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Euclidean geometry

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

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Overview

The Elements

Notation and terminology

Some important or well known results

System of measurement and arithmetic

In engineering

Other general applications

Later history

As a description of the structure of space

Treatment of infinity

Logical basis

Classical theorems

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Map overview Semantic statistics

Euclidean geometry

Nodes280
Edges279
Triples155
Avg. degree1.99
Density0.007143
Components1

How this topic connects Entity context

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Euclidean geometry

Top relations

related to Axiomatic formulations · 19
Euclidean geometry → Alfred Tarski, Bertrand Russell, Birkhoff, Birkhoff's, Cambridge, Euclid's, Euclidean, George Pólya, Gödel's, Hilbert's, How, In, It, Solve It, Tarski, Tarski's, The, This, Trinity College
related to 20th century and relativity · 13
Euclidean geometry → Earth's, Einstein, Einstein's, Euclidean, For, GPS, However, Minkowski, Sun, Sun's, They, This, Until
has method · 10
Euclidean geometry → Euclid, Euclid's, Euclidean, Find, For, In, Postulates, Pythagorean, Strictly, Though
related to 18th century · 10
Euclidean geometry → By, Euclidean, For, Geometers, However, In, Leading, Many, Other, Pierre Wantzel
related to External links · 10
Euclidean geometry → EMS Press, Encyclopedia, Euclidean, Geometry Unbound Archived, GFDL, Kiran Kedlaya, Mathematics, PDF, Plane, Wayback Machine
related to CAD systems · 9
Euclidean geometry → CAD/CAM, CAM, Design, Euclidean, In CAD, Much, The, These, Today
measured by · 8
Euclidean geometry → Addition, Because, Euclid, Euclidean, For, IX, Measurements, The
related to Axioms · 8
Euclidean geometry → Elements, Euclid, Euclid's, Euclidean, However, Near, Thomas Heath, Until
related to Modern standards of rigor · 8
Euclidean geometry → Alessandro Padoa, Essai, Introduction, Padoa, Paris, Peano, Placing Euclidean, The
related to Electromagnetic and fluid flow fields · 7
Euclidean geometry → Antenna, Complex, Euclidean, Field, In, The, This

Important terminology Word statistics

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Important terminology

geometry euclidean axioms euclid angles two parallel postulate euclid's angle one line system elements lines proved design space theorems infinite

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Euclidean geometryis amathematical system attributed to Euclid0.90text
Euclidean geometryis aexample of synthetic geometry0.90text
Euclidean geometryis amodel0.90text
pointsinstance ofin that it proceeds logically from axioms describing basic properties of geometric objects0.80text
linesinstance ofin that it proceeds logically from axioms describing basic properties of geometric objects0.80text
to propositions about those objectsinstance ofin that it proceeds logically from axioms describing basic properties of geometric objects0.80text
prime numbersinstance ofNotions0.80text
rationalinstance ofNotions0.80text
irrational numbers are introducedinstance ofNotions0.80text
set theoryinstance ofEuclidean geometry is more concrete than many modern axiomatic systems0.80text
which often assert the existence of objects without saying how to construct theminstance ofEuclidean geometry is more concrete than many modern axiomatic systems0.80text
or even assert the existence of objects that cannot be constructed within the theoryinstance ofEuclidean geometry is more concrete than many modern axiomatic systems0.80text

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