(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... ... middle of paper ... ...ere are gears used to select which numbers you want. Though Charles Babbage will always be credited with making the first “true” computer, and Bill Gates with popularizing it
mathematician known for his research in non-Euclidean geometry, group theory, and function theory (Felix Klein German Mathematician). Felix Klein’s father was part of the Prussian government. His father was secretary to the head of the government. After Felix Klein graduated from the gymnasium in Düsseldorf, he went to the University of Bonn and studied math and physics from 1865-1866. Before Felix Klein had studied non-Euclidean geometry, he first wanted to be a physicist. While still at the
In this essay the conic sections in taxicab geometry will be researched. The area of mathematics used is geometry. I have chosen this topic because it seemed interesting to me. I have never heard for this topic before, but then our math teacher presented us mathematic web page and taxicab geometry was one of the topics discussed there. I looked at the topic before and it encounter problems, which seemed interesting to explore. I started with a basic example, just to compare Euclidean and taxicab
Gauss Carl Friedrich Gauss was a German mathematician and scientist who dominated the mathematical community during and after his lifetime. His outstanding work includes the discovery of the method of least squares, the discovery of non-Euclidean geometry, and important contributions to the theory of numbers. Born in Brunswick, Germany, on April 30, 1777, Johann Friedrich Carl Gauss showed early and unmistakable signs of being an extraordinary youth. As a child prodigy, he was self taught in the fields
inspired by the math he read about and his work related to those mathematical principles. This is interesting because he only had formal mathematical training through secondary school. He worked with non-Euclidean geometry and “impossible” figures. His work covered two main areas: geometry of space and logic of space. They included tessellations, polyhedras, and images relating to the shape of space, the logic of space, science, and artificial intelligence (Smith, B. Sidney). Although Escher worked
Combinations in Pascal’s Triangle Pascal’s Triangle is a relatively simple picture to create, but the patterns that can be found within it are seemingly endless. Pascal’s Triangle is formed by adding the closest two numbers from the previous row to form the next number in the row directly below, starting with the number 1 at the very tip. This 1 is said to be in the zeroth row. After this you can imagine that the entire triangle is surrounded by 0s. This allows us to say that the next row (row
well-known division of math, known as Geometry. Thus, he was named ‘The Father of Geometry’. Euclid taught at Ptolemy’s University, Egypt. At the Alexandria Library, It was said that he set up a private school to teach Mathematical enthusiasts like himself. It’s been also said that Euclid was kind and patient, and has a sense of humor. King Ptolemyance once asked Euclid if there was an easier way to study math and he replied “There is no royal road to Geometry”. Euclid wrote the most permanent mathematical
deductive geometry. He also discovered theorems of elementary geometry and is said to have correctly predicted an eclipse of the sun. Many of his studies were in astronomy but he also observed static electricity. Phythogoras was a Greek philosopher. He discovered simple numerical ratios relating the musical tones of major consonances, to the length of the strings used in sounding them. The Pythagorean theorem was named after him, although this fundamental statements of deductive geometry was most
The Ellipse, Parabola and Hyperbola Mathematicians, engineers and scientists encounter numerous functions in their work: polynomials, trigonometric and hyperbolic functions amongst them. However, throughout the history of science one group of functions, the conics, arise time and time again not only in the development of mathematical theory but also in practical applications. The conics were first studied by the Greek mathematician Apollonius more than 200 years BC. Essentially, the conics form
determining absolute or relative locations of points by measurement of distances, using the geometry of circles, spheres or triangles. In addition to its interest as a geometric problem, trilateration does have practical applications in surveying and navigation, including global positioning systems (GPS). In contrast to triangulation, it does not involve the measurement of angles. In two-dimensional geometry, it is known that if a point lies on two circles, then the circle centers and the two radii
