Greek Geometry

Although the original roots of geometry can be traced to the Egyptians, the Greeks built on most Egyptian theories that we use today. Greek astronomy and Greek geometry were both used in order to answer many difficult questions of the time. Without geometry, the study of astronomy would have been almost impossible, and vice versa. Even though many Greek theorems and principles were later built on by geniuses such as Einstein and Lobachevsky, the basis still remains the same.

The development of Greek geometry is said to be started by Thales of Miletus. Thales came from Egypt with a number of geometric principles that the Greeks were able to use for practical purposes. He lived towards the beginning of the sixth century B.C, and has been credited with many geometric theorems. Some of the most important theorems developed by Thales included:

- If two triangles have two angles and one side is respectively equal, then both triangles are congruent to each other.

- Angles at the base of any isosceles triangle are equal.

- If two straight lines intersect, then the opposite angles formed are equal.

Thales also did much work with the height of pyramids by measuring the height of the pyramid's shadow only at a specific time of the day. While most of his theorems were proven, some that were not pertained to a ship's distance from shore and the bisector of a circle. His discoveries led to the formation of many other theorems by later Greeks such as Pythagoras and Plato. These two men (next to Thales) contributed the most to Greek geometry. Pythagoras discovered and proved many different theorems and ideas that contributed greatly to the development of geometry. Some of Pythagoras's proven discoveries included:

- All of the angles in a triangle add up to the sum of two right angles.

- The development and use of geometrical algebra.

- The theorem of Pythagoras. a^2 + b^2 = c^2

Pythagoras also did many studies with triangles and developing or editing shapes. His most famous discovery was the Pythagorean theorem (listed above). This theorem combined the sides of a right triangle, and this led to the development of irrational numbers by Pythagoras later on. Pythagoras discovered that the square root of 2 was an irrational number.

Plato, another great mind of Greece, did more than just develop theorems for geometry, he stressed that geometry was essential. Plato believed that everyone should be well educated in mathematics as well as geometry.

Although the original roots of geometry can be traced to the Egyptians, the Greeks built on most Egyptian theories that we use today. Greek astronomy and Greek geometry were both used in order to answer many difficult questions of the time. Without geometry, the study of astronomy would have been almost impossible, and vice versa. Even though many Greek theorems and principles were later built on by geniuses such as Einstein and Lobachevsky, the basis still remains the same.

The development of Greek geometry is said to be started by Thales of Miletus. Thales came from Egypt with a number of geometric principles that the Greeks were able to use for practical purposes. He lived towards the beginning of the sixth century B.C, and has been credited with many geometric theorems. Some of the most important theorems developed by Thales included:

- If two triangles have two angles and one side is respectively equal, then both triangles are congruent to each other.

- Angles at the base of any isosceles triangle are equal.

- If two straight lines intersect, then the opposite angles formed are equal.

Thales also did much work with the height of pyramids by measuring the height of the pyramid's shadow only at a specific time of the day. While most of his theorems were proven, some that were not pertained to a ship's distance from shore and the bisector of a circle. His discoveries led to the formation of many other theorems by later Greeks such as Pythagoras and Plato. These two men (next to Thales) contributed the most to Greek geometry. Pythagoras discovered and proved many different theorems and ideas that contributed greatly to the development of geometry. Some of Pythagoras's proven discoveries included:

- All of the angles in a triangle add up to the sum of two right angles.

- The development and use of geometrical algebra.

- The theorem of Pythagoras. a^2 + b^2 = c^2

Pythagoras also did many studies with triangles and developing or editing shapes. His most famous discovery was the Pythagorean theorem (listed above). This theorem combined the sides of a right triangle, and this led to the development of irrational numbers by Pythagoras later on. Pythagoras discovered that the square root of 2 was an irrational number.

Plato, another great mind of Greece, did more than just develop theorems for geometry, he stressed that geometry was essential. Plato believed that everyone should be well educated in mathematics as well as geometry.

Related

- Good Essays
## Greek Geometry Essay

- 988 Words
- 2 Pages

For this reason, geometry is the study of mathematics relating to concepts including sizes, shapes, and position with the properties of space. But it is worth noting, the Greek did not “invent” Geometry but they did help mold our understanding of it into how we view modern geometry today. We also have to understand the Greeks had a very unique culture. They were extremely sophisticated and prized philosophical and scientific thought. To give an idea of who the key people were who played a major role in the history of geometry and also mathematics as a whole in Greece, we will look at five different mathematicians and briefly discuss their findings.

- 988 Words
- 2 Pages

Good Essays - Powerful Essays
## Mathematics In Ancient Greek Mathematics

- 1340 Words
- 3 Pages

(Allen) The Greeks built more onto what the Egyptians began building during the time of the pyramids. Many of the Greek mathematic manuscripts were lost over time, but there are many postulates, theories, and systems that still remain today and are used regularly by people all through out the world. One of the most important mathematical system that came out of the Greek time period was the Pythagorean theorem. Pythagoras was born in approximately 569 BC in Samos Greece. He is said to be the first pure mathematician.

- 1340 Words
- 3 Pages

Powerful Essays - Good Essays
## Mathematical and Scientific Discoveries of India, China and Greece

- 2290 Words
- 5 Pages

The Ancient Indians had some mathematical achievements. One of their mathematical achievements, which was shown in the Vedic texts, is that they had names for every number up to one billion. The Vedic texts also show that they managed to calculate irrational numbers, such as√3, very accurately (Whitfield, Traditions 42).... ... middle of paper ... ...affect us in numerous ways, such as in architecture, modern mathematics, modern science, the medical world, technology, and much more. Ancient India, China, and Greece all contributed to math and science, however, the Greek achievements influenced us the most. They invented Pythagorean Theorem, calculated the value of pi, discovered atoms, accurately found the size of the Earth, and had much more accomplishments than India or China.

