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Leonardo of Pisa, better known as Fibonacci, was born in Pisa, Italy, about 1175 AD. He was known as the greatest mathematician of the middle ages. Completed in 1202, Fibonacci wrote a book titled Liber abaci on how to do arithmetic in the decimal system. Although it was Fibonacci himself that discovered the sequence of numbers, it was French mathematician, Edouard Lucas who gave the actual name of "Fibonacci numbers" to the series of numbers that was first mentioned by Fibonacci in his book. Since this discovery, it has been shown that Fibonacci numbers can be seen in a variety of things today.
He began the sequence with 0,1,… and then calculated each successive number from the sum of the previous two. This sequence of numbers is called the Fibonacci Sequence. The Fibonacci numbers are interesting in that they occur throughout both nature and art. Especially of interest is what occurs when we look at the ratios of successive numbers. The Fibonacci numbers play a significant role in nature and in art and architecture. When you construct a set of rectangles using the seque...
Leonardo Da Vinci was born on Saturday April 19, 1452, just outside the small village of Vinci, in Italy’s Tuscany region (Kalz 20). He was born from a peasant woman named Caterina and fathered by a lawyer with the name of Ser Piero Da Vinci. His parents were not married (Macdonald 5). When Leonardo was a one year old his mother left him with his father for some other man. His father wanted him to be successful, so at the age of fourteen his father sent him to become an apprentice of a famous artist in Florence, Italy called Andrea Del Verrocchio (Macdonald 5). His apprenticeship lasted twelve years (Kalz 23), in which time Verrocchio inspired and encouraged Leonardo to be a free-thinker (Reed 28). Before his apprenticeship Leonardo had little formal education (Reed 9). After his apprenticeship under Andrea Del Verrocchio he began to work under Lorenzo de’ Medici (Kalz 23). In 1482, at the age of thirty, Leonardo moved to Milan and gained favor of the duke of Milan, Ludovico Sforza due to his singing voice and talent on the flute (Kalz 23). In 1483, while still living in Milan, Leonardo started his Treatise on Painting, which has many notes on experiments he continued on different ideas on optics such as the eyes, light, and shapes (Reed 28). Leonardo’s good fortune was interrupted in 1499 when the French inv...
Fibonacci traveled the Mediterranean world to study about Arab mathematicians of the time. Leonardo returned from his travels around 1200. In 1202, at age 32, he published what he had learned and introduced Hindu-Arabic numerals to Europe. His book was called Liber abaci. The book explained numeration with the digits 0?9 and place value. It also showed the importance of the new numeral system. The book educated Europe and had an impact on European thought. However, the use of decimal numerals did not become widespread until much later. Liber Abaci also solved a problem involving the growth of a supposed population of rabbits. The solution was a series of numbers known as Fibonacci numbers. The number sequence was known to Indian mathematicians as early as the 6th century, but Fibonacci's Liber Abaci introduced it to the West.
Lamb, Robert. "How are Fibonacci numbers expressed in nature?" HowStuffWorks. Discovery Communications, 24 June 2008. Web. 28 Jan. 2010. .
Nevertheless, that day followed me, and I tried to understand more about fractals through the resources I already had at my disposal-- through courses I was taking. Sophomore year, through my European History and Architecture courses, I learned about many ancient architectural feats-- Stonehenge, the Pyramids of Giza, the Parthenon, many Gothic Cathedrals, and the Taj Mahal-- and that they all somehow involved the use of the golden ratio. I will come back to how this relates to fractals later in the article, but for now know that each of these buildings use different aspects of their design to form the golden ratio. I was intrigued by the fact that fractals, what seemed to be something only formed by the forces of nature, were being constructed by human hands. Although I wanted badly to find out more, I waited until that summer, when I discovered a YouTube account by the name of Vihart. Vihart’s videos are not tutorials on how to do math, however Vihart’s ramblings about the nature and the concepts of the mathematical world have a lot of educational value, especially on topics that are more complicated to understand then to compute. Her videos on fractal math and their comparability to nature, helped to show me that...
The stranger explains it as a riddle of some sort and shows how you can make a drawing go on and on forever. “First you draw a square; then you draw a triangle to fit inside the square; then you draw a second triangle, and a third, and a fourth, each to fit inside the square..”. It seemed to be a fascination to the boy as it was to the stranger even though he was the one to draw it. When picturing this drawing, it seems like a spiral downwards and just continues forever, like it’s
Blaise Pascal has contributed to the field of mathematics in countless ways imaginable. His focal contribution to mathematics is the Pascal Triangle. Made to show binomial coefficients, it was probably found by mathematicians in Greece and India but they never received the credit. To build the triangle you put a 1 at the top and then continue placing numbers below it in a triangular pattern. Each number is the two numbers above it added together (except for the numbers on the edges which are all ‘1’). There are patterns within the triangle such as odds and evens, horizontal sums, exponents of 11, squares, Fibonacci sequence, and the triangle is symmetrical. The many uses of Pascal’s triangles range from probability (heads and tails), combinations, and there is a formula for working out any missing value in the Pascal Triangle: . It can also be used to find coefficients in binomial expressions (put citation). Another staple of Pascal’s contributions to projective geometry is a proof called Pascal’s theore...
Leonardo da Vinci was one of the greatest mathematicians to ever live, which is displayed in all of his inventions. His main pursuit through mathematics was to better the understanding and exploration of the world. He preferred drawing geographical shapes to calculate equations and create his inventions, which enlisted his very profound artistic ability to articulate his blueprints. Leonardo Da Vinci believed that math is used to produce an outcome and thus Da Vinci thought that through his drawings he could execute his studies of proportional and spatial awareness demonstrated in his engineering designs and inventions.
