history of geometry~day 1

Powerpoint Templates


HISTORY OF GEOMETRY:Proponents and Contributions


INTRODUCTIONINTRODUCTION“Geometry”

- derived from the Greek language:

“geo” (earth) “metre” (measure)

- means measurement of magnitude of space or planes like area, volume etc.

- Geometry combines simple conceptual building blocks to construct complex logical structures.


HISTORY HISTORY * The credit of building up geometry goes to Euclid, the great mathematician of 3rd Century B.C.


Ancient Egypt and BabyloniaAncient Egypt and Babylonia2000BC to 500BC 2000BC to 500BC

• Both the ancient Egyptians and Babylonians have works understanding geometry.

• They used these concepts for surveying, and building pyramids and other structures.

• The Rhind Papyrus and ancient Babylonian Clay Tablets have clear discussions on Pythagorean relationships (all well before Pythagoras was born!)


Rhind PapyrusRhind Papyrus


Geometry in Ancient Geometry in Ancient GreeceGreece

THALES OF MILETUS- a Greek who lived about 600 B.C.

- credited with several simple but important theorems, including the proof that an angle inscribed in a semicircle is a right angle.

- first to demonstrate the truth of a geometric relationship by showing that it followed in a logical , orderly fashion from a set of universally accepted statements, called postulates or axioms.

- teacher of the famous Pythagoras.



PYTHAGORAS- proved many theorems about triangles, circles, proportions and certain solids.

- his famous proof, a theorem that bears his name, states that the square of the longest side of a right triangle is equal to the sum of the squares of the other two sides.



EUCLID - Considered as the “Father of Geometry”

- brought the various unconnected postulates and theorems together into one system in his publication “Elements” (one of the greatest achievements of the human mind).

- most of the theorems he proved had been known for many years.

- he established the value of deductive method of reasoning.


Euclid’s ElementsEuclid’s Elements- Made up of 13 books, each supported by definitions,

propositions, axioms and postulates.

I. Fundamentals of GeometryII. Geometric Algebra (Analytic

Geometry)III. Theory of CirclesIV. Inscribing and Circumscribing

PolygonsV. Ratio and ProportionVI. Similar PolygonsVII.Introduction to Number TheoryVIII. Continuation of Number TheoryIX. Continuation of Number TheoryX. Irrationals (Incommensurables)XI. Solid GeometryXII.Measurement of SolidsXIII.Construction of Regular Solids



APOLLONIUS OF PERGA- Post-Eucledian Mathematician

- a Greek Mathematician who studied the family of curves know as conic sections and discovered many of their fundamental properties about 300 B.C.



ARCHIMEDES- one of the greatest scientists who made a number of contributions to geometry during the 3rd Century B.C.

- he devised ways to measure the areas of a number of curved figures and the surface areas and volumes of solids bounded by curved surfaces, such as cylinders.


Geometry during the Geometry during the Middle AgesMiddle Ages

Geometry , like most other sciences, advanced little from the fall of the Roman Empire in the 5th century AD to the end of the Middle Ages in the 15th century.

After the fall of the Greek and Roman civilizations, Europe entered the Dark Ages. Advances in Geometry were made largely by Muslims in the Middle East and North Africa and Hindus in India. Most of the works of the Greeks were scattered or lost.


RENE DESCARTES- he published the influential treatise Discourse on Method in 1637. - introduced a method of representing geometric figures within a coordinate system. - his works forged a link between geometry and algebra by showing how to apply the methods of one discipline to the other.

1717thth and 18 and 18thth Century Century GeometryGeometry


GERARD DESARGUES- Known upon the discovery

of Projective Geometry.

PROJECTIVE GEOMETRYPROJECTIVE GEOMETRY*the study of how projections are

relate became the motivating question for a new field of Mathematics.

FUNDAMENTAL QUESTION:FUNDAMENTAL QUESTION:If an object is viewed from two

different locations , then the screen images will be different.



GASPARD MONGE- Known upon the discovery

of a new branch of Geometry known as Descriptive Geometry.

(allows the representation of three-dimensional objects in two dimensions, by using a specific set of procedures.)

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Modern GeometryModern Geometry- Non-Euclidean Geometries were developed by Carl

Friedrich Gauss, Janos Bolyai, Nikolai I. Lobachevsky, and George Friedrich Bernhard Riemann.

- In 1872 German mathematician Felix Klein used a relatively new branch of mathematics called group theory.

- In 1916 the theory of relativity gave impetus to studies in differential geometry and topology.

- Another dimensional concept, that of fractional dimensions, also arose in the 19th century. In the 1970s this concept this concept was developed into a new field of geometry known as fractal geometry.


JANOS BOLYAI

Modern GeometryModern Geometry

- Discovered and first to write about non-Euclidian Geometry in 1820 published in 1823.


NIKOLAI LOBACHEVSKY


- Along with Bolyai, he also discovered Non-Euclidean Geometry known as hyperbolic geometry


BERNHARD REIMANN


- Also discovered another branch of geometry and still in line with the Non Euclidean Geometry known as Elliptic Geometry


Euclidean VS. Non-Euclidean VS. Non-EuclidianEuclidianEUCLIDEAN for any given line and point

not on the line, there is one parallel line through the point not intersecting the line.

HYPERBOLIC for any given point there exists more than one line that can be extended through that point and run parallel to another line of which that point is not part

ELLIPTIC for any given line and point not on the line, there NO parallel line through the point not intersecting the line.


FELIX KLEIN


- He classified Euclidean and non-Euclidean Geometry.

history of geometry~day 1

Documents

3rd century

powerpoint

rhind papyrus

euclidean

parallel line

number

theory

geometry