1. Who were the Pythagoreans? How did they try to solve the dilemma of Anaximander?
The Pythagoreans were a group of people who followed Pythagoras in 530 B.C. They are well known for their work in mathematics and for numerology, they tried to prove that everything is made up of numbers. The Pythagoreans tried to solve the problem of Anaximander by the theory of the Limit which was the flaw in Anaximander’s theory.
2. What are the basic characteristics of the Pythagorean philosophy? The characteristics of the Pythagorean philosophy is that all things are numbers, and the odd are the limited and the even the unlimited, and that that everything in the universe is the result of the two opposite but the same, forces.
3. What are the aspects of the phenomenon of change that makes it a “riddle”?
The aspects of the phenomenon of change that make it a riddle is that the way that it is worded means that people have to think about the answer, but if you don’t know how something changes or why it changes then you can’t really get an answer.
4. What was Heraclitus’s answer to the riddle?
Heraclitus’s answer to the riddle was “you can’t step into the same river twice” meaning that the river is not the same as the one you stepped in (Parker, 20).
5. What was Parmenides’ answer to the same riddle?
Parmenides’ answer to the riddle was that “change is an illusion” meaning all there is already exists and nothing can change. Parmenides disbelieves in his senses thus his reason that change
The creations of Pythagoras were very powerful during the era in which he lived in. He created a community of followers (known as the Pythagoreans) who believed that mathematics was fundamental and ‘at the heart of reality’ (source 1). The people in the society were all proficient mathematicians took mathematics very seriously, to the extent that it was similar to a religion (source 1).
Pythagoras made influential contributions to philosophy and religion in the late 6th century BC. He is often revered as a great mathematician and scientist and is best known for the Pythagorean theorem which relates the two sides of a triangle to the hypotenuse using the formula a squared plus b squared equals c squared. However, because legend and obfuscation cloud his work even more than that of other pre-Socratic philosophers, one can give only a tentative account of his teachings, and some have questioned whether he contributed much to mathematics or natural philosophy. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his colleagues and successors. Some accounts mention that the philosophy associated with Pythagoras was related to mathematics and that numbers were
The Pythagorean School, for example, contributed many ideas to the mathematic community, among them, studies of geometry and the theory of proof.5 Euclid also lived in the time of ancient Greece and became a prominent mathematician, as well as author of a book about geometry called, The Elements, considered the second best-selling book of all time.6 The works of Pythagoras and Euclid have become fundamental building blocks for any person with an eighth-grade understanding mathematics. With these advancements, as well as innovations from Archimedes and Apollonius of Perga, Islamic scholars translated their works and contributed even more, growing the worldwide understanding of mathematics.7 Greek progressions in geometry as well as the theory of proof contributed greatly to our ultimate understanding of contemporary mathematics, without which, our modern society would be
Hipparchus was a greek astronomer, geographer, and mathematician born 190 B.C. in Nicaea and died in 120 B.C. Rhodes, Rhodes, Greece. Hipparchus is accredited as the inventor of trigonometry because of his discovery of the first table of chords and also because he's the only person with valid data of the discovery and usage of trigonometry. In order to calculate the rising and setting of zodiacal signs, Hipparchus brought to light the division of circles into 360 degrees and the calculation of chords by looking at the triangles (spherical triangles or triangles that made up a circle) differently. Hipparchus experimented putting all triangles to be within a circle and with the three points each touching the
Many of the theorems we have today our proven fact, while back in Pythagoras’ day math was more critical thinking rather than problem solving. One example of Pythagoras’ critical thinking comes in the form of a simple triangle which he called Tetractys. A tetractys, or also known as tetrad, a triangular figure consisting of ten points arranged in four rows: one, two, three, and four points in each row, which is the geometrical representation of the fourth triangular number. This later became the mystic symbol of the Pythagoreans.
In order understand the events leading to the failure to recognize change, comprehension of the mechanism by which change is successfully recognized is requisite. According to the traditional understanding of this process, an individual must form an internal
Some may describe change as a transformation that may happen in stages or continuously, including any alteration that modifies how the world is or was. And even if it goes unrecognised, the world will continue to change.
The Greeks made several inventions, most notably in the subject of math, which are still studied today and taught in school. Mathematician Euclid is often credited as the “Father of Geometry” for all his work and studies in this subject, which are compiled in his books called The Elements. He organized known geometrical statements called theorems and logically proved all of them. He proved the theorem of Pythagoras (another Greek mathematician), which stated that the equation (c2 = a2 + b2) is true for every right triangle.
