標(biāo)題: Titlebook: Geometry; A Metric Approach wi Richard S. Millman,George D. Parker Textbook 19811st edition Springer-Verlag Inc. 1981 Cartesian.Euclid.Geom [打印本頁] 作者: VERSE 時(shí)間: 2025-3-21 16:51
書目名稱Geometry影響因子(影響力)
書目名稱Geometry影響因子(影響力)學(xué)科排名
書目名稱Geometry網(wǎng)絡(luò)公開度
書目名稱Geometry網(wǎng)絡(luò)公開度學(xué)科排名
書目名稱Geometry被引頻次
書目名稱Geometry被引頻次學(xué)科排名
書目名稱Geometry年度引用
書目名稱Geometry年度引用學(xué)科排名
書目名稱Geometry讀者反饋
書目名稱Geometry讀者反饋學(xué)科排名
作者: Adornment 時(shí)間: 2025-3-21 23:30
Plane Separation,Plane and the Hyperbolic Plane, do satisfy this new axiom. In the third section we shall prove Pasch’s Theorem, which gives an alternative formulation of the plane separation axiom in terms of triangles. This means that Pasch’s Theorem follows from the plane separation axiom and the plane separation axiom follows from assuming Pasch’s Theorem.作者: 鄙視 時(shí)間: 2025-3-22 03:07
0172-6056 ugh use of real numbers) rather than Hilbert‘s synthetic approach to the subject. Throughout the text we illustrate the various axioms, definitions, and theorems with models ranging from the familiar Cartesian plane to the Poincare upper half plane, the Taxicab plane, and the Moulton plane. We hope 作者: Lymphocyte 時(shí)間: 2025-3-22 07:16
https://doi.org/10.1007/978-3-663-07180-8 the hyperbolic results. In the second section we will be concerned with the theory of similar triangles and proportion. The third section will cover certain classical results of Euclidean geometry, including the Euler Line, the Nine Point Circle, and Morley’s Theorem.作者: Audiometry 時(shí)間: 2025-3-22 09:59 作者: predict 時(shí)間: 2025-3-22 14:42
https://doi.org/10.1007/978-3-663-07177-8erent in any geometric sense. Furthermore, as we develop additional axioms to verify we will need a more tractable notation. For these reasons we introduce an alternative description of the Euclidean Plane, one that is motivated by ideas from linear algebra, especially the notion of a vector.作者: predict 時(shí)間: 2025-3-22 18:38
https://doi.org/10.1007/978-3-663-04786-5 measures are defined in our two basic models. In the second section we shall develop a new model with some very interesting properties. In the third section, some of the basic results associated with angle measure are discussed. The last section is devoted to the technical details of verifying the existence of angle measure on ?. and ?.作者: Tdd526 時(shí)間: 2025-3-22 23:27 作者: 記憶法 時(shí)間: 2025-3-23 05:25 作者: stress-test 時(shí)間: 2025-3-23 06:33 作者: BACLE 時(shí)間: 2025-3-23 11:44 作者: sleep-spindles 時(shí)間: 2025-3-23 15:14
Area,nd hyperbolic geometries respectively. In the last section we will consider a beautiful theorem due to J. Bolyai which says that if two polygonal regions have the same area then one may be cut into a finite number of pieces and rearranged to form the other.作者: 夸張 時(shí)間: 2025-3-23 20:08
Textbook 19811st edition is to introduce and develop the various axioms slowly, and then, in a departure from other texts, illustrate major definitions and axioms with two or three models. This has the twin advantages of showing the richness of the concept being discussed and of enabling the reader to picture the idea more作者: CLASH 時(shí)間: 2025-3-24 01:49 作者: 品嘗你的人 時(shí)間: 2025-3-24 03:23
https://doi.org/10.1007/978-3-663-04785-8h other by a collection of ., or first principles. For example, when we discuss incidence geometry below, we shall assume as a first principle that if . and . are distinct points then there is a unique line that contains both . and ..作者: 女歌星 時(shí)間: 2025-3-24 08:17
https://doi.org/10.1007/978-3-663-07176-1 satisfied. After the definitions are made, we will give a number of examples which will serve as models for these geometries. Two of these models, the Euclidean Plane and the Hyperbolic Plane, will be used throughout the rest of the book.作者: institute 時(shí)間: 2025-3-24 13:07
https://doi.org/10.1007/978-3-663-07177-8 the most intuitive method and led to simple verification of the incidence axioms. However, treating vertical and non-vertical lines separately does have its drawbacks. By making it necessary to break proofs into two cases, it leads to an artificial distinction between lines that really are not diff作者: calorie 時(shí)間: 2025-3-24 15:40
Herwart Opitz,Wilfried K?nig,Manfred Schütteght expect it to be a consequence of our present axiom system. However, as we shall see in Section 4.3, there are models of a metric geometry that do not satisfy this new axiom. Thus the plane separation axiom does not follow from the axioms of a metric geometry, and it is therefore necessary to add作者: Climate 時(shí)間: 2025-3-24 21:38 作者: penance 時(shí)間: 2025-3-25 00:18 作者: Antioxidant 時(shí)間: 2025-3-25 05:23
