4. Identities, and more identities

Author(s):  
Glen Van Brummelen

The world of trigonometry is full of identities: some of them extremely useful, others beautiful, and a few that are simply bizarre. ‘Identities, and more identities’ takes a tour of the menagerie of identities, viewing a little from each of these categories. The first two examples are known as triangle identities, because they refer to angles and lengths in a given triangle. The Law of Sines and the Law of Cosines are discussed, along with Mollweide’s formulas, the Law of Tangents, Morrie’s Law, and the introduction of logarithms, which became the preferred computing tool in mathematical astronomy, and then in practical disciplines like surveying and architecture in the early 17th century.

Author(s):  
Courtney Fox

This workshop gives participants an outline of a full unit in Trigonometry that covers right triangle trigonometry, the law of sines, and the law of cosines. Attendees will participate in abbreviated student tasks. In the unit students are introduced to the world water crisis and how it affects women and children the most and why this is. Using their knowledge of trigonometry and the Desmos (or other graphing) calculator to “solve” a water crisis in a town and bring clean sanitation to a remote island. This unit helps students develop critical thinking and problem-solving skills, numerical literacy, and global awareness. Students make connections to the “real world” using mathematics and become world citizens.


Author(s):  
Karen J. Alter

In 1989, when the Cold War ended, there were six permanent international courts. Today there are more than two dozen that have collectively issued over thirty-seven thousand binding legal rulings. This book charts the developments and trends in the creation and role of international courts, and explains how the delegation of authority to international judicial institutions influences global and domestic politics. The book presents an in-depth look at the scope and powers of international courts operating around the world. Focusing on dispute resolution, enforcement, administrative review, and constitutional review, the book argues that international courts alter politics by providing legal, symbolic, and leverage resources that shift the political balance in favor of domestic and international actors who prefer policies more consistent with international law objectives. International courts name violations of the law and perhaps specify remedies. The book explains how this limited power—the power to speak the law—translates into political influence, and it considers eighteen case studies, showing how international courts change state behavior. The case studies, spanning issue areas and regions of the world, collectively elucidate the political factors that often intervene to limit whether or not international courts are invoked and whether international judges dare to demand significant changes in state practices.


2018 ◽  
pp. 38-74
Author(s):  
Barry Rider

This article is focused on exploration not merely proposed developments in and refinements of the law and its administration, but the very significant role that financial intelligence can and should play in protecting our societies. It is the contention of the author that the intelligence community at large and in particular financial intelligence units have an important role to play in protecting our economies and ensuring confidence is maintained in our financial institutions and markets. In this article the author considers a number of issues pertinent to the advancement of integrity and in particular the interdiction of corruption to some degree from the perspective of Africa. The potential for Africa as a player in the world economy is enormous. So far, the ambiguous inheritance of rapacious empires and the turmoil of self-dealing elites in post-colonial times has successfully obscured and undermined this potential. Indeed, such has been the mismanagement, selfishness and importuning that many have grave doubts as to the ability of many states to achieve an ordered transition to what they could and should be. South Africa is perhaps the best example of a society that while avoiding the catastrophe that its recent past predicted, remains racked by corruption and mismanagement. That there is the will in many parts of the continent to further stability and security by addressing the cancer of corruption, the reality is that few have remained or been allowed to remain steadfast in their mission and all have been frustrated by political self-interest and lack of resources. The key might be education and inter-generational change as it has been in other parts of the world, but only an optimist would see this coming any time soon – there is too much vested interest inside and outside Africa in keeping things much as they are! The author focuses not so much on attempting to perfect the letter of the law, but rather on improving the ways in which we administer it.


2018 ◽  
Author(s):  
Xiaoyang Yu

Nomological determinism does not mean everything is predictable. It just means everything follows the law of nature. And the most important thing Is that the brain and consciousness follow the law of nature. In other words, there is no free will. Without life, brain and consciousness, the world follows law of nature, that is clear. The life and brain are also part of nature, and they follow the law of nature. This is due to scientific findings. There are not enough scientific findings for consciousness yet. But I think that the consciousness is a nature phenomenon, and it also follows the law of nature.


Author(s):  
Donald R. Davis

This chapter examines the history and use of maxims in legal traditions from several areas of the world. A comparison of legal maxims in Roman, Hindu, Jewish, and Islamic law shows that maxims function both as a basic tools for legal interpretation and as distillations of substantive legal principles applicable to many cases. Maxims are characterized by their unquestionable character, even though it is often easy to demonstrate contradictions between them. As a result, legal maxims seem linked to the recurrent desire for law to have a moral foundation. Although maxims have lost their purchase in most contemporary jurisprudence and legal practice, categories such as “canons of construction,” “legal principles,” and “super precedents” all show similarities to the brief and limited collections of maxims in older legal traditions. The search for core ideas underlying the law thus continues under different names.