Pierre de Fermat Pierre de Fermat was born in the year 1601 in Beaumont-de-Lomages, France. Mr. Fermat's education began in 1631. He was home schooled. Mr. Fermat was a single man through his life. Pierre de Fermat, like many mathematicians of the early 17th century, found solutions to the four major problems that created a form of math called calculus. Before Sir Isaac Newton was even born, Fermat found a method for finding the tangent to a curve. He tried different ways in math to improve the system. This was his occupation. Mr. Fermat was a good scholar, and amused himself by restoring the work of Apollonius on plane loci. Mr. Fermat published only a few papers in his lifetime and gave no systematic exposition of his methods. He had a habit of scribbling notes in the margins of books or in letters rather than publishing them. He was modest because he thought if he published his theorems the people would not believe them. He did not seem to have the intention to publish his papers. It is probable that he revised his notes as the occasion required. His published works represent the final form of his research, and therefore cannot be dated earlier than 1660. Mr. Pierre de Fermat discovered many things in his lifetime. Some things that he did include: -If p is a prime and a is a prime to p then ap-1-1 is divisible by p, that is, ap-1-1=0 (mod p). The proof of this, first given by Euler, was known quite well. A more general theorem is that a0-(n)-1=0 (mod n), where a is prime...
Carl Friedrich Gauss was born April 30, 1777 in Brunswick, Germany to a stern father and a loving mother. At a young age, his mother sensed how intelligent her son was and insisted on sending him to school to develop even though his dad displayed much resistance to the idea. The first test of Gauss’ brilliance was at age ten in his arithmetic class when the teacher asked the students to find the sum of all whole numbers 1 to 100. In his mind, Gauss was able to connect that 1+100=101, 2+99=101, and so on, deducing that all 50 pairs of numbers would equal 101. By this logic all Gauss had to do was multiply 50 by 101 and get his answer of 5,050. Gauss was bound to the mathematics field when at the age of 14, Gauss met the Duke of Brunswick. The duke was so astounded by Gauss’ photographic memory that he financially supported him through his studies at Caroline College and other universities afterwards. A major feat that Gauss had while he was enrolled college helped him decide that he wanted to focus on studying mathematics as opposed to languages. Besides his life of math, Gauss also had six children, three with Johanna Osthoff and three with his first deceased wife’s best fri...
‘Nature abounds with example of mathematical concepts’ (Pappas, 2011, .107). It is interesting how much we see this now we know, regarding the Fibonacci Sequence, which is number pattern where the first number added to itself creates a new number, then adding that previous number to the new number and so on. You will notice how in nature this sequence always adds up to a Fibonacci number, but alas this is no coincidence it is a way in which plants can pack in the most seeds in a small space creating the most efficient way to receive sunlight and catches the most
Fibonacci Numbers originated from India hundreds of years ago. Though Fibonacci Numbers came from India, Leonardo of Pisa, better known as Fibonacci, made it known to the world. Leonardo came from a wealthy Italian family and traveled to North America to join his father. He was educated by the Moors and sent on business trips. “After returning to Pisa around 1200, Leonardo wrote his most famous literature, Liber Abaci” (Pearson). Leonardo featured a rabbit question in the book. The question was asked in a mathematical competition, he appeared in when he was young. Leonardo Fibonacci used the Fibonacci Numbers to solve it. Fibonacci Numbers is now used throughout our society.
The history of math has become an important study, from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. Mathematics started with counting. In Babylonia mathematics developed from 2000B.C. A place value notation system had evolved over a lengthy time with a number base of 60. Number problems were studied from at least 1700B.C. Systems of linear equations were studied in the context of solving number problems.
The Fibonacci Series was discovered around 1200 A.D. Leonardo Fibonacci discovered the unusual properties of the numeric series, that’s how it was named. It is not proven that Fibonacci even noticed the connection between the Golden Ratio meaning and Phi.
The man behind the Fibonacci numbers, Leonardo Fibonacci, was born in Pisa in 1175 A.D. During his life, he was a customs officer in Africa and businessman who traveled to various places. During these trips he gained knowledge and skills which enabled him to be recognized by Emperor Fredrick II. Fredrick II noticed Fibonacci and ordered him to take part in a mathematical tournament. This place would eventuall...
A rectangle is a very common shape. There are rectangles everywhere, and some of the dimensions of these rectangles are more impressive to look at then others. The reason for this, is that the rectangles that are pleasing to look at, are in the golden ratio. The Golden Ratio is one of the most mysterious and magnificent numbers/ratios in all of math. The Golden Ratio appears almost everywhere you look, yet not everyone has ever heard about it. The Golden Ratio is a special number that is equal to 1.618. An American mathematician named Mark Barr, presented the ratio using the Greek symbol “Φ”. It has been discovered in many places, such as art, architectures, humans, and plants. The Golden Ratio, also known as Phi, was used by ancient mathematicians in Egypt, about 3 thousand years ago. It is extraordinary that one simple ratio has affected and designed most of the world. In math, the golden ratio is when two quantities ratio is same as the ratio of their sum to the larger of the two quantities. The Golden Ratio is also know as the Golden Rectangle. In a Golden Rectangle, you can take out a square and then a smaller version of the same rectangle will remain. You can continue doing this, and a spiral will eventually appear. The Golden Rectangle is a very important and unique shape in math. Ancient artists, mathematicians, and architects thought that this ratio was the most pleasing ratio to look at. In the designing of buildings, sculptures or paintings, artists would make sure they used this ratio. There are so many components and interesting things about the Golden Ratio, and in the following essay it will cover the occurrences of the ratio in the world, the relationships, applications, and the construction of the ratio. (add ...