areas and used a method of exhaustion to calculate pi. The document provides context on Plato, Aristotle, and others who helped develop mathematics.
history of trigonometry
Trigonometry is the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six trigonometric functions - sine, cosine, tangent, cotangent, secant, and cosecant. Trigonometry originated in ancient civilizations for practical geometry applications and was further developed by Greek mathematicians like Hipparchus and Ptolemy. Indian and later Islamic mathematicians made important contributions, including the first tables of sines and tangents. Trigonometry was an important tool for astronomy and passed to Europe during the Middle Ages, with major works by Menelaus and Regiomontanus.
History of Early Geometry
1. Geometry originated in ancient Egypt and was further developed by ancient Greek mathematicians like Thales, Pythagoras, Plato, Euclid, Archimedes, and others who made discoveries in areas like triangles, circles, volumes, and mechanics.
2. Euclid's Elements collected earlier geometric theorems into a coherent logical system and was used as the standard geometry textbook for over 2000 years.
3. Many of these early geometers were based around the Mediterranean, including Thales in Miletus, Pythagoras on Samos island, Plato in Athens, and Archimedes in Syracuse.
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Qin Jiushao was an important Chinese mathematician who introduced the use of zero in mathematics. He developed methods for solving high-order numerical equations, including a 4th order equation. Mathematics emerged independently in China by the 11th century BC and the Chinese made contributions to large and negative numbers, decimals, place value, algebra, geometry, and trigonometry. During the Song and Yuan dynasties, mathematicians like Yang Hui, Qin Jiushao, Li Zhi, and Zhu Shijie developed methods for solving simultaneous, quadratic, cubic, and quartic equations hundreds of years before Europeans.
Chapter 1 ( Basic Concepts in Geometry )
Chapter 1 Basic Concepts in Geometry
1.1 Points, Lines and Planes
1.2 Line Segment
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1.4 Some Special Angles
1.5 Angles Made By A Transversal
1.6 Transversal Across Two Parallel Lines
1.7 Conditions For Parallelism
Introduction to Rational numbers
This is meant for age group 11 to 14 years.
For Class VIII CBSE.
Some viewers have requested me to send the file through mail.
So I allowed everybody to download.My request is whenever you are using plz acknowledge me.
Pratima Nayak ,Teacher,Kendriya Vidyalaya,Fort William,Kolkata
pnpratima@gmail.com
Based on Text book
Congruent Triangles
1. Triangles are congruent if all corresponding sides and angles are congruent. They will have the same shape and size but may be mirror images.
2. There are four main postulates and theorems used to prove triangles congruent: SSS (three sides), SAS (two sides and included angle), ASA (two angles and included side), and AAS (two angles and non-included side).
3. Corresponding parts of congruent triangles are also congruent based on the CPCTC theorem. This allows using previously proven congruent parts in future proofs.
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The document defines an axiomatic system and its key properties:
1. An axiomatic system consists of undefined terms, definitions, axioms, and theorems which are logical consequences of the axioms.
2. Axioms are independent if they cannot be deduced from other axioms. A set of axioms is complete if no independent axioms can be added.
3. A set of axioms is consistent if no theorem can be deduced that contradicts an axiom or previously proved theorem.
4. Euclidean geometry is an example axiomatic system based on 5 axioms, including the parallel postulate which distinguishes it from
Congruent shapes in real life
Two shapes are congruent if one can be transformed into the other by a combination of rotations, reflections, and translations, leaving their size and shape unchanged. Many real-world objects exhibit congruence, such as the two halves of a bicycle or a pair of gloves. Congruence is an important geometric concept with applications in architecture, design, manufacturing, and other fields where precise replication of shapes is required.
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.
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The document provides information and examples about using do and does in short answer sentences in English, including affirmative and negative examples. It also gives examples of question words used with do/does in questions, such as what, where, when, and how. The document concludes with directions for an activity where students work in pairs to interview each other and complete a diagram with information about favorite superheroes.
Math PYRAMIDS
The document discusses various types of pyramids including right, oblique, regular, irregular, convex, and concave pyramids. It defines pyramids and their key characteristics. Formulas are provided for calculating the lateral surface area, total surface area, and volume of regular pyramids using measurements of the base and height. The concept of a frustum of a pyramid is introduced along with how to calculate the area and volume of a pyramidal frustum. An example problem demonstrates calculating measurements for a truncated square pyramid.