counting and record keeping, and they both developed systems of arithmetic (Allen, 2001, p.1). They used computation to find area, volume, circumference, and both used fractions. For both, the arithmetic was used for distribution of goods and the geometry for building. Their mathematics was very practical. What survives from both civilizations is records of problems solved by example. There is no record of generalizing principles or teaching principles supported by examples. This lack of mathematical
of his system.” Postulate 5, the parallel postulate, is today very controversial. Next, Euclid created a list of five common notions, of which only the fourth sparked a little debate. These common notions were more general and were not specific to geometry. After completing all these “preliminaries,” Euclid proved 48 propositions in Book 1. His first proposition was the equilateral triangle construction. However, this proof sparked a lot of controversy because EUclid didn’t prove that the two circles
Leonhard Euler was a Swiss mathematician born on April 15, 1707 in Basel, Switzerland. His parents were Paul Euler and Marguerite Brucker. Euler had two sisters,named Anna Maria and Maria Magdalena, and he was raised in a religious family and would be a faithful calvinist for the rest of his life because of his father being a priest of the Reformed Church and his mother being raised by a dad who was a pastor. Soon after Leonhard Euler was born, his parents moved
my time learning something that I possibly may never use outside of school?” Well, you’d be surprised if you knew all the different careers and jobs that use advanced math every day. For example, carpenters, contractors, and even optometrists use geometry and algebra quite often. Whether you want to believe it or not, math is around you everyday. The buildings you live in, the glasses you wear, and even furniture you sit on all starts with math. A carpenter is a type a craftsman, usually dealing with
Mathematics has been an essential part of man’s cognitive orientation and heritage for more than twenty-five hundred years. However, during such a long-time period, no universal acceptance has been formed because of the essence of the subject matter, nor has any widely justifiable interpretation has been provided for it. Mathematicians have endeavored to achieve patterns and forms, and have implemented them to devise advanced speculations and assumptions. Mathematics have advanced from counting,
strict rules. Pythagoras taught all the members of the society individually and personally. Due to the strict rules, there is not much known of Pythagoras’s school. Pythagoras has commonly been credited for discovering the Pythagorean Theorem of geometry. Though this theorem was previously utilized by Babylonians and Indians; it is widely believed that Pythagoras was first to prove it. He also studied properties of numbers which would be familiar to us today, like even and odd numbers. There are
and therefore called him Megarensis. Proclus supported his date for Euclid by writing “Ptolemy once asked Euclid if there was not a shorter road to geometry than through the Elements, and Euclid replied that there was no royal road to geometry.” It was in this city where Euclid developed, imparted, and shared his knowledge on mathematics and geometry with the rest of the world. Although little is known about Euclid's early and personal life, he was known as the forerunner of geometrical knowledge
dated as far back as 2690 C.A. They are also believed to be the first to use fractions, although they wrote their fractions differently than we do today. Their mathematics had an emphasis on measurement and calculations. With their vast knowledge in geometry they were able to calculate the areas of triangles, bricks, trapezoids and pyramids. The Egyptians practiced the mathematical arts through hieroglyphics, pyramids, and the Rhind Papyrus. Ancient Egyptians used hieroglyphics for many things including
beginning of the risen of Greece mathematics. Some famous people who achieve the Greece mathematic were Thales, Pythagoras, Hippocrates, Theaetetus, Eudoxus, and, Euclid. They all help construct the basic fundamental that we practice in elementary and geometry. One of the famous scholar, Euclid was able to develop some of the first rules for algebra. If all of these people didn’t have a love or complicated relationship with math, none of what we do in school would exist. For about three centuries, these
Pherekydes. Thales was also a teacher for himself and he learned some from him but he mainly inspired him. Thales was old when Pythagoras was 20 and so Thales told him to go to Egypt and learn more about the subjects he enjoyed which were cosmology and geometry. In Egypt most of the temples where the learning took place refused him entry and the only one that would was called Diospolis. He was then accepted into the priesthood and because of the discussions between the priests he learned more and more about