شرح دروس الرياضيات بالمجان طريقة نيوتن في الحصول على حل تقريبي للجذور التكعيبية او الجذر المعب

Ahmad

الثلاثاء، 9 أكتوبر 2012

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هل ترغب في تعلم الرياضيات بسهولة؟ هل تجد صعوبة في فهم دروس الرياضيات في المدرسة؟ هل تجد شرح وتفسير المعلم مملا وغامضا وغير مفهوم في فهم دروس ودورات الرياضيات؟ إن كانت هذه هي مشاكلك وصعوباتك في الرياضيات سوف يفيدك هذا الفيديو, مجموعة من الدروس المجانية في تعلم الجبر والهندسة وحساب التفاضل والتكامل والمعادلات والدالات بأنواعها, سوف نقدم لك كل ما تحتاجه لاجتياز اختبارات الرياضيات في الباكالوريا والجامعة, لطلبة علوم الرياضيات والعلوم الأخرى المختلفة, كما سوف نشاهد دروس تعليم تقنيات حساب الأعداد الجمع الضرب الطرح والقسم الذهني, سوف تحسب مثل آلة حاسبة بسهولة دون تفكير. We discuss cubes, cube roots and the impossibility of finding a cube root of 5 exactly. However Newton's method applies to allow us to find numbers whose cubes are approximately equal to 5. In this case there is also a higher variant which uses tangent conics instead of tangent lines. This lecture is part of the MathFoundations series, which tries to lay out proper foundations for mathematics, and will not shy away from discussing the serious logical difficulties entwined in modern pure mathematics. The full playlist is at http://www.youtube.com/playlist?list=PL5A714C94D40392AB&feature=view_all In this video you pose a question about the ratio 2:1 is optimal. The first question is if we change the ratio, why r_n will converge to the same number? The second question is, is this ratio indeed the optimal? And if yes, why? (Maybe you are talking about these things in other vidios, if so please direct me) alexzarhin 3 months ago These are questions to investigate. njwildberger in reply to alexzarhin 3 months ago On slide 3, you say, "But there is no such number r" which is equal to the cube root of 5. It might instead be clearer to assert, "No element of Rat that is equal to the square root of 5." peterhi503 6 months ago Well so far those are all the numbers we have considered, but you are quite right. Eventually we will be able to construct extension fields of the rational numbers, which have at least some claim to also containing numbers, which contain objects whose cube is the analog of 5 in these fields. njwildberger in reply to peterhi503 6 months ago Since you can have an extension field of Rat that includes many things, root-2, cube-root-5, etc., is it not possible that we have an "overly large" field that includes all such extensions that fills in the 'gaps' in Rat? Might we even call it the real numbers and it has perfectly sound algebraic properties as any other extension field? The argument against infinite decimals is neither here nor there, since we can just say we don't require any such decimal representations of these entities. Bryan Goodrich in reply to njwildberger 3 months ago in playlist MathFoundations This is an interesting and worthwhile idea that requires exploring. We will talk about extension fields of the rational numbers. However it will become apparent that the bigger such an extension field, ie the more square roots and cube roots etc that one wants to include, the more cumbersome and difficult becomes the arithmetic. It will become clear that including "all" possible irrationals is a dream. njwildberger in reply to Bryan Goodrich 3 months ago see all All Comments (16) Sam Kamal Respond to this video... 6^3 = 216. You have it as 218 sharon yash 3 weeks ago While there are modified Newton's methods that (may) converge more quickly, your quadratic method seems a bit misleading because while you show its speed in the one example, you wash over the necessary sub-steps required to find solutions to the quadratic equations (which would need a specified tolerance to be "solved enough"). I would be interested how your algebraic approach can be used to specify the time-complexity of the method (Newton's converges in quadratic time). Bryan Goodrich 3 months ago True, but it just suggests (to me) that we need an alternative approach to constructing a (complete ordered) field of real numbers. The intuition about being able to algebraically define the 'gaps' between rational numbers where we know they don't exist (e.g., root-2) is what Dedekind cuts aim to do, and I would say do so successfully (w/o any more semantic baggage than already exists in acknowledging a set of rational, integer, etc. numbers exist). If we accept infinite sets :) Bryan Goodrich in reply to njwildberger (Show the comment) 3 months ago 218 isn't 6 cubed. 6x6x6 = 216 NathanLiii 4 months ago I can take a 5th root on the calculator by raising a number to the (1/5) power using the ^ or y^x key. And so on for other roots.