Probably the most famous name during the development of Greek geometry is Pythagoras , even if only for the famous law concerning right angled triangles. This mathematician lived in a secret society which took on a semi-religious mission.
From this, the Pythagoreans developed a number of ideas and began to develop trigonometry. The Pythagoreans added a few new axioms to the store of geometrical knowledge.
Most of these rules are instantly familiar to most students, as basic principles of geometry and trigonometry. One of his pupils, Hippocrates , took the development of geometry further. He was the first to start using geometrical techniques in other areas of maths, such as solving quadratic equations, and he even began to study the process of integration. He studied the problem of Squaring the Circle which we now know to be impossible, simply because Pi is an irrational number.
He solved the problem of Squaring a Lune and showed that the ratio of the areas of two circles equalled the ratio between the squares of the radii of the circles. Alongside Pythagoras, Euclid is a very famous name in the history of Greek geometry. He gathered the work of all of the earlier mathematicians and created his landmark work, 'The Elements,' surely one of the most published books of all time. In this work, Euclid set out the approach for geometry and pure mathematics generally, proposing that all mathematical statements should be proved through reasoning and that no empirical measurements were needed.
This idea of proof still dominates pure mathematics in the modern world. Archimedes was a great mathematician and was a master at visualising and manipulating space. He perfected the methods of integration and devised formulae to calculate the areas of many shapes and the volumes of many solids. He often used the method of exhaustion to uncover formulae. For example, he found a way to mathematically calculate the area underneath a parabolic curve; calculated a value for Pi more accurately than any previous mathematician; and proved that the area of a circle is equal to Pi multiplied by the square of its radius.
He also showed that the volume of a sphere is two thirds the volume of a cylinder with the same height and radius. This last discovery was engraved into his tombstone. Apollonius was a mathematician and astronomer, and he wrote a treatise called 'Conic Sections. He also wrote extensively on the ideas of tangents to curves, and his work on conics and parabolas would influence the later Islamic scholars and their work on optics.
Greek geometry eventually passed into the hands of the great Islamic scholars, who translated it and added to it. In this study of Greek geometry, there were many more Greek mathematicians and geometers who contributed to the history of geometry, but these names are the true giants, the ones that developed geometry as we know it today. Martyn Shuttleworth Jan 8, Greek Geometry. Retrieved Nov 11, from Explorable. These types of situations were directly related to the geometric concepts of vertical, parallel, and perpendicular.
The geometry of the ancient days was actually just a collection of rule-of-thumb procedures, which were found through experimentation, observation of analogies, guessing, and sometimes even intuition.
Basically, geometry in the ancient days allowed for approximate answers, which were usually sufficient for practical purposes. For example, the Babylonians took p to be equal to 3. It is said that the Babylonians were more advanced than the Egyptians in arithmetic and algebra. They even knew the Pythagorean theorem long before Pythagoras was even born. The Babylonians had an algebraic influence on Greek mathematics. Egyptian geometry was not a science in the way the Greeks viewed geometry.
It was more of a grab bag for rules for calculation without any motivation or justification. Sometimes they guessed correctly, but other times they did not. One of their greatest accomplishments was finding the correct formula for the volume of a frustum of a square pyramid.
However, they thought that the formula that they had for the area of a rectangle could be applied to any quadrilateral. Primitive people could not escape geometry in the same way that we cannot escape it today. The concept of the curve was found in flowers and the sun, a parabola was represented by tossing an object, and spider webs posed an excellent example of regular polygons.
Symmetry could be seen in many living objects, including man, and the idea of volume had to be addressed when constructing a device to hold water. This is the type of geometry that very young children experience as they begin to play with objects. This type of geometry involves concrete objects.
Still before the time of recorded history, man began to consider situations that were more hypothetical. They were able to take the knowledge they had learned from observation of concrete objects and come up with general algorithms and procedures to be used in particular cases. Procedures such as trial and error, induction, and rule-of thumb were being used to discover.
This was mainly the geometry of the Babylonians and the Egyptians. In particular, Euclid created a thirteen volume series of books called the Elements of Geometry that describe different principals of geometry. The surviving portions of this source are still used today to help us understand geometry even further. One thing that set Euclid apart is that he spent a lot of time specifically defining different aspects of geometry.
These are geometric principals that are still taught in schools today, and many of these principals form the building blocks of other geometric principals. Archimedes is considered by many to be the last great geometer in Ancient Greece. After the Hellenistic period, the study of geometry declined steadily. There were many reasons for this, but the burning of the great library in Alexandria, Egypt, a Greek colony, the pursuit of geometry declined even further.
Although the reason why the library burned is under debate, the fact remains that much of the knowledge that was contained within was lost.
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