標(biāo)題: Titlebook: Geometric Constructions; George E. Martin Textbook 1998 Springer Science+Business Media New York 1998 Mathematica.Scratch.algebra.boundary [打印本頁] 作者: 撒謊 時(shí)間: 2025-3-21 16:20
書目名稱Geometric Constructions影響因子(影響力)
作者: Iniquitous 時(shí)間: 2025-3-21 23:24 作者: GIST 時(shí)間: 2025-3-22 03:23
The Compass and the Mohr-Mascheroni Theorem,ginal with Napoleon, the problem has become known as .. During his campaign in northern Italy, Napoleon had encountered the poet and geometer Lorenzo Mascheroni (1750-1800). Mascheroni was a professor at the University of Pavia, where Christopher Columbus had once been a student. Mascheroni’s most f作者: 易改變 時(shí)間: 2025-3-22 07:39
The Ruler,e ruler and the compass are such basic tools that most of us accept them without ever having considered the implication of life without them. Suppose you are faced with the problem of coming to an examination on geometric constructions only to find that in making sure that you have not forgotten you作者: debble 時(shí)間: 2025-3-22 09:15 作者: 不出名 時(shí)間: 2025-3-22 13:04 作者: 不出名 時(shí)間: 2025-3-22 18:26 作者: synovitis 時(shí)間: 2025-3-22 23:10
Sticks,order to do the modeling, we must first have some familiarity with what it is we are to model. Therefore, we should first play around with stacks of toothpicks just to see what we can do with them. Paper and pencil is just not satisfactory; straws or even long, thin strips of paper will serve the pu作者: 蒼白 時(shí)間: 2025-3-23 02:45 作者: 勾引 時(shí)間: 2025-3-23 06:25
Paperfolding,it is evident that all ruler and compass constructions are possible by paperfolding. However, Sundara Row’s angle trisection is admittedly only an approximation and he mistakenly implies that constructing a cube root is impossible in general and, in particular, that the duplication of the cube canno作者: 偽造 時(shí)間: 2025-3-23 12:14 作者: flamboyant 時(shí)間: 2025-3-23 14:48 作者: Exposure 時(shí)間: 2025-3-23 18:33
Analogical Interpretation and Beyond,tly doubled the volume of the existing one. . then was to construct a cube having a side . times as long as a side of the original cube. This problem also has the somewhat misleading name .. According to another legend, Eratosthenes reported that the problem was sent to the geometers at Plato’s Acad作者: 難管 時(shí)間: 2025-3-24 01:29 作者: attenuate 時(shí)間: 2025-3-24 05:40
Entwicklungsphasen des Bildungsraumse ruler and the compass are such basic tools that most of us accept them without ever having considered the implication of life without them. Suppose you are faced with the problem of coming to an examination on geometric constructions only to find that in making sure that you have not forgotten you作者: 征稅 時(shí)間: 2025-3-24 07:17
Stephen K. Rice,Michael D. Maltzompass with two points and no place for a pencil, that was a dividers. As a compass is sometimes called a pair of compasses, a dividers is often called a pair of dividers. Given points . with ., the dividers is used to construct the point . on . such that .. Therefore, with the dividers we can copy 作者: 小鹿 時(shí)間: 2025-3-24 14:16
https://doi.org/10.1007/978-3-030-46870-5ry. Jacob Steiner (1796–1863) worked on his father’s farm until the age of nineteen, before going off to Berlin to become what some regard as the greatest geometer of modern times. Jean-Victor Poncelet (1788–1867) entered the French army corps of engineers just in time to take part in Napoleon’s dis作者: cocoon 時(shí)間: 2025-3-24 15:33
Participant-Observation as a Research Methodeen discovered that the study of the rusty compass goes back to the ancient Greeks. However, the name most associated with the rusty compass is that of the tenth-century Arab scholar Abül-Wefa (940–998). Not only did he give the most elementary ruler and rusty compass constructions, but Ab?l-Wefa al作者: EWE 時(shí)間: 2025-3-24 21:50
Problemstellung und Forschungsperspektive,order to do the modeling, we must first have some familiarity with what it is we are to model. Therefore, we should first play around with stacks of toothpicks just to see what we can do with them. Paper and pencil is just not satisfactory; straws or even long, thin strips of paper will serve the pu作者: 多節(jié) 時(shí)間: 2025-3-25 02:53 作者: Commemorate 時(shí)間: 2025-3-25 07:18
https://doi.org/10.1007/978-3-658-18133-8it is evident that all ruler and compass constructions are possible by paperfolding. However, Sundara Row’s angle trisection is admittedly only an approximation and he mistakenly implies that constructing a cube root is impossible in general and, in particular, that the duplication of the cube canno作者: Virtues 時(shí)間: 2025-3-25 08:56 作者: olfction 時(shí)間: 2025-3-25 13:58 作者: 巨碩 時(shí)間: 2025-3-25 16:18 作者: macrophage 時(shí)間: 2025-3-25 22:44