Historia de la geometría
La geometría tiene sus orígenes hace aproximadamente 3000 años a.C. en el antiguo Egipto, donde se construyeron grandes pirámides y el templo de Ramsés II. Tales de Mileto, que vivió en el 600 a.C., aprendió de los sacerdotes egipcios y helénicos y sentó las bases de la geometría griega. Euclides desarrolló los principios fundamentales de la geometría en su obra "Los Elementos" alrededor del 300 a.C., estableciendo las bases de la geometría euclidiana
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Euclid ppt about him and his inventions
Euclid of Alexandria, known as the "Father of Geometry", wrote his influential treatise Elements around 300 BC. In it, he defined fundamental geometric terms like points, lines, and planes and established basic principles called axioms and postulates that could be used to prove other geometric results without needing further proof. Some of Euclid's key definitions included that a point has no size, a line has length but no width, and a plane surface has length and width. His axioms and postulates laid the groundwork for deductive reasoning in geometry.
History of Math
History of Math is a project in which students worked together in learning about historical development of mathematical ideas and theories. They were exploring about mathematical development from Sumer and Babylon till Modern age, and from Ancient Greek mathematicians till mathematicians of Modern age, and they wrote documents about their explorations. Also they had some activities in which they could work "together" (like writing a dictionary, taking part in the Eratosthenes experiment, measuring and calculating the height of each other schools, cooperating in given tasks) and activities that brought out their creativity and Math knowledge (making Christmas cards with mathematical details and motives and celebrating the PI day). Also they were able to visit Museum, exhibition "Volim matematiku" and to prepare (and lead) workshops for the Evening of mathematics (Večer matematike). At the end they have presented their work to other students and teachers.
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.
Introduction to euclid’s geometry
This document provides an overview of geometry and Euclidean geometry. It discusses that geometry is the branch of mathematics concerned with shape, size, position, and space. Euclidean geometry is based on Euclid's work in the Elements and uses undefined terms like point and line, along with definitions, axioms, and postulates to develop theorems about flat space. Some of Euclid's key definitions, axioms, and postulates are presented, including the parallel postulate which caused debate as it did not seem as obvious as the others. Alternative versions of the parallel postulate are also mentioned.
Geometry in real life
Geometry is a branch of mathematics that deals with measurement and spatial relationships. It is used to calculate areas, perimeters, volumes, and other properties of shapes and spaces. Geometry is applied in many fields like carpentry, painting, gardening, engineering, surveying, astronomy, graphic design, and medical imaging. It allows people in these occupations to perform measurements and calculations essential to their work.
Mathematics in Ancient Greece
The document provides an overview of mathematics in ancient Greece, covering important Greek mathematicians and their contributions. It discusses Thales of Miletus, who made early advances in geometry. It also covers Pythagoras and the Pythagorean school, whose discoveries included relationships between musical intervals and ratios. Euclid is discussed for writing the influential Elements, compiling earlier work. Archimedes made advances in areas and used a method of exhaustion to calculate pi. The document provides context on Plato, Aristotle, and others who helped develop mathematics.
history of trigonometry
Trigonometry is the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six trigonometric functions - sine, cosine, tangent, cotangent, secant, and cosecant. Trigonometry originated in ancient civilizations for practical geometry applications and was further developed by Greek mathematicians like Hipparchus and Ptolemy. Indian and later Islamic mathematicians made important contributions, including the first tables of sines and tangents. Trigonometry was an important tool for astronomy and passed to Europe during the Middle Ages, with major works by Menelaus and Regiomontanus.
History of Early Geometry
1. Geometry originated in ancient Egypt and was further developed by ancient Greek mathematicians like Thales, Pythagoras, Plato, Euclid, Archimedes, and others who made discoveries in areas like triangles, circles, volumes, and mechanics.
2. Euclid's Elements collected earlier geometric theorems into a coherent logical system and was used as the standard geometry textbook for over 2000 years.
3. Many of these early geometers were based around the Mediterranean, including Thales in Miletus, Pythagoras on Samos island, Plato in Athens, and Archimedes in Syracuse.
