Rene Descartes Analytic Geometry Essays - Analytic Geometry

Rene' Descartes Analytic Geometry Essays - Analytic Geometry Rene' Descartes Analytic Geometry Analytic geometry was brought fourth by the famous French mathematician Rene' Descartes in 1637. Descartes did not start his studying and working with geometry until after he had retired out of the army and settled down. If not for Descartes great discovery then Sir Isaac Newton might not have ever invented the concept of calculus. Descartes concept let to calculus and Newton and G.W. Leibniz would not be know as well as they are today if it were not for the famous mathematician Rene' Descartes. Analytic geometry is a, branch of geometry in which points are represented with respect to a coordinate system, such as Cartesian coordinates, and in which the approach to geometric problems is primarily algebraic. (Analytic Geometry) Analytic geometry is used to find distances, slopes, midpoints, and many many other things using special equations and formulas to determine what a person is looking for. Analytic geometry concentrates very much on algebra, generally, it is taught to students in algebra classes and becomes very helpful when being used in geometry. It is not very often when geometry is taught not using the algebra to solve the problems, unless proving statements, analytic geometry is used most often when speaking of geometry, it is the guidelines of geometry. It is a set way to find out answers to problems. There are many simple formulas to analytic geometry, but some of them get very complex and difficult. Analytic geometry is not only used in math, it is very common to see it being used in any kind of science, logic, and any other mathematical subjects. There are formulas in this form of mathematics in which the volume of a gas is measured, and other formulas along those lines (Encyclopedia.com). Some formulas and equations of analytic geometry are: The midpoint formula- (change in x/2, change in y/2) Distance formula- square root of (change in x) squared -(change in y) squared Formula for slope- (Change in y)/(Change in x) Formula for a line- y=mx+b where m is the slope of the line and b is the y intercept. Equation of a line- ax+by+c=0 (Fuller, Gordon) To find perpendicular lines you take to slope of each line and multiply them together, if the result is one then the lines are said to be perpendicular. To find parallel lines the Slope must be exactly the same. These are just some simple facts about analytic geometry, it actually can get very complicated. When finding out about parabolas and ellipse's it gets difficult, there are many difficult and extended formulas in analytic geometry (Fuller, Gordon 7, 12, 18). Obviously these are just a few examples and analytic geometry goes on much further than what you see in these formulas. There are so many geometric formulas and theorems that they are almost impossible to put in a list. Analytic geometry has been combined with many other branches of geometry, now there are some things that are hard to decide wheater to label them algebraic or otherwise. Analytic geometry is broken up into two sections, finding an equation to match points and finding points to match equations. (Geometry) There are many other kinds of geometry such as demonstrative geometry that involves measuring fields and right angles. The early Egyptians developed this kind of geometry when building. There is descriptive geometry that involves using shapes that do not change when moved, they are definite, defined shapes. Another is non-three- dimensional geometry that uses analytic and projective geometry to study four dimensional figures. All of these kinds of geometry are commonly used (Geometry). Analytic geometry is used every day, it is defiantly something that can be extremely helpful if learned. Analytic geometry is used in architecture, surveying, and even business. In business analytic geometry can be used to find the maximum profit that can be made from a sale or event. As with all skills that are generally learned, analytic geometry is a great thing to know. Even the simple things, the basics, are very helpful. This subject can be broken down into the simplest things, such as having to walk to say Wal-mart and knowing when you are about half way, that is taking the distance from the starting point to the destination and dividing it by two

Herodotus, the Greek Historian

Herodotus, the Greek Historian Herodotus is known as  the father of history. We may think all the famous ancient Greeks came from Athens, but its not true. Like many important ancient Greeks, Herodotus was not only not born in Athens but wasnt even born in what we think of as Europe. He was born in the essentially Dorian (Hellenic or Greek, yes; but not Ionian) colony of Halicarnassus, on the southwest coast of Asia Minor, which at the time was part of the Persian Empire. Herodotus had not yet been born when Athens defeated Persia in the renowned Battle of Marathon (490 B.C.) and was only a young child when the Persians defeated the Spartans and allies at the Battle of Thermopylae (480 B.C.).​ Herodotus Homeland Lyxes, the father of Herodotus, was probably from Caria, in Asia Minor. So was Artemisia, the female despot of Halicarnassus who joined Xerxes in his expedition against Greece in the Persian Wars. Following victories over the Persians by the mainland Greeks, Halicarnassus rebelled against foreign rulers. In consequence of his part in rebellious actions, Herodotus was sent into exile to the Ionian island of Samos (homeland of Pythagoras), but then returned to Halicarnassus around 454 to take part in the overthrow of Artemisias son, Lygdamis. Herodotus of Thurii Herodotus calls himself Herodotus of Thurii rather than Halicarnassus because he was a citizen of the pan-Hellenic city of Thurii, which was founded in 444/3. One of his fellow colonists was the philosopher, Pythagoras of Samos, probably. Herodotus Travels the Known World Between the time of the overthrow of Artemisias son Lygdamis and Herodotus settling in Thurii, Herodotus traveled around most of the known world.  Herodotus traveled to learn about foreign countries. He traveled to have a look, the Greek word for looking is related to our English word theory. He also lived in Athens, spending time in the company of his friend, the renowned writer of great Greek tragedy Sophocles. The Athenians so appreciated Herodotus writing that in 445 B.C. he awarded him 10 talents- an enormous sum. The Father of History Despite major shortcomings in the area of accuracy, Herodotus is called the father of history even by his contemporaries. Sometimes, however, more accuracy-minded people describe him as the father of lies. In China, another man earned the father of history title, but he was centuries later: Sima Qian. Herodotus Histories Herodotus Histories, celebrating the Greek victory over the Persians, were written in the mid-fifth century B.C. Herodotus wanted to present as much information about the Persian War as he could. What sometimes reads like a travelogue, includes information on the entire Persian Empire, and simultaneously explains the origins (aitia) of the conflict, by reference to mythological prehistory. Even with the fascinating digressions and fantastic elements, Herodotus history was an advance over the previous writers of quasi-history, who are known as logographers.Sources East Is East And West Is West - Or Are They? National Stereotypes In HerodotusAncient History Sourcebook: 11th Brittanica: HerodotusCicero  De legibus 1.5: Herodotum patrem historiae