In this short paper, I will be discussing the history of geometric thought surrounding the Greeks. I will also include what the Greek culture contributed to geometry and how they used it. It is almost unavoidable for a student in nearly any math course, regardless of level, to hear about famous Greek mathematicians. This is because they made so many discoveries that are directly related to many of the math principles in use today. A small example of this idea is that we are in an entire course dedicated to geometry. This is for a good reason, because as I will now discuss, the geometry discoveries of the Greeks are invaluable to the world of mathematics. Looking through all the most famous mathematicians, you will find that quite a few of them
For this reason, geometry is the study of mathematics relating to concepts including sizes, shapes, and position with the properties of space. But it is worth noting, the Greek did not “invent” Geometry but they did help mold our understanding of it into how we view modern geometry today. We also have to understand the Greeks had a very unique culture. They were extremely sophisticated and prized philosophical and scientific thought. To give an idea of who the key people were who played a major role in the history of geometry and also mathematics as a whole in Greece, we will look at five different mathematicians and briefly discuss their findings. The first Greek mathematician I will discuss is Thales of Miletus. Thales of Miletus is not only known to be the first Greek mathematician, but also the first mathematician in the whole world. In order to find the various heights of pyramids and how far ships were from the shore, Thales used geometry. Additionally, Thales is known to be the first person to use deductive reasoning applied to geometry and also to have a mathematical discovery attached to their name. Thales theorem states that an inscribed angle in a semicircle is a right angle. One interesting
Pythagoras and his followers held the belief that “all things are numbers”. He also thought the designs of buildings should include ratios. One building that used geometry was the Parthenon in Greece. The ratio of the width to length is the same value of the ratio of height to width. Making a ratio with the height, width, and length would give 4:6:9 which is in accordance with the discoveries of Pythagoras and his theorem. Archimedes also used his knowledge to help create and improve catapult weapons. He used these to help defend the Greek against the Romans. The Greeks also connected their understanding of geometry and astronomy. They connected ideas they did not understand to the stars, such as the motion of the earth and the
Athenian architecture had an influence on us today as a modern society. The Parthenon’s constructed columns (Doc 6) were a part of Athenian architecture and thus Athenian culture. The column architecture are used in political buildings today such as the Lincoln Memorial so the we have copied the architecture. Mathematics in Athens was being developed by the mathematician Pythagoras. He created a method to solve for the long-diagonal side of a right triangle (hypotenuse), stating that a (one of the right triangle’s legs) squared plus b (one of the right triangle’s legs) squared equals c squared (Doc 9), and we still use this equation in measuring today. Socrates, an Athenian philosopher, said that we must question life, in fact, saying that without questioning life, it was not wrth living (Doc 7) and we think of that philosophy
Geometry, a cornerstone in modern civilization, also had its beginnings in Ancient Greece. Euclid, a mathematician, formed many geometric proofs and theories [Document 5]. He also came to one of the most significant discoveries of math, Pi. This number showed the ratio between the diameter and circumference of a circle.
For centuries, mathematicians tried to contradict Euclid's Postulate V, and determine that there was more than one line parallel to that of another. It was declared impossible until the 19th century when Non-Euclidean Geometry was developed. Non-Euclidean geometry was classified as any geometry that differed from the standards of Euclidean geo...
...other and it's always good to discover new things. Your mind should be wide open to things especially from the past, such as Ancient history. Also, comparing past rituals to modern day rituals are a good way to advance today's modern knowledge. The Romans & Greeks have accomplished so many things that we now take for granted. Looking into history can help you better understand what the people did for us back then in order to make us more thankful and open minded in the present day! A little bit of background information about the Ancient Greeks and Romans will be much more clearer for you to interpret. They made up lots of things relating to Mathematics & Science such as the discoveries of number theory, Mathematical analysis, and integral calculus. Despitethe fact that they impacted the U.S. in many different ways, it shows how knowledgeable & determined they were!
Euclidean distance was proposed by Greek mathematician Euclid of Alexandria. In mathematics, the Euclidean distance or Euclidean metric is the distance between two points, which is shown as a length of a line segment and is given by the Pythagorean theorem. The formula of Euclidean distance is a squ...
It is no mystery that without the Ancient Greeks, math as we know it today would not be the same. It is mind blowing to think that people who had no access to our current technology and resources are the ones who came up with the basic principles of the mathematics that we learn and use today without any preceding information on the topic. One of the best examples of such a person is Archimedes. Not only did he excel as a physicist, inventor, engineer, and astronomer, but he is still known today as one of the greatest mathematicians of all time. His contributions to the field laid out many of the basics for what we learn today and his brilliance shocked many. Long after his time, mathematicians were still stumped as to how he reached the genius conclusions that he did. Nicknamed “The Wise One,” Archimedes is a person who can never be forgotten.