CHİNESE MATHEMATCS
Qin Jiushao was an important Chinese mathematician who introduced the use of zero in mathematics. He developed methods for solving high-order numerical equations, including a 4th order equation. Mathematics emerged independently in China by the 11th century BC and the Chinese made contributions to large and negative numbers, decimals, place value, algebra, geometry, and trigonometry. During the Song and Yuan dynasties, mathematicians like Yang Hui, Qin Jiushao, Li Zhi, and Zhu Shijie developed methods for solving simultaneous, quadratic, cubic, and quartic equations hundreds of years before Europeans.
Chapter 1 ( Basic Concepts in Geometry )
Chapter 1 Basic Concepts in Geometry
1.1 Points, Lines and Planes
1.2 Line Segment
1.3 Rays and Angles
1.4 Some Special Angles
1.5 Angles Made By A Transversal
1.6 Transversal Across Two Parallel Lines
1.7 Conditions For Parallelism
Introduction to Rational numbers
This is meant for age group 11 to 14 years.
For Class VIII CBSE.
Some viewers have requested me to send the file through mail.
So I allowed everybody to download.My request is whenever you are using plz acknowledge me.
Pratima Nayak ,Teacher,Kendriya Vidyalaya,Fort William,Kolkata
pnpratima@gmail.com
Based on Text book
Congruent Triangles
1. Triangles are congruent if all corresponding sides and angles are congruent. They will have the same shape and size but may be mirror images.
2. There are four main postulates and theorems used to prove triangles congruent: SSS (three sides), SAS (two sides and included angle), ASA (two angles and included side), and AAS (two angles and non-included side).
3. Corresponding parts of congruent triangles are also congruent based on the CPCTC theorem. This allows using previously proven congruent parts in future proofs.
Euclids geometry
Euclid's Elements is based on axioms, postulates, and definitions from which 465 propositions are deduced using deductive reasoning. The Elements covers plane and solid geometry, including definitions of basic shapes, proofs of important theorems like the Pythagorean theorem, and the establishment of concepts like prime numbers. It has had an immense influence on mathematics since its publication over 2000 years ago.
Geometry in real life
Uses Of Geometry In Real Life
How geometry was discovered ?
What are its uses in IT , Maths , Chemistry , Physics ETC ?
The greatest mathematicians of all times
Maths club activity conducted during the activity period by INDIA INTERNATIONAL SCHOOL, SHARJAH, on 30/10/14
HISTORY of GEOMETRY.ppt
Early developments in trigonometry began with the ancient Egyptians and Babylonians who studied ratios of sides in similar triangles. Trigonometry advanced significantly through the works of Hipparchus, Euclid, Archimedes, and later Islamic mathematicians such as Al-Khwarizmi, who produced the first table of tangents. Nasir al-Din al-Tusi established spherical trigonometry as an independent field and listed the six cases of right triangles. Modern analytic trigonometry was established by Euler, while Brook Taylor derived general Taylor series for all six trigonometric functions.
Geometry Introduction-c
The document defines an axiomatic system and its key properties:
1. An axiomatic system consists of undefined terms, definitions, axioms, and theorems which are logical consequences of the axioms.
2. Axioms are independent if they cannot be deduced from other axioms. A set of axioms is complete if no independent axioms can be added.
3. A set of axioms is consistent if no theorem can be deduced that contradicts an axiom or previously proved theorem.
4. Euclidean geometry is an example axiomatic system based on 5 axioms, including the parallel postulate which distinguishes it from
Congruent shapes in real life
Two shapes are congruent if one can be transformed into the other by a combination of rotations, reflections, and translations, leaving their size and shape unchanged. Many real-world objects exhibit congruence, such as the two halves of a bicycle or a pair of gloves. Congruence is an important geometric concept with applications in architecture, design, manufacturing, and other fields where precise replication of shapes is required.
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.
Math: Venn and Carroll Diagrams
The document provides information and examples about using do and does in short answer sentences in English, including affirmative and negative examples. It also gives examples of question words used with do/does in questions, such as what, where, when, and how. The document concludes with directions for an activity where students work in pairs to interview each other and complete a diagram with information about favorite superheroes.
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The document discusses various types of pyramids including right, oblique, regular, irregular, convex, and concave pyramids. It defines pyramids and their key characteristics. Formulas are provided for calculating the lateral surface area, total surface area, and volume of regular pyramids using measurements of the base and height. The concept of a frustum of a pyramid is introduced along with how to calculate the area and volume of a pyramidal frustum. An example problem demonstrates calculating measurements for a truncated square pyramid.