Anaximander was the first astronomer during his time. Anaximander believed that water was not the try reality. He thought if water was one true reality then the other 3 elements would be wiped out by it. Anaximander believed the ultimate reality is The Boundless. The boundless does not have a problem with opposing anything, which makes the boundless in everything. He believed the ultimate reality was unobservable and unspecific. So he determined the ultimate reality as unlimited or boundless. Anaximander also thought air was the life principle, air held all things together. Pythagoras was also a Pre- Socratic Philsopher from 570 BCE, he also had a different thinking of the ultimate reality. There is not a lot of imforamtion on Pythagoreas because he did not write anything about himself or about his beliefs. He may be known as the mand of science or a preacher of mystic of doctrines. Not much is known about about him but sources say he was from Samos. Pythagoreas was known as the greatest scientist during his time. He was Anaximanders disciple and followed his teacher teachings, He learns about aastrnomy from Anaxnimander and developed formulas like the pythagoreantherom. What he believed to be the ultimate reality was numbers. He believed reality is expressed in mathematical formulas. He tried to get away from the elements of physical life and only use numbers. In present day there are many laws that
For Pythagorean shapes and numbers was so important. He believed that the most perfect shape of the nature is circle. Therefore he put the earth in the center of a spherical world. According to Plato the movement of planets is in perfect circles. However now its known that the planetary orbits are ellipses and not
Defining Change Change can be defined as an event that occurs when something passes from one state or phase to another, the result of alteration or modification, to lay aside, abandon, or leave for another, become different in essence; to lose one's or its original nature, to make different; cause a transformation, or to make or become different in some particular way, without permanently losing one's or its former characteristics or essence. There are many different views as to the complexity of change. Some may believe change is an illusion and nothing ever really changes. However, the majority, such as the post structuralism theorists, believe that change is inevitable. Change can be viewed
Greeks such as Aristotle, Pythagoras, and Hippocrates have left concepts still used in modern science and mathematics. Their ideas laid a basis for future European thoughts and studies in the fields. Their contributions such as the creating the Pythagorean theory, the writing a comprehensive classification of species and the systematizing of medical knowledge would influence the way Europeans thought and studied the world. Hippocrates’ Oath is still sworn by all medical practitioners. The contributions of the Ancient Greeks in science and math built a foundation upon which future Europeans would build and lead to the development of modern
In Famous scientist’s (2015) article Pythagoras it states that five 3D solids were brought into existence by Pythagoras and the Pythagoreans, these items are identical on all of the sides and today they are called dice. The ranged from four sides all the way up to twenty and later Plato believed they belonged to the five Greek elements including aether (n.pag). They said “Pythagoras believed that, like everything else, music was based on whole number ratios. He also believed in its healing properties.”(n.pag) He later would learn that music was controlled by rations, like if a sting is shortened by half it raises an octave or if it’s shortened two-thirds then it moved the pit up one-fifth discovering that octaves are split into fifths not halves (n.pag). Those are the biggest discoveries of Pythagoras and the Pythagoreans, but they still has many more different discoveries. He has been accredited with a lot for being an enigma, and having written no books in his life. Even so the thoughts from learning of this brilliant mathematician tickles the mind and creates great and wonderful thoughts and ideas for many people. Learning about all of this should inspire anyone to travel and learn the ways of other countries and customs and even grasp their mathematical
Change. It is a concept often discussed as being an inevitable part of human life, something people has experienced numerous of times, and will continue to experience throughout their lives. Change comes in many forms and has a range of effects, which are either negative or positive on those who experience it and respond to it. Change, particularly in relation to the topic ¡°Changing perspective creates awakening¡±, is a view that is repeatedly explored and been written in poem/film by thousands of composers.
Euclid of Alexandria was born in about 325 BC. He is the most prominent mathematician of antiquity best known for his dissertation on mathematics. He was able to create “The Elements” which included the composition of many other famous mathematicians together. He began exploring math because he felt that he needed to compile certain things and fix certain postulates and theorems. His book included, many of Eudoxus’ theorems, he perfected many of Theaetetus's theorems also. Much of Euclid’s background is very vague and unknown. It is unreliable to say whether some things about him are true, there are two types of extra information stated that scientists do not know