Arrow's impossibility theorem

At about twenty centuries ago there was an amazing discovery about right angled triangles: “In a right angled triangle the square of the hypotenuse is equal to the sum of squares of the other two sides.” It is called Pythagoras Theorem and can be written in one short equation: a²+b²=c² where c is the longest side of triangle and a and b are the other two sides. Pythagoras was born in the island of Samos in 570 BC in Greek in the eastern Agean. He was the son of Mnesarchus and his mother's name…

The Greek mathematician and philosopher Pythagoras (c. 580-c. 500 B.C.) is one of the few figures in ancient times, or indeed in any age, who warrants comparison to the extraordinary Imhotep. Although he is best known for his famous geometrical theorem, his accomplishments ranged far beyond mathematics and involved areas as diverse as music, politics, and religion. Like Imhotep, he was a figure larger than life. Some historians suggest that he never really lived; in fact it appears highly likely…

Hypatia was born in Alexandria, Egypt at the fourth century around 350 – 370 AD. Her father was Theon of Alexandria, a great philosopher and mathematician. He was the last attested member of the Alexandrian museum. Hypatia was raised by her father in an educated environment in an era that was not usual for women to learn and be educated. She was an intellectual teacher, philosopher, mathematician, astronomer and inventor Although Hypatia’s works did not stay preserved until now, we know a…

If Ahmed used string and tied it to the Castle Rock point and labeled it as point “A” on paper it would be basically 2x + 6 paces. With this being the radius you will know that it is the same anyway you fit this from the circle. So to find the Treasure we will use “C”. Vanessa will use her compass to find north from Castle Rock. From there she will walk “X” paces in a straight line northward. At the end of her distance she will call this point “B”. Vanessa will now turn 90 degrees to the right…

One of my favorite ways to use technology to engage students is through videos and songs to help them grasp difficult or unfamiliar concepts; this could be a rap about the Pythagorean theorem or a short film on life in Nazi Germany during World War II. Providing students with visual and auditory input in addition to traditional learning styles allows children of multiple intelligences to find aspects of the lesson they connect with and…

Changing Our School Gold Beach High School has some good to it being in a small town, but because it’s in a small town it also has some issues that could be changed to make a huge difference. If I could change three things about GBHS and how things were run the first thing would be adding more classes for students to take. Doing this would help add classes that are more relevant to students and they could learn what they wanted to. The next thing I would change is how long the school day was and…

If R and r is the Circumradius and Inradius of a non-degenerate triangle then due to Euler we have an Inequality stated as and the equality holds when the triangle is equilateral. This ubiquitous inequality occurs in the literature in many different equivalent forms [4] and also Many other different simple approaches for proving this inequality are known. (some of them can be found in [2], [3], [5], [17], and [18] ). In this article we present a proof for this Inequality based on two basic…

Famous philosopher Thales once said, “The most difficult thing in life is to know yourself.”, meaning it takes a while to fully understand one’s self and the strengths or weaknesses within (“Thales”). Thales is an ancient Greek philosopher born in the city of Miletus (“Thales of Miletus” Science). Although, he was a Milesian, his parents, Examyes and Cleobuline, were Phoenicians themselves (“Thales of Miletus” Science). Very little was known about Thales, such as his exact birth and death…

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…

Is Algebra Necessary? By The New York Times Algebra is necessary because it is the branch of mathematics that studies l combining elements of abstract structures according to certain rules . Originally these elements would put be interpreted as numbers or quantities, so that the algebra somewhat originally was a generalization . The adjective " algebraic " usually denotes a relationship with algebra , such as in algebraic structure . For historical reasons, it may also indicate a relationship…