標(biāo)題: Titlebook: Euclidean Geometry and its Subgeometries; Edward John Specht,Harold Trainer Jones,Donald H. Book 2015 Springer International Publishing S [打印本頁(yè)] 作者: Jurisdiction 時(shí)間: 2025-3-21 19:34
書(shū)目名稱(chēng)Euclidean Geometry and its Subgeometries影響因子(影響力)
書(shū)目名稱(chēng)Euclidean Geometry and its Subgeometries影響因子(影響力)學(xué)科排名
書(shū)目名稱(chēng)Euclidean Geometry and its Subgeometries網(wǎng)絡(luò)公開(kāi)度
書(shū)目名稱(chēng)Euclidean Geometry and its Subgeometries網(wǎng)絡(luò)公開(kāi)度學(xué)科排名
書(shū)目名稱(chēng)Euclidean Geometry and its Subgeometries被引頻次
書(shū)目名稱(chēng)Euclidean Geometry and its Subgeometries被引頻次學(xué)科排名
書(shū)目名稱(chēng)Euclidean Geometry and its Subgeometries年度引用
書(shū)目名稱(chēng)Euclidean Geometry and its Subgeometries年度引用學(xué)科排名
書(shū)目名稱(chēng)Euclidean Geometry and its Subgeometries讀者反饋
書(shū)目名稱(chēng)Euclidean Geometry and its Subgeometries讀者反饋學(xué)科排名
作者: antiandrogen 時(shí)間: 2025-3-21 20:28 作者: frivolous 時(shí)間: 2025-3-22 01:38
Ordering a Line in a Pasch Plane (ORD),pper bound, and lower bound of a subset of an ordered line are developed, as well as the connections between order, segments, and rays. Ordering will assume great importance in later chapters which develop the correspondence between a line and the set of all rational (or real) numbers.作者: emulsify 時(shí)間: 2025-3-22 07:36
Neutral Geometry (NEUT),s. Every line is an axis for some reflection. A line of symmetry for a set is a line whose reflection maps that set onto itself. Every angle has a line of symmetry, its angle bisector. Compositions of reflections are isometries, and isometric sets are congruent. These concepts provide access to the 作者: 高深莫測(cè) 時(shí)間: 2025-3-22 11:31
Free Segments of a Neutral Plane (FSEG),ve the trichotomy property. Addition of free segments is defined, and its elementary properties and interactions with ordering are studied. These developments are sufficient to prove the triangle inequality, and provide a first step toward defining distance on a neutral plane.作者: Optic-Disk 時(shí)間: 2025-3-22 16:19
Euclidean Geometry Basics (EUC),xiom to arrive at Euclidean geometry. It explores many well-known elementary results from plane geometry involving parallel lines, perpendicularity, adjacent and complementary angles, parallelograms and rectangles.作者: Optic-Disk 時(shí)間: 2025-3-22 20:29 作者: Notify 時(shí)間: 2025-3-22 23:41 作者: Expressly 時(shí)間: 2025-3-23 02:31
Similarity on a Euclidean Plane (SIM),gs are used to define the similarity of two sets. Similarity is shown to be an equivalence relation, and criteria are developed for similarity of triangles. The chapter concludes with a proof of the Pythagorean Theorem, and a proof that the product of the base and altitude of a triangle is constant.作者: LAST 時(shí)間: 2025-3-23 07:41
Rational Points on a Line (QX), a rational multiple of a point on this line, develops the arithmetical properties of such multiples, and uses these to show the existence of an order-preserving isomorphism between the set of all rational numbers and a subset of the line.作者: mucous-membrane 時(shí)間: 2025-3-23 18:42
exercises; solutions to many of these, including all that are needed for this development, are available online at the homepage for the book at www.springer.com. Supplementary material is available online cover978-3-319-79533-1978-3-319-23775-6作者: 不知疲倦 時(shí)間: 2025-3-24 00:05 作者: Density 時(shí)間: 2025-3-24 05:46
https://doi.org/10.1007/978-3-642-69250-5trices and determinants are given; there is also discussion of the roles of axioms, theorems, and definitions in a mathematical theory. The main development of the book begins here with the statement of eight incidence axioms and proof of a few theorems including one from Desargues.作者: syncope 時(shí)間: 2025-3-24 06:55 作者: 有角 時(shí)間: 2025-3-24 14:31
Book 2015ailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors p作者: 打谷工具 時(shí)間: 2025-3-24 14:57
Devotion to St. Anne in Texts and Imagesexistence of a line (not necessarily unique) through a given point parallel to a given line. Ordering of angles is defined, leading to the notions of acute angle, obtuse angle, and maximal angle of a triangle.作者: 胰島素 時(shí)間: 2025-3-24 21:38 作者: hardheaded 時(shí)間: 2025-3-25 01:24 作者: meretricious 時(shí)間: 2025-3-25 07:11
