Essay on Number Theory

2. A female rabbit can give birth to over 40 baby rabbits a year. Suppose all of her offspring survived and reproduced, all of their offspring survived and reproduced, and so on. If that happened, in only eight

1. A black guinea pig is crossed with an albino guinea pig, producing 12 black offspring. When

As an extracurricular program our school extends our knowledge by having a program called electives. The school offers art, sport stats, comic creation, The Number Devil, P.E, coding, and Puzzle Solving. One of the electives that helps you in math is The Number Devil. The Number Devil is a book that talks about a boy named Robert that always had terrible dreams. Each Wednesday, your group and you will have a conversation about the dreams you read about. Then our math teacher, will help us understand the math concept that we read about. At the end of the book, you start to learn things that you will learn next year. The Number Devil is a great book, and you will learn numerous of things.

A lawyer researched the average number of years served by 45 different justices on the Supreme Court. The average number of years served was 13.8 years with a standard deviation of 7.3 years. What is the 95% confidence interval estimate for the average number of years served by all Supreme Court justices? Place your limits, rounded to 1 decimal place, in the blanks. Place you lower limit in the first blank.  Place your upper limit in the second blank.  When entering your answer do not use any labels or symbols. Simply provide the numerical value. For example, 12.3 would be a

The defendant was verbally abusive to the arresting officer and refused to show any identification. These facts caused her to be arrested for disorderly conduct. In order for the charge to stand, there needed to be a witness other than the officer who heard her shouting profanities. This is per RSA 644:2, III(a)- He purposely causes a breach of the peace, public inconvenience, annoyance or alarm, or recklessly creates a risk thereof, by: (a) Making loud or unreasonable noises in a public place, or making loud or unreasonable noises in a private place which can be heard in a public place or other private places, which noises would disturb a person of average sensibilities. The defendant argued in her appeal that since she did not meet

1, 3, 5, 7, 9, 11, … (The common difference is 2. (Bluman, A. G. 2500, page 221)

Over the course of human events, men and women of all ages fought and worked relentlessly to better their lives and their families' lives as well. Despite the arduous efforts, each and every one of those people ended up or will end up exactly the same: buried six feet under the ground. Life and death are the largest eventualities to happen to humans as a whole, yet most sentient beings, particularly humans, are afraid of death, due mainly to the natural fear of the unknown. "Numbers" by Mary Cornish seems to beg the question of what does it mean to truly be alive. Being alive is to expand horizons and to feel what life has to offer or simply to be happy, but in layman's terms, life is more than just being born, surviving and finally dying.

I am writing with the intention of describing the math skills that I acquired prior to taking the Math 2414 course. I further intend to explain how my previous math skills have helped me to succeed in the calculus II course. As I intend to pursue a career as an electrical engineer, the Math 2414 course has provided me with skills that I will need in order to succeed in many of my future science courses, as well as in my career as an engineer.

It all began in 1987 at Osaka University when a molecular biologist by the name of Yoshizumi Ishino was examining the E. coli bacteria genome and discovered that in the bacteria’s DNA there were repeating sequences formally known as palindromes. Palindromes mean that the

One of my favorite sources happens to be a video produced by Phil Riehl; entitled Fibonacci Numbers in Lateralus. [6] As the video points out what antiquity has amply annotated, math has been and continues to be utilized by all types of composers to fill sheets of astonishing emotional melodies for the masses to adore. Fibonacci Numbers in Lateralus blends history and fundamental mathematical approaches in music composition in order to provide a simple design methodology pertaining to Fibonacci numbers. Riehl’s analyzation of Tool’s song Lateralus (composed by Danny Carey) walks viewers through the Fibonacci numbers application, beginning with the drum introduction and through the sequencing of the lyrics. This study leaves no room for debate, as the evidence it produces is simply overwhelming.

The introduction and understanding of sequences, arithmetic and geometric in 8th grade was reviewed for content and standards in CPM CC Integrated 1 and MacDougall Littel Algebra 2. Sequences are defined as an ordered list of numbers that are in a specific pattern. Arithmetic Sequences are an ordered list of numbers where the difference between successive numbers is a constant value. Geometric sequences are an ordered list of numbers where the successive numbers differ by a common ratio.

Pi is an irrational number that represents the ratio of a circle’s circumference to its diameter. In the Mile of Pi, Numberphile printed out the first million digits of Pi in a continuous long piece of paper, which stretched for over a mile. They printed out pi and rolled it out for one mile to show that there are cycles of repeating sequences within pi and that every number does not appear evenly. Brady Haran also presents some interesting things that could be found along the way. He points out the Feynman Point which has the number 9 repeated six times. He also pointed out the point where Akira Haraguchi (known for memorizing the most digits of pi) memorized up to. When they reached the end of the mile long paper, the last digit was 1 in

Fibonacci sequence can have a connection with piano scales. Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89………… The C scale has 13 keys. The ratio is close to 0.618, this is known as the golden rule.

One of these is the Golden section. The Golden section is also referred to as the Golden ratio, which is a irrational number which is approximately equal to 1.618. The Golden ratio is found in many places in nature, however the most popular one is the gastropod shell, which is seen on snails and other organisms. If you take several squares and give them the side lengths of the Fibonacci sequence like 1,2,3,5,8 and 13 and the create a whirling rectangle using the squares and then if you start at the 1x1 square connect the opposite corners of each square without removing your pencil will create a gastropod shell (Freitag). The golden ratio comes into play when you divide the second square length with the first and then the third with the second and so on, like the following 2/1 = 2, 3/2= 1.5, 5/3 = 1.666…, 8/5 = 1.6, 13/8 = 1.625. And as can be seen they approach 1.618 which is the Golden ratio (Freitag). This beautiful structure helps supports intelligent design. One of the ways is because a structure or art represents its creator. Art and buildings today do not just spring up out of the ground without the hand of a creator. In the same sense it would be absurd to say that this art found in nature happened by chance, without the intervention of a creator, which we believe to be

Through the pursuit of a greater understanding of the known universe, our forefathers encountered patterns and anomalies which, through their extensive study, they were able to further their understanding of the universe which so intrigued them. Patterns are a reliable sample of traits, tendencies, or other observable characteristics of a person, group or institution. They are a combination of qualities, acts or tendencies that form a consistent or characteristic arrangement. Their counterparts, Anomalies are irregularities. They are a deviation from the common rule, type, arrangement or form. In other words, they are deviations from what is considered to be the norm, socially or scientifically. Patterns and anomalies have occurred within several instances in history. Dating back to the study of the heliocentric (the earth is round) nature of our planet by the famous Italian mathematician, physicist, philosopher and astronomer Galileo, man has always had a deep interest in the pursuit of knowledge to further our understanding of the natural world. And even as far back as the 17th century, patterns and anomalies had begun to arise and would later shape the way knowledge is gathered. Within Theory of Knowledge, patterns and anomalies have also occurred in the pursuit of knowledge. But first, what is this enigma we know to be knowledge. Knowledge can be said to be the fact or state of knowing; the perception of fact or truth; clear and certain mental apprehension. It is the