This a power point presentation about Euclid, the mathematician and mainly his contributions to Geometry and mathematics. For the full effects, please download it and watch it as a slide show. All comments and suggestions are welcome.
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,.....................
Mathematics Euclid's Geometry - My School PPT ProjectJaptyesh Singh
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..
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,.....................
Mathematics Euclid's Geometry - My School PPT ProjectJaptyesh Singh
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..
Its a presentation about euclid's axioms and its definations
so please everyone see it and save it. It will be very useful for all who is using it.It will provide you about all the information and diagrams related to the euclid's definations and axioms
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.
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.
Its a presentation about euclid's axioms and its definations
so please everyone see it and save it. It will be very useful for all who is using it.It will provide you about all the information and diagrams related to the euclid's definations and axioms
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.
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.
Aryabhatt and his major invention and worksfathimalinsha
Aryaabhatt ,one of the most renewed scientist and mathematician indian history. this ppt is about him and his
major invention or works or discoveries in science,mathematics.this ppt contains information regarding aryabhattia,his knowledge on Place value system and zero Pi as irrational Mensuration and trigonometry Indeterminate equations Algebra
and in astronomy
Motions of the solar system Eclipses Sidereal periods Heliocentrism.
Srinivasa Ramanujan A great INDIAN MATHEMATICIANSchooldays_6531
We Indians are not too great but we have some GREATEST personalities like Aryabhatta -- Who gave the world ZERO
This is a small presentation on life history of Srinivasa Ramanujan.
Please LIKE and SHARE.
b.) GeometryThe old problem of proving Euclid’s Fifth Postulate.pdfannaindustries
b.) Geometry:
The old problem of proving Euclid’s Fifth Postulate, the \"Parallel Postulate\", from his first
four postulates had never been forgotten. Beginning not long after Euclid, many attempted
demonstrations were given, but all were later found to be faulty, through allowing into the
reasoning some principle which itself had not been proved from the first four postulates. Though
Omar Khayyám was also unsuccessful in proving the parallel postulate, his criticisms of
Euclid\'s theories of parallels and his proof of properties of figures in non-Euclidean geometries
contributed to the eventual development of non-Euclidean geometry. By 1700 a great deal had
been discovered about what can be proved from the first four, and what the pitfalls were in
attempting to prove the fifth. Saccheri, Lambert, and Legendre each did excellent work on the
problem in the 18th century, but still fell short of success. In the early 19th century, Gauss,
Johann Bolyai, and Lobatchewsky, each independently, took a different approach. Beginning to
suspect that it was impossible to prove the Parallel Postulate, they set out to develop a self-
consistent geometry in which that postulate was false. In this they were successful, thus creating
the first non-Euclidean geometry. By 1854, Bernhard Riemann, a student of Gauss, had applied
methods of calculus in a ground-breaking study of the intrinsic (self-contained) geometry of all
smooth surfaces, and thereby found a different non-Euclidean geometry. This work of Riemann
later became fundamental for Einstein\'s theory of relativity.
William Blake\'s \"Newton\" is a demonstration of his opposition to the \'single-vision\' of
scientific materialism; here, Isaac Newton is shown as \'divine geometer\' (1795)
It remained to be proved mathematically that the non-Euclidean geometry was just as self-
consistent as Euclidean geometry, and this was first accomplished by Beltrami in 1868. With
this, non-Euclidean geometry was established on an equal mathematical footing with Euclidean
geometry.
While it was now known that different geometric theories were mathematically possible, the
question remained, \"Which one of these theories is correct for our physical space?\" The
mathematical work revealed that this question must be answered by physical experimentation,
not mathematical reasoning, and uncovered the reason why the experimentation must involve
immense (interstellar, not earth-bound) distances. With the development of relativity theory in
physics, this question became vastly more complicated.
c.) Algebra:
1. Babylonian algebra
The origins of algebra can be traced to the ancient Babylonians, who developed a positional
number system that greatly aided them in solving their rhetorical algebraic equations. The
Babylonians were not interested in exact solutions but approximations, and so they would
commonly use linear interpolation to approximate intermediate values. One of the most famous
tablets is the Plimpton 322 tablet, .
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
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!
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
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.
