Pythagorean theorem

Introduction The concept of a spooky action at a distance, which describe the how an object could be affected, moved, or changed without being physically affected by another object, has raised different arguments throughout history. Some believe that action at a distance would describe all the uncertainties of quantum physics and would help us understand the unknowns of quantum mechanics. There have been varies experiments that support the claims of action at a distance and those who disagree…

A. Defining Reaction Mechanisms and Catalyst Structure The methane-to-methanol reactions that we aimed to evaluate consist of four critical steps starting from the initial reactants (CH4, NH4+, oxo): C-H activation followed by a hydrogen atom abstraction (HAA) from CH4 to form some combination of the hydrogenated complex, ammonium or ammonia, and a methyl radical; a radical rebound (RR) to form a methanol adduct and ammonium; methanol dissociation from the metal; and catalysis regeneration via…

Pascal’s Triangle emerged in 1068 discovered by Hindu mathematician Bhattotpala (c.1068) who recorded the first 16 rows of the triangle (Wilson, 2013, p170). Meanwhile, in Persia, Al-Karaji (953-1029) also found the binomial theorem according to Pascal’s Triangle as well as several theorems related to it (Coolidge, 1949, p151). Although the original work from Al-Karaji had lost, the later Persian mathematician Khayyam (1048-1122) referred Al-Karaji’s work about Pascal’s Triangle and uses it to…

This September, I started my MSc at UBC SPPH with a goal of becoming a researcher on clinical trials. During the past semester, I discovered I love it more than I could imagine. I enjoy everything that I am doing, especially my research which I can work until 3 am in the morning without feeling tired or exhausted. I count myself as a fortunate person as I have found what I love, unlike many other people who spend their entire life looking for what they like. However, as a person who wants to…

The second source is a book which introduced the basic concepts and applications of this methodology. The authors concentrated on the causal discovery of networks and the techniques of using Bayesian networks. Furthermore, they discussed the utilisation of this methodology for causal modelling. This source is important at the initial stage of the project as it contributes to the decision-making process at the modelling technique selection stage. However, it is not as important as the other two…

In this essay, we present a discussion about Bayesian methods in Spatial Statistics. Bayesian methods are approaches to statistical inferences which have been around for several decades and are also used in Geographic Information Systems. The application of these methods in practical problems has increased significantly within the last few years due to recent advances in tools for computation and simulation [1]. At the heart of any Bayesian data analysis method are the likelihood function, which…

PROCEDURE Maximum power and Norton’s Theorem will be performed to solve the unknowns within the given circuit. How to use both Maximum Power and Norton’s Theorem properly, are to be explained in order to solve a circuit using these approaches. THEORY MAXIMUM POWER Maximum power states that a load receives max power from a network when it’s resistance is exactly equal to the Thevenin and Norton resistance of the network supplying the power (as shown below): If the load resistance is…

Marie-Sophie Germain Although she is not well known, Marie-Sophie Germain contributed much to the fields of mathematics, philosophy, and physics and proved to be an exceptional physicist, mathematician, and philosopher throughout her lifetime. Overcoming all obstacles thrown her way, Germain fought relentlessly for her education and proved to not only her parents, but the whole mathematic and scientific community that women could be successful. From the start of her life, Germain was blessed…

To the best of our knowledge, humans are the only creatures on earth that are able to contemplate infinity. We commonly talk about the infinite universe (which cosmologists now tell us is almost certainly finite but unbounded), we speak of infinite number series, such as the set of even numbers, and we use it metaphorically, as in saying someone has “infinite patience.” Time itself is spoken of as infinite, though it is always tied to finite objects which are changing and we can 't even come…

Sophie Germain is one of France’s greatest female mathematician prior to revolutionary war, she was the daughter of Ambroise-François Germain and Marie-Madeleine Gruguelu. Her father worked as a part time deputy to the State-General. In his speeches he gave he referred to himself as a merchant and ardently defended the rights of the Third Estate, which he was there to represent. Somewhat later in his life time he became one of the directors of the Banque de France or in English the Bank of…