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.
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.
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.
Euclid's Elements was considered as the foundation of Mathematics till the end of 19th century. Is there a connection with his period and Alexander the Great's eastward battles ? Is there any possibility that the origin of his thought and the principles itself was from the Indian subcontinent ?
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.
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.
Euclid's Elements was considered as the foundation of Mathematics till the end of 19th century. Is there a connection with his period and Alexander the Great's eastward battles ? Is there any possibility that the origin of his thought and the principles itself was from the Indian subcontinent ?
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..
Pythagoras was a Greek mathematician who contributed much to the mathematical world, mainly because of Pythagorean Theorem. The following PPT contains all the necessary information about Pythagoras's early and later life, as well as about his works and explanations.(If you find the fonts a little weird, its not my fault as Slideshare doesn't supports many fonts)
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..
Pythagoras was a Greek mathematician who contributed much to the mathematical world, mainly because of Pythagorean Theorem. The following PPT contains all the necessary information about Pythagoras's early and later life, as well as about his works and explanations.(If you find the fonts a little weird, its not my fault as Slideshare doesn't supports many fonts)
A String Sculpture Illustrating Fermat's Little TheoremJames Smith
Please see also, the video https://www.youtube.com/watch?v=4lyhoAMnAc0. Fermat's Little Theorem states that if p is any prime number, and a is any integer, then a^p is congruent to a, modulus p. This document shows how to construct a string sculpture that illustrates that relationship for p=13.
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.
Is Space Exploration Worth the Money (in 3d)Rahul Jaiswal
The ppt is actually in 3D so put on your 3D (red and cyan) glasses to watch it properly.
The images may seem to have copyright problem so dont claim it yours.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
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Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
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.
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Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Biological screening of herbal drugs: Introduction and Need for
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Introduction to AI for Nonprofits with Tapp NetworkTechSoup
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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!
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.
2. Eclids Work in the field
Eclids Work in the field of
of Mathematics
Mathematics
Euclid was, also known as Euclid of
Alexandria, was a Greek
mathematician, often referred to as the
"Father of Geometry". His Elements is
one of the most influential works in the
history of mathematics, serving as the
main textbook for teaching
mathematics (especially geometry). 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. Euclid's Geometry
● The word 'geometry' is derived from the greek
word 'geo' meaning 'Earth' and 'metron'
meaning 'measuring'. Thus, the word geometry
means 'earth measurement'.
● Euclid was the first mathematician who initiated
a new way of thinking the study of geometry
results by deductive reasoning based upon
previously proved results and some self-evident
specific assumptions called axioms.
AXIOMS : The basic fact which are taken for
granted, without proofs, are called axioms.
4. EUCLID's Definations
In the first Book of Elements, Euclid gave 23
definations and some of them are as follows :-
● A piont is that which has no part. .
● A line is breadthless lenght.
● The ends of a lina are points.
● A staight line is a line whick lies evenly with
the points on itself.
● A surface is that which has lenght and breadth
only.
● The edges of a surface are lines.
5. EUCLID's Axioms and
Postulates
Euclid assumed certain properties, which were
not be proved. These are actually 'obvious
universal truths'. He divided them into two types:
axioms and postulates
Postulates Axioms
● Postulates are universal
truths with out any proofs.
● Postulates are
assumptions used
specifically used for
geometry.
● Axioms are universal
thruths without any
proofs.
● Axioms are assumptions
used throughout
mathematics and not
specifically geometry.
6. Some Axioms and Postulates of
Euclid
Axioms
● Things which are equal
to the same things are
equal to one another.
● If equals are added to
equals, the wholes are
equal.
● The whole is greater
than a part.
● Things which are half of
the same things are
equal
Postulates
● A straight line may be
drawn from any one
point to any other point.
● A terminated line can be
produced indefinitely.
● A circle can be drawn
with any centre and any
radius.
● All right angles are equal
to one another
7. Euclid's Division Lemma
Theorem :If there two positive integers a and b,
there exist unique ineger q and r satisfying
a = bq + r
0 < r < b.
Trough this lemma the formation of the
fundamental theorem of arithematic took place
and Euclid's division algorithm is based on this
lemma.
8. Euclid's division lemma
Euclid's division lemma are used to obtain
the HCF of two positive integer, say c and d,
with c > d, follow the steps below:-
● Step 1: Apply Euclid's division lemma, to c
and d. So we find whole numbers, q and r
such that c = dq + r, 0 < r< d.
● Step 2: If r = 0, dis the HCF of c and d. If r is
not equal to 0, apply the division lemma to d
and r
● Step 3: Continue the process till the
remainder is zero. The divisor at this stage
will be the required HCF.
Euclid's division algorithm is also use full to
find the number of tiles and the dimention to
fill a space as shown in the animation.
10. Euclid's work on Data
The Data is closely related to the first
four books of the Elements. It opens
with definitions of the different senses
in which things are said to be ``given.''
Thus lines, angles, and ratios may be
given in magnitude, rectilinear figures
may be given in species or given in
form, points and lines may be given in
position,etc.
11. Euclid's work on Catoptrics
Catoptrics, which
concerns the
mathematical theory of
mirrors, particularly the
images formed in plane
and spherical concave
mirrors. The attribution
is held to be
anachronistic however
by J J O'Connor and E
F Robertson who name
Theon of Alexandria as
a more likely author.
12. Euclid's work on Phaenomena
Phaenomena, a treatise on
spherical astronomy,
survives in Greek; it is quite
similar to On the Moving
Sphere by Autolycus of
Pitane, who flourished
around 310 BC.
13. Euclid' work on Optics
Optics is the earliest surviving
Greek treatise on perspective. In
its definitions Euclid follows the
Platonic tradition that vision is
caused by discrete rays which
emanate from the eye. One
important definition is the fourth:
"Things seen under a greater
angle appear greater, and those
under a lesser angle less, while
those under equal angles
appear equal
14. Euclid's Elements
● The Euclid's Elements is a collection of 13
books. Each book contains a sequence of
propositions or theorems, around 10 to 100,
introduced with proper definitions. For
instance in Book I, 23 definitions are followed
by five postulates, after which five common
notions or axioms are included.
● These Elements are dividedinto 13 books in
which
1-6 are of plane geometry
7-9 are of number theory
10 is the theory of irrational numbers
11-13 are of 3-D geometry