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 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
[ Instructional strategies include the use of craft materials, such as scissors, measuring tape, push pins, geoboards, and algebra tiles. These support the learning task as it provides a manipulative for student to gain a conceptual understanding for perimeter and how the lengths can be represented with an expression containing a variable. As misguided errors appear, thought provoking questions will be given that lead the student toward recognizing their error and lead them toward the proper solution path.
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
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.
There is a need for students to understand and be able to construct geometric figures using a compass and straightedge. A compass and straightedge can benefit students to form accurate constructed geometric figures, also when technology isn’t available there’s always a compass and straightedge, and students will surpass a basic understanding using hand held tools vs. online tools.
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
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
The compass might seem like a simple resource, but it actually has a wacky history to it. The compass was actually made for coordinating buildings instead of navigation. It has changed in extreme amounts than before. The compass was even made in a different way and had more than 1 version! Ancient China invented the compass which was used and created in different ways.
Compass is an instrument for determining directions, as by means of a freely rotating magnetized needle that indicates magnetic north. The compass become very important for navigation. Before compass navigation they navigated with the stars. However, this mean of navigate wouldn’t last long because the stars aren’t out during day and when there is storm the stars aren’t visible either. The weather is unpredictable and this could occur for many days and night. The compass help navigate through storm and when star wasn’t visible, making traveling across the sea easier.
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
Construct is defined as "a representation of the universe, a representation erected by a living creature and then tested against the reality of that universe" (Kelly, 1955, p.12). According to Kelly, people make sense of the world by formulating their own models. They interpret things happened around them and organize those interpretations to construe their own models of reality. These models are called "constructs" by Kelly.
Euclid’s assumptions about his postulates have set the groundwork for geometry today. He provided society with definitions of a circle, a point, and line, etc and for 2000 was considered “the father of geometry.” His postulates proved to be a framework from which mathematics was able to grow and evolve, from two thousand years ago, till Newton and even to all our classrooms today.