Historia de la geometría
La geometría tiene sus orígenes hace aproximadamente 3000 años a.C. en el antiguo Egipto, donde se construyeron grandes pirámides y el templo de Ramsés II. Tales de Mileto, que vivió en el 600 a.C., aprendió de los sacerdotes egipcios y helénicos y sentó las bases de la geometría griega. Euclides desarrolló los principios fundamentales de la geometría en su obra "Los Elementos" alrededor del 300 a.C., estableciendo las bases de la geometría euclidiana
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This document provides a timeline of important developments in geometry and mathematics from 2600 BC to the present. It mentions early Egyptian, Babylonian and Chinese mathematical texts and discoveries. It then outlines major developments and texts from ancient Greece like Euclid's Elements and works by Ptolemy and Kepler. It notes early modern developments in geometry by Descartes, Da Vinci and advances in projective geometry. The timeline highlights increasing precision in measuring areas, volumes and structures as well as applications in fields like transportation, chemistry and physics.
La Historia De La GeoméTríA
Este documento resume brevemente la historia de la geometría desde sus orígenes en el Antiguo Egipto hasta la actualidad. En Egipto, los agrimensores utilizaban cuerdas para medir y replantear los límites de las tierras de los agricultores después de las inundaciones del Nilo. Más tarde, los egipcios desarrollaron fórmulas para calcular el volumen de las pirámides. En la antigua Grecia, Euclides escribió "Los Elementos", uno de los textos matemáticos más influyentes
Breve Reseña Historia de la Geometría
La geometría ha evolucionado a lo largo de la historia, comenzando con los primeros intentos de medir y dividir la tierra por parte de los antiguos egipcios y babilonios, pasando por los avances realizados por los griegos como Euclides y sus postulados geométricos fundamentales, hasta llegar a los desarrollos modernos en geometría no euclidiana y geometría fractal.
Historia de la Geometria
Este documento resume la historia de la geometría desde sus orígenes en la antigua Grecia hasta los desarrollos modernos. Comenzó como una geometría empírica para medir tierras y construir edificios, pero los griegos la sistematizaron basándola en axiomas y postulados. Euclides expuso de forma rigurosa la geometría griega en Los Elementos. Más tarde, Descartes conectó la geometría y el álgebra a través de la geometría analítica. En el siglo XIX surgieron nuevos conceptos como la
El origen de la geometría
El documento describe la evolución de la geometría desde sus orígenes en las primeras civilizaciones hasta la geometría analítica de Descartes. Señala que la geometría surgió de forma intuitiva en Egipto y Mesopotamia con fines prácticos como la medición de tierras, y que los griegos como Tales, Pitágoras y Euclides la desarrollaron de forma más abstracta y deductiva. Finalmente, Descartes introdujo la geometría analítica que relaciona la geometría con las ecuaciones algebraicas.
Origen y desarrollo de la Geometría
El documento resume la historia y el origen de la geometría. Comenzó como una herramienta práctica para medir tierras en el antiguo Egipto, luego los griegos le dieron un enfoque más científico al incorporar demostraciones lógicas. Euclides es considerado el padre de la geometría por su influyente trabajo "Los Elementos". La geometría ha evolucionado a incluir diferentes ramas y sigue siendo útil para describir formas en el mundo real.
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GEOMETRY AROUND US
Geometry is a branch of mathematics concerned with shapes, sizes, and relative positions of figures and objects in space. Some key concepts in geometry include points, lines, planes, angles, and shapes. Geometry has been studied and applied since ancient times, with important developments in geometry made by ancient Greek mathematicians like Thales, Pythagoras, and Euclid. Geometry has many practical applications in fields like construction, engineering, and space exploration.
Math & Science of Ancient Greece and Egypt
The Ancient Egyptians and Greeks made many contributions to math and science. The Egyptians excelled in areas like measurement, construction of pyramids using precise angles and geometry, and early astronomy to develop calendars. They also had early understandings of medicine and anatomy from animal mummification. The Greeks advanced fields like formal geometry and were the first to calculate the circumference of the Earth. Both civilizations established foundations of math concepts still used today.