Dilations of a Euclidean Plane (DLN),in an intricate process; these, in turn, are used to define dilations, which are shown to be belineations. A method is provided for point-wise construction of a dilation having a given action. A classical proposition attributed to Pappus of Alexandria is proved.作者: LIKEN 時(shí)間: 2025-3-25 07:37
Edward John Specht,Harold Trainer Jones,Donald H. Provides a complete and rigorous axiomatic treatment of Euclidean geometry..Proofs for many theorems are worked out in detail..Takes a modern approach by replacing congruence axioms with a transformat作者: 嫌惡 時(shí)間: 2025-3-25 15:04
http://image.papertrans.cn/e/image/316423.jpg作者: CRAB 時(shí)間: 2025-3-25 19:08 作者: 寬容 時(shí)間: 2025-3-25 21:23
https://doi.org/10.1057/9781137436719s of segments, rays, and lines that are needed for a coherent geometry. The remainder of the chapter is a study of the basic interactions between lines, angles, triangles, and quadrilaterals, comprising Pasch geometry.作者: 暫時(shí)別動(dòng) 時(shí)間: 2025-3-26 01:40
Bernard Burrows,Geoffrey Dentonpper bound, and lower bound of a subset of an ordered line are developed, as well as the connections between order, segments, and rays. Ordering will assume great importance in later chapters which develop the correspondence between a line and the set of all rational (or real) numbers.作者: 觀點(diǎn) 時(shí)間: 2025-3-26 05:42 作者: aptitude 時(shí)間: 2025-3-26 09:27 作者: Protein 時(shí)間: 2025-3-26 12:57
Mead on the Self and Moral Situations,e multiplication on such a line; when equipped with these operations, the line becomes a field (defined in Chapter 1 Section 1.5). An ordering of the line is defined, so that the line becomes an ordered field. These concepts are used to define distance between points, and the length of a segment.作者: amputation 時(shí)間: 2025-3-26 19:56 作者: Fraudulent 時(shí)間: 2025-3-27 00:35 作者: Cabg318 時(shí)間: 2025-3-27 03:17 作者: 甜得發(fā)膩 時(shí)間: 2025-3-27 09:01
Pasch Geometry (PSH),s of segments, rays, and lines that are needed for a coherent geometry. The remainder of the chapter is a study of the basic interactions between lines, angles, triangles, and quadrilaterals, comprising Pasch geometry.作者: 有特色 時(shí)間: 2025-3-27 13:11 作者: metropolitan 時(shí)間: 2025-3-27 16:55
Free Segments of a Neutral Plane (FSEG),ve the trichotomy property. Addition of free segments is defined, and its elementary properties and interactions with ordering are studied. These developments are sufficient to prove the triangle inequality, and provide a first step toward defining distance on a neutral plane.作者: tympanometry 時(shí)間: 2025-3-27 19:05
Euclidean Geometry Basics (EUC),xiom to arrive at Euclidean geometry. It explores many well-known elementary results from plane geometry involving parallel lines, perpendicularity, adjacent and complementary angles, parallelograms and rectangles.作者: Interregnum 時(shí)間: 2025-3-28 00:18 作者: 壟斷 時(shí)間: 2025-3-28 02:52
Similarity on a Euclidean Plane (SIM),gs are used to define the similarity of two sets. Similarity is shown to be an equivalence relation, and criteria are developed for similarity of triangles. The chapter concludes with a proof of the Pythagorean Theorem, and a proof that the product of the base and altitude of a triangle is constant.作者: flavonoids 時(shí)間: 2025-3-28 06:35
Rational Points on a Line (QX), a rational multiple of a point on this line, develops the arithmetical properties of such multiples, and uses these to show the existence of an order-preserving isomorphism between the set of all rational numbers and a subset of the line.作者: Commodious 時(shí)間: 2025-3-28 14:26
A Line as Real Numbers (REAL); Coordinatization of a Plane (RR),uclidean/LUB plane (which has been built into an ordered field) real multiples of points are defined and their algebraic properties derived. These properties are used to show the existence of an order-preserving isomorphism between the set of all real numbers and the whole line. The chapter ends with coordinatization of a Euclidean/LUB plane.作者: amenity 時(shí)間: 2025-3-28 15:38