1996 ◽  
Vol 89 (1) ◽  
pp. 1-18 ◽  
Author(s):  
John C. Poirier ◽  
Joseph Frankovic

The diversity among introductions to Paul is a tribute to the apostle's genius. There are two basic reasons for the diversity of opinion that exists today: First, internal incoherency—the difficulty of sorting Paul's thought into center and periphery (or event and context); and second, external incoherency—the gaps in our information about one of the most famous and interesting lives of all time. No consensus has emerged on the question of Paul's place in the world. We make this point not because this study will address the problem directly, but because we shall make inferences from one of the views in current circulation, namely that there is a basis to Paul's claim to Pharisaism (Phil 3:5). Attacking this view, some scholars have thought of him as a “would-be Pharisee” at best. We, nevertheless, think that the preponderance of evidence situates Paul in a universalist Jewish, probably Pharisaic, context. Paul believed that many of the law's prescriptions were still valid. As an illustration of Paul's belief in the continuing validity of the law, this essay attempts to show that 1 Cor 7:5–7 is best understood in the context of ritual purity concerns. These concerns include both the injunction for spouses to abstain from sexual activity for a time of prayer and Paul's defense of a celibate lifestyle within his own charismatic self-understanding.


2018 ◽  
Vol 60 (2) ◽  
pp. 221-232
Author(s):  
Tareq Na’el Al-Tawil ◽  
Prabhakar Gantasala ◽  
Hassan Younies

Purpose This paper aims to discuss the benefits and disadvantages of the law on the expansion of the jurisdiction of the Dubai International Financial Centre (DIFC) Court. The major role of DIFC Courts in the Arab community is to handle cases related to commerce and business. For a long time, the court had been acting only in their geographical area until a new law was enacted to extend their jurisdiction all over the world. Afterward, a lot of criticism emerged as for why and how the court will benefit from such actions. The law has drawn a harsh response, although most benefits have also been experienced since the court received quite a large number of new signings. Interaction at the world business forum has benefited the economy of Dubai thanks to the law. Design/methodology/approach The following study focuses on a description of such benefits and drawbacks. The study does not evaluate a factual process of expansion but indicates the most distinct evidence of positive, as well as negative consequences of the expansion. Findings It is appropriate to make a general comment on the fact that the expansion of DIFC Court is not sufficiently effective at the current stage. Needless to say, it contains numerous positive aspects, but the gaps are evidently essential because they place the entire Court in a hard circumstance. The Court does not have a well-developed legal framework for its new area of jurisdiction as long as its limited volume of prior precedent is a distinct sign of the Court’s dependence on the UAE’s Law. In such way, DIFC Court will not be able to address issues within new fields of jurisdiction, as it simply lacks an expertise and international law in its legal framework. Moreover, the jurisdiction over new areas of international business was not verified with a plain system of mediation, which is why a current expansion of DIFC Court has to be recognized as redundant. However, its advantages are tending to produce their effects provided that the Court manages to address its current problems. Originality/value The study has described the basic benefits and drawbacks of DIFC Court expansion. To speak about the main benefits, they can be depicted as appliance of the common law, unification of English language for proceedings, presence of a preliminary arbitration and guarantees of award enforcement. In a similar way, the drawbacks of the expansion have been issued. The study has identified such drawbacks as lack of international and sophisticated expertise, untested legal framework, strong influence of forum non conveniens, and existence of a limited volume of prior precedent. The paper has not assessed a success of a factual expansion of DIFC Court jurisdiction, but it has managed to fulfill its primary purpose. Thus, the paper has identified a certain tendency concerning the expansion.


2021 ◽  
Vol 20 (8) ◽  
pp. 23-33
Author(s):  
Natalya S. Gurianova

The article studies the religiosity of Russian population in the 17th century in order to find out the type of this state of public mind. Special attention is drawn to the acuteness of eschatological expectations in society, which intensified during periods of crises. After the Time of Troubles (Smuta), the Church, trying to bring society out of the spiritual crisis, had been exploiting the “end of the world” topic through publishing relevant texts. This trend was especially noticeable during the time of Patriarch Joseph. The decision of the Moscow Printing House (Pechatnyi Dvor) to extend the amount of eschatological publications was determined not only by the direction of church policy, but also by the request in society, the desire of the population to get a more complete picture of the Christian teaching about the ultimate destinies of the world and man, since the spiritual crisis had presupposed an increase of apocalyptic moods. This desire indicates that the population was characterized by the religiosity of the medieval type. The article scrutinizes in particular the 2nd half of the 17th century, which modern researchers rightly designate as the early Modern era. In a society with such a keen perception of the time, the church reform, initiated in the middle of the century by Patriarch Nikon, was naturally not supported by a part of the population. In the interpretation of the defenders of the Old Belief, the actions of the reformers turned into clear signs of the advent of the kingdom of Antichrist, as it was prophesied in Christian teaching. It was not some peculiarity of the worldview of the opponents of church reform, their behavior adjusted the religiosity of the epoch. To justify these thoughts the position of Patriarch Nikon could be mentioned. Nikon found himself in a situation of disapproval and, arguing to be wrongfully convicted and misunderstood, he also used the eschatological doctrine. Based on the analysis of such facts, the article concludes that the 2nd half of the 17th century was characterized by religiosity of the medieval type.


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