4. EuclideanGeometryis the study of geometrybasedon definitions,undefinedpoints, whichare a point,a lineand a
plane,and the assumptionsof ‘TheFatherof Geometry’.
The geometry of plane figure is known as ‘Euclid’sGeometry’.
Euclid’sGeometryincludessets of Axioms,and many theorems deducedfromthem.
Euclid’stext elements was the first systematicdiscussionof geometry.While many of Euclid’sfindingshad been
previouslystatedby earlierGreek mathematicians, Euclidis creditedwith developingthe first comprehensive deductive
system
Euclid’sapproachto geometryconsistedof proving all theoremsfroma finite number of postulesand axions.
The concepts of Euclid’sgeometry remainedunchallengeduntilthe early 19th century. At that time, otherformsof
geometry startedto emerge, callednon-Euclidean geometries.It was no longerassumedthatEuclid’sgeometry could be
used to describeall physical space.
Euclid’s Geometry
5. Basis of Euclid’s Geometry
The elements of Euclid is based on theorems proved by other
mathematical work.
Euclid put together many of Eudoxus’ theorems, many of Theaetetus
theorems, and also made the theories, vaguely proved by his
predecessors, more relevant.
Most of books I and II were based on Pythagoras, book III on
Hippocrates of Chios, and book V on Eudoxus , while books IV, VI, XI,
and XII probably came from other Pythagorean or Athenian
mathematicians
Euclid often replaced misleading proofs with his own.
The use of definitions, postulates, and axioms dated back to Plato.
The Elements may have been based on an earlier textbook by
Hippocrates of Chios, who also may have originated the use of letters to
refer to figures.
6. Many results about plane figures are proved.
Pons Asinorum i.e. If a triangle has two equal angles, then the sides
subtended by the angles are equal is proved.
The Pythagorean theorem is proved.
It deals with numbers treated geometrically through their representation as
line segments with various lengths.
Prime Numbers and Rational and Irrational numbers are introduced.
The infinitude of prime numbers is proved.
A typical result is the 1:3 ratio between the volume of a cone and a cylinder
with the same height and base.
CONTENTS OF THE BOOK
Euclid’s Geometry has 13 books, of which, books I–IV and VI discuss plane geometry; books V
and VII–X deal with number theory and books XI–XIII concern solid geometry.
7. The Greek mathematicians of Euclid’s time thought of geometry as an
abstract model of the world they lived in. The notions of point, line,
plain, etc. were derived from what was seen around them. Euclid
summarised these notions as definitions.
The Elements begins with a list of definitions.
It has been suggested that the definitions were added to the Elements
sometime after Euclid wrote them. Another possibility is that they are
actually from a different work, perhaps older
Though Euclid defined a point, a line, and a plane, the definitions are
not accepted by mathematicians. Therefore, these terms are now taken
as undefined.
Euclid deduced a total of 131 definitions. There were 23 in Book I, 2 in
Book II, 11 in Book III, 7 in Book IV, 18 in Book V, 4 in Book VI, 22 in
Book VII, 16 in Book X and 28 in Book XI.
8.
9.
10. • Things which equal the same thing also equal one another.
– If a=b and b=c, then a=c
• If equals are added to equals, then the wholes are equal.
– If a=b, then a+c = b+c
• If equals are subtracted from equals, then the remainders are equal.
– If a=b, then a-c=b-c
• The whole is greater than the part.
– 1 > ½
• Things which are double of the same things are equal to one another.
– If a=2b and c=2b, then a=b
• Things which are halves of the same things are equal to one another.
– If a= ½ b and c= ½ b, then a=c
11.
12. After Euclid stated his postulates and axioms, he used them to
prove other results. Then using these results, he proved some
more results by applying deductive reasoning. The statements
that were proved are called propositions or theorems.
Euclid deduced 465 propositions using his axioms, postulates,
definitions and theorems proved earlier in the chain.
There were 48 propositions in Book I, 14 in Book II, 37 in Book
III, 16 in Book IV, 25 in Book V, 33 in Book VI, 39 in Book VII,
27 in Book VIII, 36 in Book IX, 115 in Book X, 39 in Book XI,
18 in Book XII and 18 in Book XIII.