作者: START 時(shí)間: 2025-3-21 21:53 作者: 有其法作用 時(shí)間: 2025-3-22 03:36 作者: 幸福愉悅感 時(shí)間: 2025-3-22 07:15
Nicole Burzan,Ronald Hitzler,Heiko Kirschneres can be expressed in terms of certain fundamental quantities called the metric coefficients. The theory discussed here and in Chapter 13 was invented single-handedly in the early part of the 19th century by the great mathematician Gauss (whose biography is sketched in Chapter 14). It was a major turning point in the history of geometry.作者: Ondines-curse 時(shí)間: 2025-3-22 10:20 作者: 帶來(lái) 時(shí)間: 2025-3-22 16:08 作者: 帶來(lái) 時(shí)間: 2025-3-22 19:48 作者: 使習(xí)慣于 時(shí)間: 2025-3-23 00:14
Curves,duced in earlier chapters. Our aim is to proceed from intuitive notions about curves to a clear, abstract definition. This process - the clarification of ideas - is really one of the most important activities of the mathematician.作者: Rodent 時(shí)間: 2025-3-23 03:40
Tangent,rough .. The fact that Euclid felt compelled to . this result, which most of us would regard as “obvious”, attests to the high level of rigor that permeated Greek mathematics in the days of Plato’s Academy.作者: 取消 時(shí)間: 2025-3-23 06:00 作者: Arthritis 時(shí)間: 2025-3-23 11:16 作者: 金盤(pán)是高原 時(shí)間: 2025-3-23 16:42 作者: stroke 時(shí)間: 2025-3-23 19:27 作者: HARD 時(shí)間: 2025-3-24 01:37
http://image.papertrans.cn/f/image/320272.jpg作者: languor 時(shí)間: 2025-3-24 04:31
https://doi.org/10.1007/978-3-322-80274-3Gaussian curvature; commonplace curved objects; curvature; euklidische Geometrie; experiments; geometry; m作者: aneurysm 時(shí)間: 2025-3-24 06:47 作者: blithe 時(shí)間: 2025-3-24 13:08
https://doi.org/10.1007/978-3-662-28437-7ral curve. In other words, the Greek mathematicians were unable to put into mathematical language an idea that every ancient rope-stretcher and tailor must have known! To understand the nature of the difficulty, let us start with an experiment.作者: abracadabra 時(shí)間: 2025-3-24 17:50
https://doi.org/10.1007/978-3-663-07941-5inly, the curvature of a straight line should be considered zero. Perhaps then, we can regard a curve as a deviation from a straight line? Let us explore how this idea can be given quantitative meaning.作者: BAIT 時(shí)間: 2025-3-24 19:20 作者: 表兩個(gè) 時(shí)間: 2025-3-25 02:30 作者: 改進(jìn) 時(shí)間: 2025-3-25 04:45 作者: notification 時(shí)間: 2025-3-25 11:16
Keeping Track of Magnitude, Direction and Sense: Vectors,quantities can be represented mathematically by .. It turns out that vectors are also very useful in geometry, and you will have ample opportunity to see this when we study curves and surfaces. In the present chapter, the basic properties of vectors are described.作者: bioavailability 時(shí)間: 2025-3-25 13:35 作者: 拘留 時(shí)間: 2025-3-25 16:19
Curvature of Curves,inly, the curvature of a straight line should be considered zero. Perhaps then, we can regard a curve as a deviation from a straight line? Let us explore how this idea can be given quantitative meaning.作者: Detain 時(shí)間: 2025-3-25 20:41 作者: cleaver 時(shí)間: 2025-3-26 04:10
Gaussian Curvature,r. We learned that this variation is governed by Euler’s formula (15.30). In the present chapter, a completely different approach is taken, which is not based at all on the curvature of curves. Here, we study a brilliant idea of Gauss’s, which will enable us to define a unique value of . at each point on a smooth surface.作者: maroon 時(shí)間: 2025-3-26 04:31
,Levi-Civita (1873–1941), Christoffel (1829–1901), Beltrami (1835–1900), and others. During the closing decades of the 19th century, a powerful school of mathematics developed at the University of Padua. It was here that Levi-Civita came into contact with modern geometry.作者: SHOCK 時(shí)間: 2025-3-26 09:08
978-3-528-06475-4Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden 1996作者: champaign 時(shí)間: 2025-3-26 12:42
Studies of Phase Transformations,es give rise. Modem geometry is an extremely active field of research by pure and applied mathematicians, and it also has significant applications in physics and engineering. In the present book, we will explore in a physical manner the geometrical properties of curves and surfaces, and will discuss作者: Biguanides 時(shí)間: 2025-3-26 17:14 作者: morale 時(shí)間: 2025-3-27 00:38 作者: Obsessed 時(shí)間: 2025-3-27 03:26
https://doi.org/10.1007/978-3-662-28437-7ral curve. In other words, the Greek mathematicians were unable to put into mathematical language an idea that every ancient rope-stretcher and tailor must have known! To understand the nature of the difficulty, let us start with an experiment.作者: 口音在加重 時(shí)間: 2025-3-27 07:47 作者: 食道 時(shí)間: 2025-3-27 11:51 作者: 索賠 時(shí)間: 2025-3-27 16:21 作者: 品牌 時(shí)間: 2025-3-27 19:31 作者: GROWL 時(shí)間: 2025-3-28 01:55 作者: 決定性 時(shí)間: 2025-3-28 05:26
Materialflu?gestaltung in Fertigungssystemenly intellectual activity, but it should not be regarded as an elitist one. Even those of us who have never created a song, or a story, or a piece of mathematics, can still experience much pleasure from playing or listening to music, or from reading a book or attending a play, or from doing a calcula作者: DAMN 時(shí)間: 2025-3-28 07:03
