Trigonometry has been used for thousands of years, but many don’t know where it all began and originated. There were many individuals that contributed to the development of this area of study, which has created the official study of the relations of the sides and angles of triangles and the relevant functions of any angles. As a Greek astronomer, geographer, and mathematician, Hipparchus of Rhodes is known as the person that laid the framework for trigonometry and is famous for his incidental discovery of precession of the equinoxes.
Philosophers have been known to take the ideas and teachings of other philosophies and then shape their own philosophies from them. Even if they do not outright claim they have done so or that they were influenced by an earlier philosophy, one can still find links between philosophers and their theories. Pythagoras, Plato, and Plotinus, though from all different historical and philosophical periods, formed philosophies similar to one another or built upon aspects from one another’s.
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).
One of Thales’ most renounced findings include his discovery in geometric studies in the area reading the rules of triangles. He came to the conclusion that if the base angles of an isosceles triangle are equal, the sum of the angles of a triangle are equivalent to two right angles. With the application of “geometric principles to life situations, Thales was able to calculate the height of a pyramid by measuring its shadow, and the distance of a boat to the shore, by using the concept of similar triangles” (pg. 5, Muehlbauer). Realizations such as these helped shape the beginning for the formation of natural law based on observations of the world through explanation.
a2+b2=c2 is the famous theorem that Pythagoras discovered and named, calling it the Pythagorean Theorem. This theorem applies to the right triangle stating, that by adding the length of both legs squared you can then find the squared length of the hypotenuse. This theorem is set up in way that if you know two of the variables, whether it is a leg(b or a) and the hypotenuse (c) or both legs (a and b), you will always be able to find the third measurement. However, why does this theorem work? Why does a2+b2=c2? That is the question that is asked hundreds of times by thousands of people. The answer to it is not a complicated one, the reasoning behind that is because there are at least 367 Pythagorean Theorem proofs out there (Source four). They
With man and nature, there is seemingly a constant curiosity that of which compels many to contemplate questions and to ultimately seek answers for those questions. In modern day, man seeks science, logic, and mathematics to name a few in order to search for those compelling thoughts. However, it was seemingly not that easy in the era of the Ancient Greeks. The Ancient Greeks did feature mathematics, however, to explain natural phenomenon, there was not a reference to science and logic, and like other nations it was rather, mythology.
In other words Claudius Ptolemy was an astronomer who was born during the year 85 AD . He spent most of his life studying how the Earth, Planets, and Sun moved. He was one of the very first astronomers so, not very much was known. A lot of people doubted him because in his time religion was very important and they thought that they only thing you couldn't see with the naked eye was Heaven and hell. His first time he published his observation was on March 26th 127. He spent almost 20 years getting his theory to make sense. He knew people wouldn't believe him so he broke down his discovery into thirteen books and each book was a part of his discovery. After he published his first one he was able to do a couple small ones, but sadly, the last of his discoveries was made on
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.
It is told that this important subject originated from a Muslim by the name of Muhammad ibn Musa al-Khwarizmi. A few interesting facts are that his works were highly based off of other greek manuscrips which had already discovered much of what is accredited to him. In addition to this, Historian Gerald Toomer writes quote,
The Greeks and the Egyptians used triangles as early as 3500 BCE. They used these triangles as rules of thumb. They could apply these rules to specific applications. For example, the Egyptians knew that the 3:4:5 ratio was a right triangle. They could derive this because for them to create a right triangle the Egyptian land surveyors used a rope divided into twelve equal parts, creating a triangle with three pieces on one side, four pieces on the second side, and five pieces on the last side. The right angle was found where the three-unit side came together with the four-unit side. This was a very efficient way to create right triangles. It’s a mystery as to how the Egyptians came up with this, but this was later used by Pythagoras (c.571 -
In the context of this article a lot of “knowledge” was math and learning from the Greek empire, which the uprising of Christianity was destroying, and the Byzantines like Hypatia wanted to preserve. Humans like the Christians tried to develop their own knowledge by destroying the works of previous scholars. They destroyed Museums, spread rumors, and killed other scholars in the streets. In this case the Byzantines preserved the knowledge of Greek scholars so that it might be used in the future. They did this by interpreting works of other scholars and commenting on them, like the successors of Diophantus.
Hypatia of Alexandria (350/370-415) was a mathematician and philosopher who “helped preserve Ptolemy’s Almagest and she wrote commentaries on Diophantus’ number theory and on the Conics of Apollonius.” (Hypatia Lessons) She was a daughter of Theon “astronomer and mathematician and the last to head the Museum at Alexandrian.” (Hypatia Lessons) He was also essential in spreading the works of Euclid and Ptolemy to future scholars. Hypatia gave lectures to her students about philosophy and mathematics at the same institute as her father as well as the possibility of giving lectures about the philosophies of Plato and Aristotle. Her students were all male and included both Christian and non-Christians alike. People came from
The pythagoreans thought of knowledge as a religion, and they had strict rules about how they did what. They did some crazy things, but they had many great ideas because of this “religion.” They considered knowledge to be the ultimate purification, thus the reason they called knowledge a type of religion. The pythagoreans were obsessed with math in a way. These people made a lot of things that are important today, so you could say that they “created some
Soc. But if he always possessed this knowledge he would always have known; or if he has acquired the knowledge he could not have acquired it in this life, unless he has been taught geometry; for he may be made to do the same with all geometry and every other branch of knowledge. Now, has any one ever taught him all this? You must know about him,