Why Beauty is truth: A History of Symmetry by Ian Stewart is in depth on how mathematicians came about symmetry. Instead of coming across symmetry by geometry as someone today might think, Stewart shows how it became an idea by algebra. Most of the book is told in chronological order from the early Egyptians and Babylonians discovery of the quadratic equation and leading up to the impossibility to solve the quintic equation. Through each chapter we see how mathematicians get one step closer to solving the quintic, and their struggles they faced along the way.
Early Equations The earliest record of the quadratic that we know of dates back to the Babylonians, solved on a tablet. Historians and Mathematicians do not have any clue about how the Babylonians came to solve the quadratic, but think that they came across is geometrically. Stewart shows how Euclid’s Elements of Geometry introduced the basic methods for constructing a proof. Included in Elements in Proposition 9 of Book I is how Euclid shows how to bisect an angle with only a compass and a straightedge. Elements did not include information on how to trisect and angle though, which could have been used for the construction of a regular 7-gon. It was Euclid’s Elements that inspired mathematicians to take it one step further and solve the things that Euclid had left out, such as squaring the circle with only a compass and a straightedge. The difficulty of these problems led mathematicians to change the way that they
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).
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.
“Beauty” by Tony Hoagland was written in 1998. In this poem, Hoagland expresses his feelings on how women care too much about physical appearances. Throughout his poem he tells the story through the eyes of a brother of a girl who learns to love herself for who she is. Hoagland’s poem stresses the importance that beauty goes deeper than the surface. Throughout his poem, Tony Hoagland uses many literary devices to perfect his poem. These devices include the message, tone, imagery, figures of speech, and personification.
Throughout his novel, Perfect Peace, Daniel Black focuses on the idea of feminine beauty and what it means to be a beautiful black woman or a pretty black girl. Black highlights the problematic nature that rigid internalized beauty standards can have on women well into their elderly years. Black uses both Emma Jean and Perfect’s characters, as well as addition characters such as Caroline and Eva Mae, to show the negativity associated with black beauty standards.
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
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.
Gazing at beauty does inexplicable things to the human mind, it is uncontrollable and difficult to maintain stability. In the story A&P by John Updike, Sam and his co-workers are engrossed by the three girls in the grocery store. One could say, the opposite sex holds the power of desire.
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.
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,
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”).
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.
Pythagoras’ biggest mathematical work was the Pythagorean Theorem. This theorem had already been discovered by the Babylonians, but Pythagoras was the first to prove that it was correct. This theorem relates to the three sides of a right triangle. It states that the square of a hypotenuse is equal to the sum of the squares of the other sides. The formula for this is “a^2+b^2=c^2.” In this formula a and b = the two shorter sides of the right triangle. C is equal to the side that is opposite of the right angle, or the hypotenuse. Pythagoras was also responsible for introducing more rigorous
Mathematics has contributed to the alteration of technology over many years. The most noticeable mathematical technology is the evolution of the abacus to the many variations of the calculator. Some people argue that the changes in technology have been for the better while others argue they have been for the worse. While this paper does not address specifically technology, this paper rather addresses influential persons in philosophy to the field of mathematics. In order to understand the impact of mathematics, this paper will delve into the three philosophers of the past who have contributed to this academic. In this paper, I will cover the views of three philosophers of mathematics encompassing their