Euclid of Alexandria “The Element” Euclid, also known as Euclid of Alexandria, lived from 323-283

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

Aeneas, the titular hero of Virgil’s Aeneid, is the flawed Trojan hero sent on a divine quest to found the new Troy and establish the basis for the Roman Empire. Along this journey, he is pushed to his limits both mentally and physically. This strain shows him to be a deeply Roman hero, especially in the values that come forward in his actions and response to tragedy. He embodies two major Roman values: pietas and respect for family, both past and future.

Greek mathematical and scientific ideas have also been a large contribution. Euclid, a Greek mathematician, wrote many theorems. His theorems have been very substantial because they are included in today’s mathematical problems. One of his theorems include “If two straight lines cut one another, the vertical, or opposite, angles shall be equal.” This specific theorem is used in proofs and it proves that all vertical angles are equal. Hippocrates was a Greek physician who created the Hippocratic Oath. This oath

King Philip II used phalanxes in his army. The greek city states could not agree on a single policy

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.

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.

The Abbasids were the first ones to study and translate important Greek and Indian mathematical book like Euclid's geometry text the Elements. They adopted a very Greek approach to mathematics of formulating theorems precisely and proving them formally in Euclid's ways.

Alexander of Macedon 356-323 B.C. By Peter Green was published on October 5, 1992. Alexander was born in 356 BC. He studied with Aristotle for three years, so he became interested in science. Him and his mother were put into exile basically disowned by Phillip, Alexander’s father. When his father remarried, he then had a stepdaughter. Because Phillip did not have another son, he longed for his sons return to become king after he passes away. Phillip was later assassinated in 336 BC. Then, Alexander became king and was ready to fulfill his dreams. Alexander made sure Macedonia would be safe before he left to achieve conquest. The youthful Alex acted rapidly to discard his residential foes and potential opponents to the throne, and to stifle an arrangement of uprisings that had risen in the wake of his father 's demise. He then set his sights on the Persian Empire, where he headed his armed force undefeated through Asia Minor. He spent his time and money training his troops a certain line-up, which is why they won almost every battle. Another reason for his success was his unpredictability. I enjoyed the book, although some of it was hard to understand and comprehend it was very well written. One of the most important things is Alexander’s ability to plan. He always wanted to do the unexpected. He would throw curve balls instead of leading his troops on a path of death. All the time he spent studying science he developed a strategic mind.

Geometry first originated as a way to solve problems in architecture and navigation. A famous figure in geometry is Euclid. Around 300 BC, he published a book, The Elements, which contained definitions, axioms, and postulates that would be regarded as a standard of mathematical reasoning for the next two thousand years (Mueller, 1969). Euclid basically gave the foundation of what is now called Euclidean geometry. However,

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

     Euclid's most famous work is his dissertation on mathematics The Elements. The book was a compilation of knowledge that became the center of mathematical teaching for 2000 years. Probably Euclid first proved no results in The Elements but the organization of the material and its exposition are certainly due to him. In fact there is ample evidence that Euclid is using earlier textbooks as he writes the Elements since he introduces quite a number of definitions, which are never used such as that of an oblong, a rhombus, and a rhomboid. This book first began the book by giving the definition of five postulates. The first three are based upon constructions. For example, the first one is that a straight line can be drawn between two points. These three postulates also describe lines, circles, and the existence of points and the possible existence of other geometric objects. The fourth and fifth postulates are written in a different nature. Postulate four states that all right angles are equal. The fifth one is very famous. It is also can be referred to as the parallel, the fifth parallel. It states that one and only one line can be drawn through a point parallel to a given line. His decision to create this

Omar was also a poet, philosopher, and astronomer. Omar’s works were translated in 1851, which was research on Euclid’s axioms. In the medieval period, he expanded on Khwarizmi’s and the Greeks mathematic works. He only worked with cubic equations only and focused on geometric and algebraic solutions of equations. In 1145AD, Al-Khwarizmi’s book was translated by Robert Chester, which made it possible for algebra to be introduced to Europe. After algebra was introduced in Europe, European mathematicians developed and expanded on algebra concepts. Even though algebra began in the Arabic countries, once European mathematicians obtained the information of algebra, they became the leaders of mathematical discoveries in the world (“Mathematics”).

Hypatia’s most well-known improvements to science and astronomy include her re-inventing of the hydrometer and charting of the stars. In mathematics, she is most notable for her contributions to working on different conic sections.Simply by dividing cones in different ways on a plane, she was able to develop the idea of different graphs and shapes such as parabolas, ellipses, and hyperbolas. Her understanding of the conic sections lead her to be one of the key contributors to the invention of the astrolabe as well (Morrow 1998). Christianity became extremely popular in Alexandria during the time when Hypatia lived there along with many riots breaking out. She was a pagan and known for defending science against any form of religion. She was mercilessly killed by an angry mob who accused her of religious turmoil. Although she died a horrible death of being stripped of her skin and limbs, her legacy lived and still lives. Mathematics was thriving in Athens, so that is where her students eagerly fled to. Although, many of her works that were stored in the library of Alexandria were destroyed by an Arab invasion. Hypatia is an important symbol for many generations and will always be considered to be the first woman in mathematics.

The Elements begins with the five postulates and their definitions, these postulates prove or define the existence of points, lines and circles and from there on go to define other aspects of geometry based upon the simpler concepts. The Elements consists of thirteen books. Some assumptions are not totally provable, such that there is only one straight line between two points. Euclid makes some assumptions that make his form of mathematics, Euclidean Geometry, sometimes at odds with other forms. His fifth postulate, states that only one line can be made through a point parallel to a given line, eventually, sometime during the 19th century this postulate was dropped in an attempt to study non-Euclidean geometries.