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Sacred geometry. As worldview and cosmology[edit] The belief that God created the universe according to a geometric plan has ancient origins. Plutarch attributed the belief to Plato, writing that "Plato said God geometrizes continually" (Convivialium disputationum, liber 8,2). In modern times the mathematician Carl Friedrich Gauss adapted this quote, saying "God arithmetizes".[2] At least as late as Johannes Kepler (1571–1630), a belief in the geometric underpinnings of the cosmos persisted among scientists. Closeup of inner section of the Kepler's Platonic solid model of planetary spacing in the Solar system from Mysterium Cosmographicum (1596) which ultimately proved to be inaccurate Natural forms[edit] Art and architecture[edit] Geometric ratios, and geometric figures were often employed in the design of Egyptian, ancient Indian, Greek and Roman architecture.

In Hinduism[edit] Unanchored geometry[edit] Music[edit] See also[edit] Notes[edit] Further reading[edit] External links[edit] Sacred geometry at DMOZ. The Theory of Abstract Objects. Home Page Introduction The equations at the top of this page are the two most important principles of the theory of abstract objects. The first principle expresses the existence conditions for abstract objects; the second expresses their identity conditions. In this document, we try to give you some idea of what these principles say. Metaphysics vs. The theory of abstract objects is a metaphysical theory. It would be a mistake to think that a theory postulating abstract objects is incompatible with our theories of natural science, which seem to presuppose that the only things that exist are the things governed by our true scientific theories.

Objectives of the Theory We can summarize the principal objectives of the theory of abstract objects as follows: To describe the logic underlying (scientific) thought and reasoning by extending classical propositional, predicate, and modal logic. Further Explanation of the Objectives of the Theory The Distinction Underlying the Theory Tutorial. The laws list. Erasing history? Temporal cloaks adjust light's throttle to hide an event in time. Researchers from Cornell University in Ithaca, N.Y., have demonstrated for the first time that it's possible to cloak a singular event in time, creating what has been described as a "history editor. " In a feat of Einstein-inspired physics, Moti Fridman and his colleagues sent a beam of light traveling down an optical fiber and through a pair of so-called "time lenses. " Between these two lenses, the researchers were able to briefly create a small bubble, or gap, in the flow of light.

During that fleetingly brief moment, lasting only the tiniest fraction of a second, the gap functioned like a temporal hole, concealing the fact that a brief burst of light ever occurred. The team is presenting their findings at the Optical Society's (OSA) Annual Meeting, Frontiers in Optics (FiO) 2011 ( taking place in San Jose, Calif. next week. To test the performance of their temporal cloak, the researchers created pulses of light directly between the two lenses.

Lectures. Video Lectures | Public lectures given at the Institute for Advanced Study. Lectures. Free university lectures - computer science, mathematics, physic. Whether your goal is to earn a promotion, graduate at the top of your class, or just accelerate your life, lectures can help get you there. Our archives of lectures cover a huge range of topics and have all been handpicked and carefully designed by experienced instructors throughout the world who are dedicated to helping you take the next step toward meeting your career goals. Lifelong learns can turn their free time turn into self-improvement time. The online lectures on this list are more than lecture notes or a slideshow on a topic -- they were designed for audiences like you, with carefully sequenced themes and topics taught by veteran educators, and often with additional resources for your own independent study.

The lectures are available to anybody, completely free of charge. Lecture courses are a valid and vital learning tool, and may be one of the best methods of learning available. College Physics. Physics text - Contents. Einstein for Everyone - StumbleUpon. Einstein for Everyone Nullarbor Press 2007revisions 2008, 2010, 2011, 2012, 2013 Copyright 2007, 2008, 2010, 2011, 2012, 2013 John D.

Norton Published by Nullarbor Press, 500 Fifth Avenue, Pittsburgh, Pennsylvania 15260 with offices in Liberty Ave., Pittsburgh, Pennsylvania, 15222 All Rights Reserved John D. An advanced sequel is planned in this series:Einstein for Almost Everyone 2 4 6 8 9 7 5 3 1 ePrinted in the United States of America no trees were harmed web*bookTM This book is a continuing work in progress. January 1, 2015. Preface For over a decade I have taught an introductory, undergraduate class, "Einstein for Everyone," at the University of Pittsburgh to anyone interested enough to walk through door. With each new offering of the course, I had the chance to find out what content worked and which of my ever so clever pedagogical inventions were failures.

At the same time, my lecture notes have evolved. This text owes a lot to many. I i i. MathAppendices. Elementary Concepts in Statistics. In this introduction, we will briefly discuss those elementary statistical concepts that provide the necessary foundations for more specialized expertise in any area of statistical data analysis. The selected topics illustrate the basic assumptions of most statistical methods and/or have been demonstrated in research to be necessary components of our general understanding of the "quantitative nature" of reality (Nisbett, et al., 1987).

We will focus mostly on the functional aspects of the concepts discussed and the presentation will be very short. Further information on each of the concepts can be found in statistical textbooks. Recommended introductory textbooks are: Kachigan (1986), and Runyon and Haber (1976); for a more advanced discussion of elementary theory and assumptions of statistics, see the classic books by Hays (1988), and Kendall and Stuart (1979).

What are Variables? Variables are things that we measure, control, or manipulate in research. Correlational vs. Dependent vs. Calculus Video Tutorials | integralCALC.com. Discrete Math Lecture Notes. Pauls Online Math Notes. Russell's Paradox. First published Fri Dec 8, 1995; substantive revision Tue Dec 3, 2013 Russell's paradox is the most famous of the logical or set-theoretical paradoxes. Also known as the Russell-Zermelo paradox, the paradox arises within naïve set theory by considering the set of all sets that are not members of themselves. Such a set appears to be a member of itself if and only if it is not a member of itself.

Hence the paradox. Some sets, such as the set of all teacups, are not members of themselves. Other sets, such as the set of all non-teacups, are members of themselves. Call the set of all sets that are not members of themselves “R.” Although also noticed by Ernst Zermelo, the contradiction was not thought to be important until it was discovered independently by Bertrand Russell in the spring of 1901. 1.

Is R a member of itself? The comprehensive class we are considering, which is to embrace everything, must embrace itself as one of its members. 2. 3. As Whitehead and Russell explain, 4. Quadratic Equations: Quadratic Formula. Consider the general quadratic equation with . First divide both sides of the equation by a to get which leads to Next complete the square by adding to both sides Finally we take the square root of both sides: or We call this result the Quadratic Formula and normally write it Remark. And Example: Use the Quadratic Formula to solve Solution. .

Please go to General Conclusion to find a summary of all the cases regarding the roots of a quadratic equation. [Algebra][Complex Variables] [Geometry][Trigonometry ] [Calculus][Differential Equations][Matrix Algebra] S.O.S MATHematics home page Do you need more help? Copyright © 1999-2019 MathMedics, LLC. The Most IMPORTANT Video You'll Ever See - FULL LECTURE HD.

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