fir+iaw Forschung für die Praxisr. We learned that this variation is governed by Euler’s formula (15.30). In the present chapter, a completely different approach is taken, which is not based at all on the curvature of curves. Here, we study a brilliant idea of Gauss’s, which will enable us to define a unique value of . at each poi作者: Flawless 時(shí)間: 2025-3-28 12:26 作者: organism 時(shí)間: 2025-3-28 14:57
Material Religion in Modern BritainWe start out by performing some geometrical operations that can be easily done on objects located in ordinary three-dimensional space. You will need a ruler and a piece of string (or a tape measure) for measuring lengths, and a protractor for measuring angles.作者: reject 時(shí)間: 2025-3-28 22:32
E. Carpene,M. Kahle,M. Han,P. SchaafIn order to examine the local geometry of a figure, we will need to focus attention on the collection of points that lie close to any given point. We will dissect the figure mentally, as it were. To be clear about what this means, it is best to employ some concepts from set theory.作者: Neuralgia 時(shí)間: 2025-3-28 23:23 作者: 爭(zhēng)吵加 時(shí)間: 2025-3-29 06:50
https://doi.org/10.1007/978-3-031-40571-6In discussing the operations described in Chapter 2, we paid particular attention to whether or not closeness between points of a figure was changed by the operations. It is worth looking into this idea more carefully.作者: 氣候 時(shí)間: 2025-3-29 07:20 作者: comely 時(shí)間: 2025-3-29 14:26 作者: 縱欲 時(shí)間: 2025-3-29 17:51 作者: 深淵 時(shí)間: 2025-3-29 21:51
Basic Operations,We start out by performing some geometrical operations that can be easily done on objects located in ordinary three-dimensional space. You will need a ruler and a piece of string (or a tape measure) for measuring lengths, and a protractor for measuring angles.作者: 蠟燭 時(shí)間: 2025-3-30 02:29
Intersecting with a Closed Ball,In order to examine the local geometry of a figure, we will need to focus attention on the collection of points that lie close to any given point. We will dissect the figure mentally, as it were. To be clear about what this means, it is best to employ some concepts from set theory.作者: 鬧劇 時(shí)間: 2025-3-30 06:34
Mappings,We now discuss the concept of a mapping (or function). The usefulness of this idea for the mathematical sciences can hardly be exaggerated.作者: Budget 時(shí)間: 2025-3-30 11:17 作者: 小丑 時(shí)間: 2025-3-30 13:40
Normal Sections,One way of exploring curved surfaces is to examine the curvature of curves lying on them. In the present chapter, we will use planes to cut a surface in a specific way, and we will study the resulting curves to gain some insight into the nature of surface curvature.作者: Licentious 時(shí)間: 2025-3-30 19:35
,Riemann (1826–1866),Like Mozart’s, Bernhard Riemann’s life was short but marvelously creative. He solved several of the most difficult problems in pure and applied mathematics, introduced entirely new concepts and techniques, and profoundly changed the way in which mathematicians, physicists, and philosophers view space.作者: nonchalance 時(shí)間: 2025-3-30 23:11
Parallel Transport of a Vector on a Surface,In this chapter, we describe a particular way of moving a vector along a given curve on a surface. It provides an especially revealing means of exploring the non-Euclideanness of the surface.作者: BILIO 時(shí)間: 2025-3-31 01:27 作者: 策略 時(shí)間: 2025-3-31 06:16
Materialflu?gestaltung in Fertigungssystemen, and Beethoven (1770–1827) seem to possess almost superhuman powers. In literature, we have Shakespeare (1564–1616), Milton (1608–1674), Goethe (1749–1832), and several others. In mathematics, Archimedes (287–212 B.C.), Newton (1642–1727), and Gauss are ranked at the top, but magnificent contributi作者: Deceit 時(shí)間: 2025-3-31 09:52 作者: 種類 時(shí)間: 2025-3-31 13:58
Textbook 1996lity should be made either to motivate mathematical assumptions, or to introduce questions out of which theorems arise, or to illustrate the results of an analysis. Such interconnections are especially important in the teaching of mathematics to science and engineering students. But, mathematics stu作者: 夾克怕包裹 時(shí)間: 2025-3-31 18:20 作者: 輪流 時(shí)間: 2025-3-31 23:13
Keeping Track of Magnitude, Direction and Sense: Vectors,quantities can be represented mathematically by .. It turns out that vectors are also very useful in geometry, and you will have ample opportunity to see this when we study curves and surfaces. In the present chapter, the basic properties of vectors are described.作者: 音樂(lè)會(huì) 時(shí)間: 2025-4-1 02:17
Curves,ew of the infinite variety of curves that can be imagined. The path of a bird flying through the air, the instantaneous shape of a swinging chain held at its top, the outlines of petals, the forms of arches and suspension bridges-all provide physical examples of curves. We wish to describe such gene作者: Graphite 時(shí)間: 2025-4-1 09:27 作者: 擋泥板 時(shí)間: 2025-4-1 13:39