https://doi.org/10.1007/978-3-663-07179-2ned two segments to be parallel if no matter how far they are extended in both directions, they never meet. Note that he was interested in . rather than .. This follows the general preference of the time for finite objects. The idea of . meeting is, however, infinite in nature. How then does one det作者: AGOG 時(shí)間: 2025-3-25 07:37 作者: Grasping 時(shí)間: 2025-3-25 12:44 作者: PHON 時(shí)間: 2025-3-25 15:57
,Versuchsprogramm und Versuchsdurchführung, investigation of the properties of a Euclidean area function. In Sections 10.2 and 10.3 we will prove the existence of area functions for Euclidean and hyperbolic geometries respectively. In the last section we will consider a beautiful theorem due to J. Bolyai which says that if two polygonal regi作者: 脫落 時(shí)間: 2025-3-25 20:36 作者: 六邊形 時(shí)間: 2025-3-26 01:55 作者: Conduit 時(shí)間: 2025-3-26 06:41
978-1-4684-0132-5Springer-Verlag Inc. 1981作者: 懶惰人民 時(shí)間: 2025-3-26 10:23
Geometry978-1-4684-0130-1Series ISSN 0172-6056 Series E-ISSN 2197-5604 作者: chuckle 時(shí)間: 2025-3-26 12:39
https://doi.org/10.1007/978-3-663-04785-8h other by a collection of ., or first principles. For example, when we discuss incidence geometry below, we shall assume as a first principle that if . and . are distinct points then there is a unique line that contains both . and ..作者: Calculus 時(shí)間: 2025-3-26 19:26
https://doi.org/10.1007/978-3-663-07176-1 satisfied. After the definitions are made, we will give a number of examples which will serve as models for these geometries. Two of these models, the Euclidean Plane and the Hyperbolic Plane, will be used throughout the rest of the book.作者: cunning 時(shí)間: 2025-3-27 00:56 作者: Seminar 時(shí)間: 2025-3-27 02:09
https://doi.org/10.1007/978-3-663-07179-2ned two segments to be parallel if no matter how far they are extended in both directions, they never meet. Note that he was interested in . rather than .. This follows the general preference of the time for finite objects. The idea of . meeting is, however, infinite in nature. How then does one determine if two lines are parallel?作者: 暴露他抗議 時(shí)間: 2025-3-27 05:26
Diskussion der Versuchsergebnisse, We shall be interested in, among other things, the sum of the measures of the angles of a triangle, in the behavior of the critical function, in classifying types of parallel Unes, and in the determination of an absolute unit of length.作者: Arrhythmia 時(shí)間: 2025-3-27 10:37
https://doi.org/10.1007/978-3-663-07183-9 object to another. Such functions are most interesting when they preserve special properties of the objects. If . = {.,?,.} and .′ = {.′,?′,.} are metric geometries and if ?:.→.′; is a function, what geometric properties could we reasonably require ? to have?作者: 劇毒 時(shí)間: 2025-3-27 17:15 作者: 走路左晃右晃 時(shí)間: 2025-3-27 19:00 作者: Commonwealth 時(shí)間: 2025-3-28 01:13 作者: Range-Of-Motion 時(shí)間: 2025-3-28 02:21
The Theory of Parallels,ned two segments to be parallel if no matter how far they are extended in both directions, they never meet. Note that he was interested in . rather than .. This follows the general preference of the time for finite objects. The idea of . meeting is, however, infinite in nature. How then does one determine if two lines are parallel?作者: 商議 時(shí)間: 2025-3-28 09:55 作者: FIR 時(shí)間: 2025-3-28 12:29
The Theory of Isometries, object to another. Such functions are most interesting when they preserve special properties of the objects. If . = {.,?,.} and .′ = {.′,?′,.} are metric geometries and if ?:.→.′; is a function, what geometric properties could we reasonably require ? to have?作者: 館長 時(shí)間: 2025-3-28 14:40
Preliminary Notions,h other by a collection of ., or first principles. For example, when we discuss incidence geometry below, we shall assume as a first principle that if . and . are distinct points then there is a unique line that contains both . and ..作者: 豐滿中國 時(shí)間: 2025-3-28 21:39
Incidence and Metric Geometry, satisfied. After the definitions are made, we will give a number of examples which will serve as models for these geometries. Two of these models, the Euclidean Plane and the Hyperbolic Plane, will be used throughout the rest of the book.作者: Innovative 時(shí)間: 2025-3-29 02:20
Betweenness and Elementary Figures, the most intuitive method and led to simple verification of the incidence axioms. However, treating vertical and non-vertical lines separately does have its drawbacks. By making it necessary to break proofs into two cases, it leads to an artificial distinction between lines that really are not diff作者: 心胸狹窄 時(shí)間: 2025-3-29 05:16 作者: arthroplasty 時(shí)間: 2025-3-29 08:31 作者: BILK 時(shí)間: 2025-3-29 13:10
Neutral Geometry,try the appropriate notion of equivalence is that of “congruence.” We have already discussed congruence for segments and angles. In this chapter we will define and work with congruence between triangles.作者: AVERT 時(shí)間: 2025-3-29 18:29 作者: Ostrich 時(shí)間: 2025-3-29 23:09
