## Greek and egyptian mathematicsBy: Andrea cardenas, juan daniel rojas and daniela angel

### Greek Mathematics

The Greeks adopted elements of mathematics from the societies they conquered, among these were Babylonians and the Egyptians. However they started to make new contributions of their own. Greeks were the first to establish the idea of mathematical proof, and the method of using logical steps to prove or disprove theorems. Most of greek mathematics were based on geometry.

“For Greek thinkers, maths wasn’t simply a means of calculating amounts but a way of testing reality and understanding the true nature of the world around them. Indeed, Pythagoras is believed to have coined both the words “philosophy” (“love of wisdom”) and “mathematics” (“that which is learned”).”
PYTHAGORAS

#### Background

Pythagoras founded a brotherhood which influenced the ideas of great mathematicians like Plato and Aristotle. He is even considered the first "true" mathematician. However most of his discoverments are known because of his scholars, due to the fact that he did not leave many writings. In his group odd numbers were considered female and even numbers were considered male.

#### Geometry

Pythagorean Theorem

Pythagoras biggest contribution was showing that geometric elements corresponded with geometry. He is mostly remembered for the Pythagorean Theorem. This theorem shows that if a triangle has a right a right angle, the square of one side plus the square of the other equals the square of the hypotenuse.

#### Music

Pythagoras also showed that the intervals between music notes will always be whole number ratios.

Music Notes
Archimedes

#### Background

Archimedes of Syracuse (c. 287 BC – c. 212 BC) was a mathematician, physicist, inventor, engineer and astronomer in Ancient Greek society. He was the first to figure out the volume of an irregular shape. Some of his most important works were Archimedes' principle, Archimedes' screw, hydrostatics, levers, and infinitesimals. He died when Syracuse was conquered by Roman general Marcus Claudius Marcellus and he was killed by a Roman soldier.

#### Geometry

Method of Exhaustion

Archimedes used the Method of Exhaustion to figure out the approximate value of pi and prove the formula A = π r2 . This formula we have used since elementary school to obtain the area of a circle using the radius, showing that is one of the basics of geometry. He was also able to calculate the area of the arc of a parabola by adding infinite serieses.

Egyptian Mathematics

### Egyptian Mathematics

The Pharaoh’s surveyors used measurements based on body parts ( the width of the hand, the measurement from elbow to fingertips) to measure land and buildings very early in Egyptian history, and a decimal numeric system was developed based on the ten fingers in our hands, the earliest fully-developed base 10 numeration system. They also demonstrated the use of unit fractions based on the symbol of the Eye of Horus, where each part of the eye represented a different fraction, each half of the previous one. They were also aware of the rule that a triangle with sides 3, 4 and 5 units yields a perfect right angle, before Pythagoras. Egyptian builders used ropes knotted at intervals of 3, 4 and 5 units in order to ensure exact right angles for their pyramids.

Eye of Horus
The study of mathematics, like the Nile, begins in minuteness but ends in magnificence.
Ahnes

#### Background

Ahmed is the first known contributor to mathematics. He was a scribe who lived during the Second Intermediate Period in Egypt and the Eighteenth Dynasty. He is known for the Rhind Papyrus, which dates back to 1650 BC.

#### Rhind Papyrus

The Rhind papyrus was written in hieratic, it includes mathematical topics such as division, fractions, problems on the 4 basic operations (addition subtraction, multiplication, and division), solutions of equations, volume, progression, the two-third rule, etc. The papyrus is divided in three parts: Algebra and Arithmetic, Geometry and Miscellany. In the first part there are 41 problems, in the second part there are 19 problems and in the third part there are around 30 problems. Nothing else is known about Ahmes, only the contributions written in this papyrus. Some small parts are displayed in the Brooklyn museum, however a fragment is missing.

The Story of 0

### The Story of zero

Zero was invented by Babylonians, Mayans and Indians. Ancient society knew the concept of ‘nothing,’ however they did not have a symbol or letter to represent it.

Babylonians developed the Sumerian counting system where they had a placeholder symbol to represent zero. The Mayans also developed zero as a placeholder. However, it was in India where zero became an important part of the number system. The Indian scholar Pingala used binary numbers and was the first to use the Sanskrit word ‘sunya’ for zero. In 628 AD, Brahmagupta used a dot below numbers to symbolize zero, instead of a blank space. Brahmagupta also used zero in writing rules for mathematical operations. The concept of zero soon spread to China and the Middle East. A Persian mathematician, Mohammed ibn-Musa al-Khowarizmi, proposed that a small circle be used if no number was being used in the tens place. The Arabians called this ‘siphr’ or empty. Al-Khowarizmi used zero to invent algebra. In around 900 AD, the number system was brought to Europe by the Arab traders. Europeans adapted the concept of zero to their number system. Zero is now an essential part of mathematics.

### Work Cited

http://www.storyofmathematics.com/egyptian.html

http://www.storyofmathematics.com/greek.html

http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Pythagoras.html