Greek mythology presentation
Greek mythology can be used across various subjects in a 4th grade classroom. It provides an exciting and interesting theme that is versatile in its applications. Greek myths and the religion of ancient Greeks can be studied in social studies, while myths involving plants and architecture can be applied to science and math lessons. Stories from Greek mythology are also well-suited for reading comprehension and lessons about myths in language arts.
Compialtion selected topics
This document discusses key concepts in the study and teaching of geography and sociology. It covers:
- The founders and early development of sociology as a field, including the contributions of Auguste Comte, Herbert Spencer, Karl Marx, Emile Durkheim, and Max Weber.
- The four traditions of geography: spatial, area studies, human-environment interaction, and earth science.
- Key concepts in sociology like social interaction, symbolic interactionism, and the development of social classes and identity.
- Tools used in geography like maps and methods like fieldwork.
It provides an overview of important topics and thinkers that shaped the development of both geography and sociology as academic disciplines
TOD-5-The Architect at Work.pdf
The document discusses four distinct ways that architects generate 3D forms for buildings:
1. Pragmatic design uses trial and error, like early humans building shelters from available materials.
2. Iconic design repeats traditional forms that effectively control the climate using local resources.
3. Analogic design generates new forms by analogy, like Egyptian tombs evolving from stone mounds.
4. Canonic design uses proportional grids and systems derived from mathematics and philosophy to impose order, like Greek temples based on Plato's geometric solids.
5.4- Measuring the Earth with Eratosthenes. Ves 2.pdf
Johannes Kepler was a German mathematician and astronomer in the late 16th and early 17th centuries. He is most famous for discovering the three laws of planetary motion, which describe how planets move around the sun in elliptical orbits. Kepler also made important contributions to optics, geometry, and astronomy through his calculations of astronomical tables and discoveries in other areas of mathematics and science. He is considered a key figure in the scientific revolution.
math as an art.pdf
Mathematics can be viewed in three ways: as an art of calculation, as a language, and as a way of thinking. It has inspired and been used in various art forms through concepts like symmetry and perspective. As a language, mathematics uses symbolic notation and formulas that are understood internationally, acting as sentences. As a way of thinking, mathematics teaches logical, analytical, and precise thinking that benefits everyone, though is not natural and requires education to fully develop.
Pedagogy of School Subject Geography
Geography is defined as the study of the Earth's physical features and human environments. It has evolved from a descriptive field to one that examines the interactions between humans and their environments. The scope of geography has broadened over time and now includes branches like physiography, economic geography, human geography, political geography, cartography, urban geography, anthropogeography, and agricultural geography. Each branch examines a different aspect of the relationship between humans and the Earth.
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Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
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Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
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Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
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2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
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Geometry powerpoint
- 1. Geometry
- 2. • Geometry is used all around us in several real-life situation •We can find it simply by looking around at the various structures in our schools •Putting geometry into this real-life perspective will help students relate on a more personal level, and further understand various principles Real Life Applications
- 3. •The word geometry comes from two Greek words – geos and metron, meaning earth and measure respectively •It is the study of angles, triangles, perimeter, area and volume •The use of geometry was vital for ancient societies and was used for a variety of reasons, including building, navigation, surveying and astronomy •Euclid, along with other mathematicians and philosophers, wrote Euclidean geometry over 2000 years ago and this text is still being used today Geometry: A brief history of the term
- 4. Intricate geometric patterns can be found on screen designs in China Muslim, Indigenous People, Aztec and Greek cultures all use or used geometric patterns in their architecture, pottery and clothing Geometry can not only be linked to art, but also literature with books like A Cloak for a Dreamer, by Alice Freidman, Big Ones, Little Ones by Tana Hoban and The Secret Birthday Message by Eric Carle Cultural and Cross Curricular Connections
- 5. Cultural and Cross Curricular Connections
- 6. A pyramid is a great example of a polyhedron for which the base is a polygon and all lateral faces are triangles Pyramid
- 7. The United States Department of Defence is a great example to show students how architecture uses geometry Pentagon
- 8. History of Geometry Egyptians c. 2000 – 500 B.C.E
- 9. Babylonians c. 2000 - 500 B.C.E
- 12. Early Renaissance Art -1400. C.E
- 13. Co-ordinate Geometry c. 1600 C.E.
- 14. Non-Euclidean Geometries c. early 1800 C.E