Euclidean Constructions,ed Cleopatra’s City. Even then, while Rome was at its height, Alexandria remained the intellectual capital of the Empire. Alexandria was a major influence for a thousand years, from the time of Euclid in 300 BC until the fall of Alexandria to the Arabs in AD 641. Greek mathematics is mostly a produc作者: chisel 時(shí)間: 2025-3-26 01:11
The Ruler and Compass,ed the algebra to prove this fact. Our task is to prove the ancient Greeks necessarily failed because they were asking for the impossible. To do this, we must formulate our problems in the language of algebra.作者: moratorium 時(shí)間: 2025-3-26 07:25 作者: Celiac-Plexus 時(shí)間: 2025-3-26 10:26 作者: 健談 時(shí)間: 2025-3-26 14:27
The Marked Ruler,oncelet-Steiner Theorem now implies all the ruler and compass constructions are possible with the marked ruler alone. The characteristic use of the marked ruler is called . or .. Given point . and two lines . and ., by . we determine two points . and . that are one unit apart and such that . is on ,作者: nascent 時(shí)間: 2025-3-26 19:53
Textbook 1998ruler and dividers, using a marked rule, using a tomahawk, and ending with a chapter on geometric constructions by paperfolding. The author writes in a charming style and nicely intersperses history and philosophy within the mathematics. He hopes that readers will learn a little geometry and a littl作者: Anticlimax 時(shí)間: 2025-3-26 23:00
Future Directions and Possible Applications,ed Cleopatra’s City. Even then, while Rome was at its height, Alexandria remained the intellectual capital of the Empire. Alexandria was a major influence for a thousand years, from the time of Euclid in 300 BC until the fall of Alexandria to the Arabs in AD 641. Greek mathematics is mostly a produc作者: 不要嚴(yán)酷 時(shí)間: 2025-3-27 01:11
Analogical Interpretation and Beyond,ed the algebra to prove this fact. Our task is to prove the ancient Greeks necessarily failed because they were asking for the impossible. To do this, we must formulate our problems in the language of algebra.作者: 附錄 時(shí)間: 2025-3-27 05:16
as two points on the line are constructed. In practice, we cannot draw a line with only a compass, but we may be able to construct some particular point on the line as the intersection of circles that are drawn with the compass. As usual, we do not expect every point on a constructed line to be cons作者: 專心 時(shí)間: 2025-3-27 11:23
https://doi.org/10.1007/978-3-030-46870-5th its center was given. Steiner published his detailed proof of this result in 1833. Both Poncelet and Steiner were ardent supporters of synthetic geometry and disliked analytic methods to the extent of attacking those who used them. Therefore, it is with apologies to both Poncelet and Steiner that作者: 一起平行 時(shí)間: 2025-3-27 14:01 作者: Consensus 時(shí)間: 2025-3-27 18:19 作者: 無底 時(shí)間: 2025-3-27 23:58
Problemstellung und Forschungsperspektive,rpose. Reading about toothpick constructions is not the same thing as discovering for yourself some of the things that follow. Since the results of this chapter are not used later, you can go on to the next chapter now and read this chapter after you have had a chance to play with toothpicks.作者: Morbid 時(shí)間: 2025-3-28 05:57 作者: 完全 時(shí)間: 2025-3-28 08:13 作者: 少量 時(shí)間: 2025-3-28 11:42
Paperfolding,t be accomplished by paperfolding. In his 1949 ., J. L. Coolidge refers to Sundara Row but limits his own folding operations to those equivalent to the use of ruler alone. The first rigorous treatment of paperfolding is apparently by R. C. Yates in 1949 in his ..作者: Aprope 時(shí)間: 2025-3-28 16:38 作者: 無關(guān)緊要 時(shí)間: 2025-3-28 19:32 作者: 集合 時(shí)間: 2025-3-28 23:21
Stephen K. Rice,Michael D. Maltzs here; we call the tooi that does that a compass. Knowing the allowed use of the dividers, you should expect the definition below. For practice in formulating these definitions, you should write down the definition of a ruler and dividers point before you read any further.作者: indicate 時(shí)間: 2025-3-29 03:39
Participant-Observation as a Research MethodFerrari (1522–1565) showed in 1547 that all the constructions in Euclid’s . could be done with the ruler and rusty compass. In 1673, Georg Mohr wrote a little book that also proves the principal theorem of this chapter.作者: HALO 時(shí)間: 2025-3-29 09:20
The Ruler,thes apart to get a thread to pull taut is of theoretical interest but is not the most practical approach. Although reflections will not play the major role here that they did in the last chapter, the idea of a reflection does provide the construction of a straightedge. You have only to fold a sheet of paper; the crease forms a straightedge.
