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卡尔达诺关于四次方程特殊法则的构造原理——兼论数学史的研究范式 总被引:4,自引:1,他引:3
复原了卡尔达诺关于四次方程的4条特殊法则的构造过程,指出这4条形式差异很大的法则所采用的相同的构造方法,由此揭示了这些法则的真正涵义和它们通过命题的形式所表达出的数学内容并不相同,同时也解释了卡尔达诺为什么能得到这些法则.对这一构造过程的复原体现了曲安京所概括的三种数学史研究范式之间的联系. 相似文献
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文章考证和呈现了卡尔达诺(1501—1576年)对托勒密著述评注的汉译。译文包含卡尔达诺对托勒密(约100—约178年)关于星占学的系统论述《四书》的评注。中国学者薛凤祚(1599/1600—1680年)和波兰耶稣会士穆尼阁(1610—1656年),进行了有选择性的翻译并将其收录在《天步真原》中。 相似文献
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文章在全面解读阿拉伯数学家萨拉夫·丁·图西(Sharaf al-Dīn al-Tūsī,1135~1213)《方程》(1209年)一书的基础上,着重分析了其中的三次方程数值解法,得出它们是在已有开方算法的基础上有规律性地构造出来。另还将其与同时代中算家秦九韶的相似算法作比较,得出二者的核心算法相同,但是由于各自数学传统的差异又表现出明显的不同。该研究对于进一步认识图西三次方程数值解算法的构造思想以及探究中阿数学在相似问题上各自的特点与传统有积极意义。 相似文献
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古人最早从自然环境中认识圆形和方形。有文字历史以来,对于圆形和方形的认识不断深化并运用于人类生活当中,尤其在建筑设计的图形选择上,经历了一个从圆到方的过程。此过程中,出现了一些特殊的历史事件,而这些事件都与礼制的产生和发展有关,据此可将此过程分为三个阶段。 相似文献
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创造性思维的认知解释 总被引:2,自引:0,他引:2
本文把创造性思维视为解题的一种特殊形式即创造性解题,根据认知科学解题理论的研究得出有关解题过程的一般原则,在构造创造性解题一般模式的基础上,用解题过程的一般原则对解题的搜索机制,解题过程中导致创造的一些关键步骤作了解释,同时评论了把顿悟看作创造机制的观点。 相似文献
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《缀术》中的“刍甍,方亭之问”初探 总被引:1,自引:0,他引:1
在分析《缉古算经》的写作目的及其具体内容的基础上,对《缀术》中的“刍甍,方亭之问”和“方邑进行之术”作了探讨,认为:前者是已知刍甍,方亭的体积及其边,高的差,求边和高的问题,因此《缀术》中有三次方程的内容,后者是解勾股形问题,类似于《缉古算经》最后6问,由此又对祖冲之的“开差幂”和“开差立”算法提出质疑,认为它们与“方邑进行之术”和“刍甍,方亭之问”无关。 相似文献
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Scott J. Hyslop 《Foundations of Science》2014,19(1):35-51
Algebraic equations in the tradition of Descartes and Frans Van Schooten accompany Christiaan Huygens’s early work on collision, which later would be reorganized and presented as De motu corporum ex percussione. Huygens produced the equations at the same time as his announcement of his rejection of Descartes’s rules of collision. Never intended for publication, the equations appear to have been used as preliminary scaffolding on which to build his critiques of Descartes’s physics. Additionally, Huygens used algebraic equations of this form to accurately predict the speeds of bodies after collision in experiments carried out at the Royal Society. Despite their deceptive simplicity, Huygens’s algebraic equations pose significant conceptual problems both mathematically and for their physical interpretation especially for negative speeds; they may very well have been the source of a new principle, the conservation of quantity of motion with direction. 相似文献
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On the use of ordered sets in problems of comparison and consensus of classifications 总被引:7,自引:7,他引:0
Ordered set theory provides efficient tools for the problems of comparison and consensus of classifications Here, an overview of results obtained by the ordinal approach is presented Latticial or semilatticial structures of the main sets of classification models are described Many results on partitions are adaptable to dendrograms; many results on n-trees hold in any median semilattice and thus have counterparts on ordered trees and Buneman (phylogenetic) trees For the comparison of classifications, the semimodularity of the ordinal structures involved yields computable least-move metrics based on weighted or unweighted elementary transformations In the unweighted case, these metrics have simple characteristic properties For the consensus of classifications, the constructive, axiomatic, and optimization approaches are considered Natural consensus rules (majoritary, oligarchic, ) have adequate ordinal formalizations A unified presentation of Arrow-like characterization results is given In the cases of n-trees, ordered trees and Buneman trees, the majority rule is a significant example where the three approaches convergeThe authors would like to thank the anonymous referees for helpful suggestions on the first draft of this paper, and W H E Day for his comments and his significant improvements of style 相似文献