- 2290 Words
- 5 Pages

Good Essays - Good Essays
## history of mathematics

- 1044 Words
- 3 Pages

Babylonians also developed other revolutionary mathematical concepts. Although, Pythagorean Theorem is attributed to Greek mathematician “Pythagoras”, the known and controversial Plimpton 322, a tablet formed out of clay, shows that long before Pythagoras, Babylonians knew the secret of the right-angled triangles. Other interesting contributions of Babylonians to our modern civilization include the use of number zero and the use of a 12 hour clock with 60 minutes per hour. Their sexagesimal number system helps the society of today in developing a 360 degree system. The use of standards in measuring lengths, weights, and volumes were also contributed by Ba... ... middle of paper ... ... possessed clarity and certainty, their concept of proof was not clear and uncertain.

- 1044 Words
- 3 Pages

Good Essays - Good Essays
## history of mathematics

- 884 Words
- 2 Pages

As the western civilization made some innovations in astronomy, Indian had already grasped the idea that the sun, moon, and the earth form a right-angled triangle when the moon is in half full and situated directly opposite the sun. It is really surprising th... ... middle of paper ... ...successors had successfully initiated the application of arithmetic and geometry of Greek to Algebra and vice versa. Al-Karaji was known to have started the algebraic approach free from geometrical operations and with the use of arithmetical types of operations which are still considered the core of today’s Algebra. In the areas of Mathematics, Indian’s and Arab’s contributions might not have yet received historical recognition and instead of giving credits, some of their works were accused to have been plagiarized from the western works. But their role for further development of mathematical ideas couldn’t be ignored.

- 884 Words
- 2 Pages

Good Essays - Good Essays
## Essay On Euclid

- 681 Words
- 2 Pages

Euclid was also famous for writing books using the topic on perspective, conic sections, spherical geometry, number theory, and rigor. Many mathematicians established the theories found in The Elements; one of Euclid’s accomplishments was to present them in a single, sensibly clear framework, making elements easy to use and easy to reference, including mathematical evidences that remain the basis of mathematics many centuries later. The majority of the theorem that appears in The Elements were not discovered by Euclid himself, but were the work of earlier Greek mathematician such as Hippocrates of Chios, Theaetetus of Athens, Pythagoras, and Eudoxus of Cnidos. Conversely, Euclid is generally recognized with ordering these theorems in a logical ... ... middle of paper ... ...discrete, because the radius may be indefinitely small. Obviously Euclid’s The Elements is by far the most famous mathematical work of classical antiquity, and also has the distinction of being the world’s oldest continuously used mathematical textbook.

- 681 Words
- 2 Pages

Good Essays - Satisfactory Essays
## The Elements of Newton's Philosophy, By Voltaire

- 515 Words
- 2 Pages

In this essay, published in 1738, Voltaire explains the philosophies of not only Newton, but in a large part Descartes because of his contributions in the fields of geometry. In Voltaire's concise explanation of Newton's and other philosophers' paradigms related in the fields of astronomy and physics, he employs geometry through diagrams and pictures and proves his statements with calculus. Voltaire in fact mentions that this essay is for the people who have the desire to teach themselves, and makes the intent of the book as a textbook. In 25 chapters, and every bit of 357 pages, as well as six pages of definitions, Voltaire explains Newton's discoveries in the field of optics, the rainbow spectrum and colors, musical notes, the Laws of Attraction, disproving the philosophy of Descarte's cause of gravity and structure of light, and proving Newton's new paradigm, or Philosophy as Voltaire would have called it. Voltaire in a sense created the idea that Newton's principles were a new philosophy and acknowledged the possibility for errors.

- 515 Words
- 2 Pages

Satisfactory Essays - Better Essays
## Prime Numbers

- 1205 Words
- 3 Pages

Prime Numbers Prime numbers and their properties were first studied extensively by the ancient Greek mathematicians. The mathematicians of Pythagoras's school (500 BC to 300 BC) were interested in numbers for their mystical and numerological properties. They understood the idea of primality and were interested in perfect and amicable numbers. A perfect number is one whose proper divisors sum to the number itself. e.g.

- 1205 Words
- 3 Pages

Better Essays - Satisfactory Essays
## Mathematical Impacts

- 1819 Words
- 4 Pages

Math had made it possible to understand this aspect of the cosmos, yet there were some differences on how they really worked. The Greeks were the first to “propose explanations for the motions of astronomical objects that relied on logic and geometry” Bennett, Donahue, Schneider, and Voit (2004). Math, helped explain, and defy the beliefs held for many years. The Greeks created a geocentric model, which places the earth in the center of the universe. This was attributed, to Thales (c. 624-546 B.C.

- 1819 Words
- 4 Pages

Satisfactory Essays - Better Essays
## Greek Contributions

- 1476 Words
- 3 Pages

(Pg. 55, Society and Technological Change) The Greek philosophers were very much drawn to mathematics. They invented its generality, analyzed its premises, and made notable discoveries of theorems by a rigid adherence to deductive reasoning. Geometry became the basic instrument for measuring all things. (Weinkopf, http://www.perseus.tufts.edu/GreekScience/Students/Chris/GreekMath.html) Plato examined the difference between the untrustworthy and changing world of the senses and that of the permanent truths that could only be found through rational thought.

- 1476 Words
- 3 Pages

Better Essays