Geometry Of Geometry And Geometry

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

David Hilbert was a German mathematician whose research and study of geometry, physics, and algebra revolutionized mathematics and went on to introduce the mathematic and scientific community with a series of mathematical equations that have yet to be solved. Furthermore, his study of mathematics laid the groundwork for a variety of ongoing mathematic analyses, which continue to influence the world today.

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.

Geometry and Algebra are so crucial to the development of the world it is taught to every public high school in the United States, around 14.8 million teenagers each year (National Center for Education Statistics). Mathematics is the engine powering our world; our stocks, economy, technology, and science are all based off from math. Math is our universal and definite language “I was especially delighted with the mathematics, on account of the certitude and evidence of their reasonings.” (Rene Descartes, 1637).

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.

Stephanie, I would like to respond back to your posting by first agreeing our reason and experience is a little more subjective, than the two other parts of Wesley's quadrilateral. One of my experiences relates to the church I attended. I have never been a baptism ceremony where the minister said I baptize you in the name of the Father, the Son and the Mother. However, I have attended church where I heard a pastor pray in the name of Father/Mother God. The person praying was assigning a male and female characteristic to God. Therefore, if one could pray in the name of Father/Mother God one should be able to Baptize in the name of Father/Mother God, The Son and the Holy Spirit.

Geometry and mathematics were the cornerstone of Greek life. While the myths of the day were still acknowledged and, for the most part, accepted, it became less prevalent in society.

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,

When it comes to Euclidean Geometry, Spherical Geometry and Hyperbolic Geometry there are many similarities and differences among them. For example, what may be true for Euclidean Geometry may not be true for Spherical or Hyperbolic Geometry. Many instances exist where something is true for one or two geometries but not the other geometry. However, sometimes a property is true for all three geometries. These points bring us to the purpose of this paper. This paper is an opportunity for me to demonstrate my growing understanding about Euclidean Geometry, Spherical Geometry, and Hyperbolic Geometry.

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.

     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

Although Euclid (or the school) may have not been first proved by him, (in fact much of his work may have been based upon earlier writings,) he did manage to insert assumptions and definitions of his own to strengthen the various postulates into the form we know today.

According to Victor Katz in “A History of Mathematics (3rd Edition)” (Pearson, 2008), trigonometry developed primarily from the needs of Greek and Indian astronomers. But today, trigonometry and geometry were used on various fields such as: architecture, physical sciences, engineering, astronomers, medical imaging (CAT scans and ultrasounds), etc.