The Palace of Knossos, a Minoan mud brick and timber structure on a shallow stone foundation, featuring a central courtyard, was constructed on an acropolis. It was a place for rulers to reside, shrines for religious ceremonies to be worshipped, the industrial production of objects, and administrative duties. Ample hallways, stairways, chambers, and light wells supplemented the ambitiously built structure. There were plenty of columns to mark he four awe inspiring entrance passages.
Our understanding of Greek Astronomy before the 4th century (BCE) is very piecemeal. Among the small number of surviving writings we have, the majority of our knowledge is composed of references and comments from Aristotle (mostly opinions and criticisms). What is clear is that the earth was believed to be spherical, and that there was an increasing determination to comprehend nature without supernatural explanations. One of the biggest sources of information for the Greeks actually came from “records of thousands of heavenly occurrences” left by the Babylonians (Ionides, Stephen A. and Margaret L.). Part of the Babylonian records left to the Greeks contained records of eclipses and had calculated the periods of their occurrences, the most famous of these was known as the Saros, which predicted that eighteen years and eleven days after an eclipse, another very similar eclipse will occur.
Over a period of time Greek art of the past has changed and evolved into what we value in todayís society as true art and services as a blue print of our tomorrow. As we take a closer look at the Geometric Period and stroll up through the Hellenistic Period allow me to demonstrate the changes and point out how these transitions have served the elements of time.
There are many different types of architecture, but they all somehow relate back to the ancient Greek’s architecture. Greeks developed their distinctive building types, and these forms, once established, remained remarkably consistent. (W.B Dinsmoor 1927) Characteristically, they combined the functional elements with close attention to the overall aesthetic effect of a building. Thus the ancient Greeks constructed glorious architectures. The Greek Architecture is divided into three main periods; the Geometric and Orientalizing periods (1100 B.C to 650 B.C), the Archaic period (660 B.C to 475 B.C), and the Classical period (475 B.C to 323 B.C). (A.W Lawrence 1957). Along with the different periods of Greek architecture, the Classical period had two main styles; Doric and Ionic.
Historically speaking, ancient inventors of Greek origin, mathematicians such as Archimedes of Syracuse, and Antiphon the Sophist, were the first to discover the basic elements that translated into what we now understand and have formed into the mathematical branch called calculus. Archimedes used infinite sequences of triangular areas to calculate the area of a parabolic segment, as an example of summation of an infinite series. He also used the Method of Exhaustion, invented by Antiphon, to approximate the area of a circle, as an example of early integration.
Physics began when man first started to study his surroundings. Early applications of physics include the invention of the wheel and of primitive weapons. The people who built Stone Henge had knowledge of physical mechanics in order to move the rocks and place them on top of each other. It was not until during the period of Greek culture that the first systematic treatment of physics started with the use of mechanics. Thales is often said to have been the first scientist, and the first Greek philosopher. He was an astronomer, merchant and mathematician, and after visiting Egypt he is said to have originated the science of 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 likely first an idea from Egyptian methods of measurements. With the help of his followers he discovered that the earth was a sphere, but he did not believe it revolved around the sun.
Pythagoras is truly a man unlike any other throughout history. Perhaps his greatest achievements are within the realm of mathematics; with his greatest known theory being the Pythagorean Theorem. His theory is so well known that even today it peaks the interests of many mathematicians, with more than 400 proofs being spawned off of his original theorem. Though his theorem is common knowledge in this modern age, his life still remains a mystery to most, similar to most pre-Socratic philosophers. What little we do know is often shrouded in rumors and conflicting reports, but despite this, it is clearly evident that his contributions to mathematics were substantial.
The 17th Century saw Napier, Briggs and others greatly extend the power of mathematics as a calculator science with his discovery of logarithms. Cavalieri made progress towards the calculus with his infinitesimal methods and Descartes added the power of algebraic methods to geometry. Euclid, who lived around 300 BC in Alexandria, first stated his five postulates in his book The Elements that forms the base for all of his later Abu Abd-Allah ibn Musa al’Khwarizmi, was born abo...
Euclid, also known as Euclid of Alexandria, lived from 323-283 BC. He was a famous Greek mathematician, often referred to as the ‘Father of Geometry”. The dates of his existence were so long ago that the date and place of Euclid’s birth and the date and circumstances of his death are unknown, and only is roughly estimated in proximity to figures mentioned in references around the world. Alexandria was a broad teacher that taught lessons across the world. He taught at Alexandria in Egypt. Euclid’s most well-known work is his treatise on geometry: The Elements. His Elements is one of the most influential works in the history of mathematics, serving as the source textbook for teaching mathematics on different grade levels. His geometry work was used especially from the time of publication until the late 19th and early 20th century Euclid reasoned the principles of what is now called Euclidean geometry, which came from a small set of axioms on the Elements. Euclid was also famous for writing books using the topic on perspective, conic sections, spherical geometry, number theory, and rigor.