https://doi.org/10.1007/978-3-319-23775-6Betweenness; Euclidean geometry; Euclidean plane; Geometric axioms; Incidence; Least Upper Bound作者: 遺忘 時(shí)間: 2025-3-28 20:26 作者: 四目在模仿 時(shí)間: 2025-3-29 00:32
https://doi.org/10.1057/9781137436719s of segments, rays, and lines that are needed for a coherent geometry. The remainder of the chapter is a study of the basic interactions between lines, angles, triangles, and quadrilaterals, comprising Pasch geometry.作者: 怕失去錢(qián) 時(shí)間: 2025-3-29 03:57 作者: Pantry 時(shí)間: 2025-3-29 08:01
Devotion to St. Anne in Texts and Imagess. Every line is an axis for some reflection. A line of symmetry for a set is a line whose reflection maps that set onto itself. Every angle has a line of symmetry, its angle bisector. Compositions of reflections are isometries, and isometric sets are congruent. These concepts provide access to the 作者: LANCE 時(shí)間: 2025-3-29 14:26 作者: Mumble 時(shí)間: 2025-3-29 18:44 作者: nitric-oxide 時(shí)間: 2025-3-29 22:31 作者: 熄滅 時(shí)間: 2025-3-30 00:30 作者: 收藏品 時(shí)間: 2025-3-30 04:56 作者: 繞著哥哥問(wèn) 時(shí)間: 2025-3-30 08:39 作者: 你敢命令 時(shí)間: 2025-3-30 12:38
https://doi.org/10.1007/978-3-642-69952-8uclidean/LUB plane (which has been built into an ordered field) real multiples of points are defined and their algebraic properties derived. These properties are used to show the existence of an order-preserving isomorphism between the set of all real numbers and the whole line. The chapter ends wit作者: rheumatology 時(shí)間: 2025-3-30 18:27 作者: HEW 時(shí)間: 2025-3-30 20:57 作者: 尾巴 時(shí)間: 2025-3-31 02:12 作者: 灰姑娘 時(shí)間: 2025-3-31 08:44
SpringerBriefs in Earth SciencesA belineation is a bijection of a plane that preserves betweenness. This chapter shows that every belineation on a Pasch plane is a collineation, and explores the interactions between belineations and segments, rays, lines, sides of a line, angles, and triangles.作者: 名字的誤用 時(shí)間: 2025-3-31 11:28
Basics of Learning Devotional Hindu Dance,This chapter defines point rotations and point reflections (about a point .) on a neutral plane, and derives their elementary properties to the extent possible without a parallel axiom. It ends with a classification of isometries of a neutral plane, and proof of the existence of a “square root” of a rotation.作者: FLIRT 時(shí)間: 2025-3-31 15:22 作者: Obedient 時(shí)間: 2025-3-31 19:24 作者: 淘氣 時(shí)間: 2025-4-1 01:17
,Schlussbetrachtung – Resümee und Ausblick,This brief chapter shows that on a Euclidean/LUB plane, any non-identity belineation which has more than one fixed point and is not the identity, is an axial affinity; it concludes with a classification of belineations. To prove the main result of this chapter we need Axiom LUB; this explains its placement after the chapter on real numbers.作者: ADOPT 時(shí)間: 2025-4-1 03:00 作者: Ringworm 時(shí)間: 2025-4-1 07:44
Collineations of an Affine Plane (CAP),Collineations are bijections of a plane onto itself which map lines to lines; this chapter explores the elementary properties of collineations on an incidence plane on which the parallel axiom holds. Several types of collineations are studied, among them translations, dilations, and axial affinities.作者: larder 時(shí)間: 2025-4-1 11:29 作者: CHOIR 時(shí)間: 2025-4-1 18:14 作者: Dappled 時(shí)間: 2025-4-1 18:38
Rotations About a Point of a Neutral Plane (ROT),This chapter defines point rotations and point reflections (about a point .) on a neutral plane, and derives their elementary properties to the extent possible without a parallel axiom. It ends with a classification of isometries of a neutral plane, and proof of the existence of a “square root” of a rotation.作者: ENNUI 時(shí)間: 2025-4-2 00:36 作者: GEAR 時(shí)間: 2025-4-2 03:35 作者: 會(huì)議 時(shí)間: 2025-4-2 10:15
Belineations on a Euclidean/LUB Plane (AA),This brief chapter shows that on a Euclidean/LUB plane, any non-identity belineation which has more than one fixed point and is not the identity, is an axial affinity; it concludes with a classification of belineations. To prove the main result of this chapter we need Axiom LUB; this explains its placement after the chapter on real numbers.
