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A Dynamic Setup for Elementary Geometry
 PROCEEDINGS OF MTCM 2000, MULTIMEDIA TOOLS FOR COMMUNICATING MATHEMATICS
, 2002
"... In this article we survey the theoretical background that is required to build a consistent and continuous setup of dynamic elementary geometry. Unlike in ..."
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In this article we survey the theoretical background that is required to build a consistent and continuous setup of dynamic elementary geometry. Unlike in
SOME PROBLEMS ON ELEMENTARY GEOMETRY
"... Elementary geometry occupied mathematicians for thousands of years. Nevertheless it is rather easy to find new and, in my opinion, interesting and probably difficult unsolved problems if one asks problems where metrical and combinatorial questions are considered. Let x 1, x2, x 3 be three points in ..."
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Elementary geometry occupied mathematicians for thousands of years. Nevertheless it is rather easy to find new and, in my opinion, interesting and probably difficult unsolved problems if one asks problems where metrical and combinatorial questions are considered. Let x 1, x2, x 3 be three points
Mechanical formula derivation of elementary geometries
 PROC. INTL. SYMP. ON SYMBOLIC AND ALGEBRAIC COMPUTATION (ISSAC
, 1990
"... A precise formulation for the relations among certain variables under a set of polynomial equations and a set of polynomial inequations (to exclude certain special cases which cannot be excluded by the selection of parameters alone) is given. Several methods are presented to find such relations. The ..."
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Cited by 2 (1 self)
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. The methods have been implemented and used to find geometry formulas, to discover geometry theorems, and to find geometry locus equations. About 120 nontrivial problems have been solved using the methods.
• A Hisory of the Teaching of Elementary Geometry
, 1906
"... r#v=onepage&q=&f=false Stamper's doctoral thesis for Columbia University, a history of geometry education before Euclid until 1906, focuses primarily on European and American educational practices. He divides his work using three historical dividers: Euclid, the rise of the Christian sc ..."
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r#v=onepage&q=&f=false Stamper's doctoral thesis for Columbia University, a history of geometry education before Euclid until 1906, focuses primarily on European and American educational practices. He divides his work using three historical dividers: Euclid, the rise of the Christian
Symposium on the Axiomatic Method WHAT IS ELEMENTARY GEOMETRY?
"... In colloquial language the term elementary geometry is used loosely to refer to the body of notions and theorems which, following the tradition of Euclid's Elements, form the subject matter of geometry courses in secondary schools. Thus the term has no well determined meaning and can be subject ..."
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In colloquial language the term elementary geometry is used loosely to refer to the body of notions and theorems which, following the tradition of Euclid's Elements, form the subject matter of geometry courses in secondary schools. Thus the term has no well determined meaning and can
ELEMENTARY GEOMETRY SPLIT INTO DIFFERENT GEOMETRICAL PARADIGMS
"... Since several years, we have developed a scientific investigation on the teaching of Geometry, especially for preservice teachers. This research is based on a specific theoretical frame. We have chosen to give some elements of our frame and we hope to present more consistent examples of our empiric ..."
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empirical studies during the working group. For us elementary geometry appears to be split into three various paradigms: natural geometry (Geometry I), natural axiomatic geometry (Geometry II) and formalist axiomatic geometry (Geometry III). We confront our approach with the approach of van Hiele, which
Fast probabilistic algorithms for verification of polynomial identities
 J. ACM
, 1980
"... ABSTRACT The starthng success of the RabmStrassenSolovay pnmahty algorithm, together with the intriguing foundattonal posstbthty that axtoms of randomness may constttute a useful fundamental source of mathemaucal truth independent of the standard axmmaUc structure of mathemaUcs, suggests a wgorous ..."
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Cited by 520 (1 self)
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and Sturm sequences are given. Probabilistlc calculatton in real anthmetlc, prewously considered by Davis, is justified ngorously, but only in a special case. Theorems of elementary geometry can be proved much more efficiently by the techmques presented than by any known arttficmlmtelhgence approach
Touch Tiles: Elementary Geometry Software with a
, 2003
"... The purpose of this paper is to report on the progress of a study that is currently underway. The goal of the Touch Tiles project is to create a multimodal interface for a geometry software program that can be used by children with visual impairment. The interface employs both haptic (tactile and ..."
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The purpose of this paper is to report on the progress of a study that is currently underway. The goal of the Touch Tiles project is to create a multimodal interface for a geometry software program that can be used by children with visual impairment. The interface employs both haptic (tactile
Nine solved and nine open problems in elementary geometry
"... In this paper we review nine previous proposed and solved problems of elementary 2D geometry [4] and [6], and we extend them either from triangles to polygons or polyhedrons,or from circles to spheres (from 2Dspace to 3Dspace), and make some comments about them. Problem 1. We draw the projections ..."
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In this paper we review nine previous proposed and solved problems of elementary 2D geometry [4] and [6], and we extend them either from triangles to polygons or polyhedrons,or from circles to spheres (from 2Dspace to 3Dspace), and make some comments about them. Problem 1. We draw the projections
Results 1  10
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952