Theorem

Pythagorean theorem. Phi is an irrational number expressed as: φ = (1+√5)/2 = 1.618033988749895... or 1.618 approximately “Phi is also known as the golden mean, golden ratio or golden number”. (Eather, 2014) Phi is the only number whose square is the same value as itself plus 1. The Pythagoras theorem states that: given a right-angled triangle, the square of the two shorter sides are equal to the square of the hypotenuse. This can be demonstrated by: Using the Pythagoras theorem and the…

chain until they reach the edge of the polygon. The stations have to be moved to where the chain reaches the edge of the polygon, which includes the original guard’s problem therefore any point P on the polygon can be guarded. Figure 3 Theorem 3: “Any simple polygon which is lazy guardable may be guarded with the same number of stations placed on the boundary of the polygon.” [1] Lemma 4: “A simple polygon is lazy k guardable (with k 2) if and only if it admits a choice of k end…

In the book “the Signal and the noise”, author Nate Silver talks about prediction from many different angles. Silver explains how prediction is a part of our everyday life and how it affects us. From math to history, inside of a class room or on a court/field, prediction is something we deal with on a day to day basis unconsciously. Silver talks about the benefits of failure and how failure is helpful in the long run with making predictions. Throughout the years we have made progress with…

Alexander the Great believed to be one of the great kings of ancient Macedonia. In his short 13 year reign as king, he conquered more land than any other king in his time. At the age of twenty-two, he was crowned king of Greece. The impact Alexander the great had in his time is that he was the king of cultural diffusion. Alexander's conquests brought Europe, North Africa and the Middle East, and Asian under one ruler. This spiked trade immensely in these areas and all the cultures from the world…

He came up with a theorem on invariants, which are things that don’t change when other things are changed. He opened many doors in the scientific and mathematical world by proving his and others theories, to be correct. His innovation of the matrix theory was far better than…

Memorandum To: the Board of Minnesota Twins From: Minyue Wu Date: November/19/2016 Re: The Sabermetrics Approach and the rebuilding of the Twins ____________________________________ Introduction After Chicago Cubs winning the World Series for the first time in 108 years, people have witnessed Epstein succeed in his team building strategies for the second time, while the first time is when he brought the first success in 103 years’ period to Boston Red Sox. The “sabermetrics” approach of…

1. Henri Lebesgue [8] Lebesgue is credited for many amazing discoveries to different areas of mathematics. In the area of topology, Lebesgue is known for his covering theorem which is used for finding the dimensions of a set. He is also credited for his work on the Fourier series. He was able to demonstrate that using term by term integration of a series that were Lebesgue integrable functions was always valid and therefore…

shown they had an understanding of the Pythagorean relationship of right triangles. The Egyptians knew that a triangle with sides of length 3,4, and 5 have to contain a right angle. Even though this is a glimpse into an important theorem known as the Pythagorean theorem, they did have insight into the geometry of 3-4-5 right triangles, but it is doubtful they had a broader understanding of other triangle constructs. Along with the notion of proving a general mathematical result by carefully…

Amalie, commonly referred to as Emmy, was a German mathematician. Her contributions to algebra have gained her recognition as “the most creative abstract algebraist of modern times” (Encyclopædia Britannica). Noether received a Ph.D. degree from the University of Erlangen in 1907 with a dissertation on algebraic invariants. Shortly after she was invited the University of Göttingen in 1915 by David Hilbert and Felix Klein, Noether used her knowledge of invariants to assist them in exploring the…

Positioning: Portola Coffee Lab is about specialty coffee. The term ‘specialty coffee was first used by Erna Knutsen, of Knutsen Coffee Ltd. In 1978, Erna used the term ‘specialty coffee’ while giving a speech to the delegates of an international coffee conference in Montreuil, France. The main idea behind specialty coffee is that the coffee beans are well prepared, freshly roasted and properly brewed. Unlike the wine where only one company is responsible for planting, husbandry, harvesting,…