How Long to Read The Elements of Non-Euclidean Geometry

How Long Does it Take to Read The Elements of Non-Euclidean Geometry?

It takes the average reader 4 hours and 38 minutes to read The Elements of Non-Euclidean Geometry by Julian Coolidge

Assuming a reading speed of 250 words per minute. Learn more

Description

The Elements of Non-Euclidean Geometryby Julian Lowell Coolidge Ph.D. - Harvard UniversityContents:CHAPTER IFOUNDATION FOR METRICAL GEOMETRY IN A LIMITED REGIONFundamental assumptions and definitionsSums and differences of distancesSerial arrangement of points on a lineSimple descriptive properties of plane and spaceCHAPTER IICONGRUENT TRANSFORMATIONSAxiom of continuityDivision of distances Measure of distanceAxiom of congruent transformations Definition of angles, their propertiesComparison of trianglesSide of a triangle not greater than sum of other twoComparison and measurement of anglesNature of the congruent groupDefinition of dihedral angles, their propertiesCHAPTER IIITHE THREE HYPOTHESESA variable angle is a continuous function of a variable distanceSaccheri's theorem for isosceles birectangular quadrilateralsThe existence of one rectangle implies the existence of an infinite numberThree assumptions as to the sum of the angles of a right triangleThree assumptions as to the sum of the angles of any triangle, their categorical natureDefinition of the euclidean, hyperbolic, and elliptic hypothesesGeometry in the infinitesimal domain obeys the euclidean hypothesisCHAPTER IVTHE INTRODUCTION OF TRIGONOMETRIC FORMULAELimit of ratio of opposite sides of diminishing isosceles quadrilateralContinuity of the resulting functionIts functional equation and solutionFunctional equation for the cosine of an angleNon-euclidean form for the pythagorean theoremTrigonometric formulae for right and oblique trianglesCHAPTER VANALYTIC FORMULAEDirected distancesGroup of translations of a linePositive and negative directed distancesCoordinates of a point on a lineCoordinates of a point in a planeFinite and infinitesimal distance formulae, the non-euclidean plane as a surface of constant Gaussian curvatureEquation connecting direction cosines of a lineCoordinates of a point in spaceCongruent transformations and orthogonal substitutionsFundamental formulae for distance and angleCHAPTER VICONSISTENCY AND SIGNIFICANCE OF THE AXIOMSExamples of geometries satisfying the assumptions madeRelative independence of the axiomsCHAPTER VIITHE GEOMETRIC AND ANALYTIC EXTENSION OF SPACEPossibility of extending a segment by a definite amount in the euclidean and hyperbolic casesEuclidean and hyperbolic spaceContradiction arising under the elliptic hypothesisNew assumptions identical with the old for limited region, but permitting the extension of every segment by a definite amountLast axiom, free mobility of the whole systemOne to one correspondence of point and coordinate set in euclidean and hyperbolic casesAmbiguity in the elliptic case giving rise to elliptic and spherical geometryIdeal elements, extension of all spaces to be real continuaImaginary elements geometrically defined, extension of all spaces to be perfectcontinua in the complex domainCayleyan Absolute, new form for the definition of distanceExtension of the distance concept to the complex domainCase where a straight line gives a maximum distanceCHAPTER VIIITHE GROUPS OF CONGRUENT TRANSFORMATIONSCongruent transformations of the straight line,, ,, ,, hyperbolic plane,, ,, ,, elliptic plane,, ,, ,, euclidean plane,, ,, ,, hyperbolic space,, ,, ,, elliptic and spherical spaceClifford parallels, or paratactic linesCHAPTER IXPOINT, LINE, AND PLANE TREATED ANALYTICALLYCHAPTER XTHE HIGHER LINE GEOMETRYCHAPTER XITHE CIRCLE AND THE SPHERECHAPTER XIICONIC SECTIONSCHAPTER XIIIQUADRIC SURFACESCHAPTER XIVAREAS AND VOLUMESVolume of a cone of revolution, a sphere, the whole of elliptic or of spherical spaceCHAPTER XVINTRODUCTION TO DIFFERENTIAL GEOMETRYCHAPTER XVIDIFFERENTIAL LINE-GEOMETRYCHAPTER XVIIMULTIPLY CONNECTED SPACESCHAPTER XVIIITHE PROJECTIVE BASIS OF NON-EUCLIDEAN GEOMETRYCHAPTER XIXTHE DIFFERENTIAL BASIS FOR EUCLIDEAN AND NON-EUCLIDEAN GEOMETRY

How long is The Elements of Non-Euclidean Geometry?

The Elements of Non-Euclidean Geometry by Julian Coolidge is 274 pages long, and a total of 69,596 words.

This makes it 92% the length of the average book. It also has 85% more words than the average book.

How Long Does it Take to Read The Elements of Non-Euclidean Geometry Aloud?

The average oral reading speed is 183 words per minute. This means it takes 6 hours and 20 minutes to read The Elements of Non-Euclidean Geometry aloud.

What Reading Level is The Elements of Non-Euclidean Geometry?

The Elements of Non-Euclidean Geometry is suitable for students ages 12 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy The Elements of Non-Euclidean Geometry?

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