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李约瑟在其论述中国科学和文明的系列巨著中,展示了他对迷人的古代文明之一-中国文明的概念细微差别与成就的敏锐。另外,他就思想与实践从一种文化传播到另一种文化所作的思考可谓不同凡响。尤为人注目的是,他在天文学、数学、炼丹术及其它方面对印之间科学传播的阐述。虽然为了解印度科学,他大体上依赖于其他学者的研究,但他对待印度科学的客观态度却令人耳目一新,并且由于其巨著对古代印度科学的某些方面提供了相当透彻的见解,因此这部巨著对印度科学史家来说确有价值。事实上,李约瑟精心筹划的多卷本系列形式以及各卷本内容上的旁征博引乃是印度科学史家们灵感之源泉。 相似文献
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中国古代历法中的三次内插法 总被引:2,自引:1,他引:2
该文根据《天文大成管窥辑要》中的史料,发现边冈在其《崇玄历》(892年)中创立的晷影公式-中国历法史上第一例三次函数,是通过令影差变化与自变量平方的比值为某个等差数列而构造出来的,与过去认为的三次内插法无关;王恂、郭守敬在《授时历》(1280年)创立的平立定三差算法,则是通过对插值函数的降阶,将问题转化为一般的二次内插公式的构造,前者可能受到了边冈立方相减相乘算法的启发,后者则与刘焯的二次插值算法 相似文献
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塞尔论社会实在的建构 总被引:1,自引:0,他引:1
社会实在建构理论是塞尔著作的一个重要主题。集体意向性、功能的施加和建构性规则是建构社会实在的三个必要条件。塞尔从哲学角度探讨这一问题富有新意,为我们从哲学角度探讨社会科学问题树立了典范。 相似文献
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Edward Slowik 《Foundations of Science》2013,18(3):419-448
This paper investigates Newton’s ontology of space in order to determine its commitment, if any, to both Cambridge neo-Platonism, which posits an incorporeal basis for space, and substantivalism, which regards space as a form of substance or entity. A non-substantivalist interpretation of Newton’s theory has been famously championed by Howard Stein and Robert DiSalle, among others, while both Stein and the early work of J. E. McGuire have downplayed the influence of Cambridge neo-Platonism on various aspects of Newton’s own spatial hypotheses. Both of these assertions will be shown to be problematic on various grounds, with special emphasis placed on Stein’s influential case for a non-substantivalist reading. Our analysis will strive, nonetheless, to reveal the unique or forward-looking aspects of Newton’s approach, most notably, his critical assessment of substance ontologies, that help to distinguish his theory of space from his neo-Platonic contemporaries and predecessors. 相似文献
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牛顿科学劳作背后的形上理念及其方法论架构乃科学史中的元问题之一,也是以往学界乏有论及的盲区。本文注重一种回到事情本身的理路,从牛顿的具体文本出发,撷取出微分定律的工具理性、力之概念的别样意蕴和运动机制的自然本态等三大理论质点,以图彰显牛顿科学纲领的别样意蕴,并澄清以往学界对牛顿的某些误解与误读之处。 相似文献
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该文以阿尔·徒思和宋元数学家为例,对阿拉伯与中国代数方程数值解法进行了比较研究,认为二者在方法的一般性和所讨论的根的范围上是相同的,而不同点则在于方程的布式和分类。他们分别受到各自传统开方法的启示,且又沿着不同的途径发展,即阿尔·徒思的整个计算程序力求和早期传统的开方法相吻合,而宋元数学家则对早期传统的开方术作了进一步推广和发展,沿着一条机械化、程序化的道路进展。该文还分析了为什么中国学者实现了由开高次方到高次方程数值解法的突破,而阿拉伯学者却未能实现突破的原因。 相似文献
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We propose and discuss improved Bayes rules to discriminate between two populations using ordered predictors. To address the
problem we propose an alternative formulation using a latent space that allows to introduce the information about the order
in the theoretical rules. The rules are first defined when the marginal densities are fully known and then under normality
when the parameters are unknown and training samples are available. Several numerical examples and simulations in the paper
illustrate the methodology and show that the new rules handle the information appropriately. We compare the new rules with
the classical Bayes and Fisher rules in these examples and we show that the misclassification probability is smaller for the
new rules. The method is also applied to data from a diabetes study where we again show that the new rules improve over the
usual Fisher rule.
Research partially supported by Spanish DGES and by PAPIJCL. The authors thank the editor and an anonymous reviewer for their
detailed reading that resulted in this much improved version of the paper. 相似文献