The different in mathematics between

the periods of the Ancient Egypt and Greek

1. Ancient Egypt

The ancient mathematics born in many areas in east world as practical science to help effort technique and agriculture. It is important to know that in mathematics east world none finds an example from that now we called verification. There is only description a process and not evidence.

For a long time, Egypt become richest area for research ancient history, because the worship that doing by Egypt people to people who have died, besides that area climate also become fascination for history researches. Civilizations in Egypt produce building in the form of temple and mausoleum. That building has important role to save the papyruses. Papyrus is an ancient material to write created by Egypt people and around 650 BC have been introduced in Greek.

There are some omissions from Ancient Egypt:

1. 3100 BC. At Egypt scepter, there are number expressing millions of and hundreds of thousand in Egypt hieroglyph, now this scepter save in Oxford museum.
2. 2900 BC. A big Pyramid in Gizeh builds by 100.000 workers in 30 years.
3. 1850 BC. There is papyrus Moscow contain 25 questions.
4. 1650 BC. There is papyrus Rhind (Ahmes), contains 85 questions in hieratic number by Ahmes. Now, this papyrus saves in British Museum.
5. 1500 BC. Indicative appliance of time with help shadow of the sun, now save in Berlin Museum.
6. 1350 BC. There is papyrus Rollin contains some calculation about bread price, now save in Louver.
7. 1167 BC. There is papyrus Harris, the document is compiled by Rameses IV contain masterworks of his father, Rameses III.

2. Greek

Greek goes forward along with the resignment of Egypt. Modern civilization emerges in small Asia, Greek, Sicilian and Italia. In there, for the first time in mathematics, peoples begin to say “why”. Paul Tannery, T.L. Heath, H.G. Zeuthan, A. Rome, J.L. Heiberg and E. Franle in tracing again history of mathematics in Ancient Greek. They only used sources from report in Arab and Nasrani report. They were reorganizing original report like Euclid, Apollonius, Archimedes, etc. A document about geometry and astronomy, which discusses the period before 355 BC by Eudemus, Aristotle’s student has losses. Then around 450 century, Neo-Platonist Proclus give his work about Commentary on Euclid, it was recognized as Eudemian Summary. This is sources of boldness which most can be trusted in Greek mathematics.

There are three important growth lines in the first 300 years in Greek mathematics. The first is the growth from the materials that compiled in unsure started from Pythagoras and his follower, Hippocrates, Eudexus, Theaterus, etc. It included the theorem that proves by Pythagoras until the solution “scandal logic” about irrational number by Eudexus. The second is the growth from ideas about infinitesimal, limit and way of quantifying which has no answer until the finding of calculus in modern-day. Then the last is about the curve in geometry except circle, straight line and area beside spherical object.

History is a key to open any memory in the past. With history, we can study many things, such as to know many famous figures with the finding, take the lesson from many fault in the past and correct it in the future.

In science of mathematics, we also know knowledge that called history of mathematics. We can study many things from a period before century until now. We can know famous figures in the past and the finding so we can use it to support our lesson. We also can more appreciate with the finding from the figures.

A. Activity in class

I never think before in science of mathematics, I will study history of mathematics. At the first meeting, our teacher asked to study history of mathematics we must have many sources, examples from books, CD, internet etc. He also gives us 4-point foundations to lesson history:

1. Dreams
2. Attitude
3. Ability in communication
4. Browsing internet

Those points can support us to study history of mathematics.

Then our teacher shows us containing from “Britannica Encyclopedia”. In there, we can get more information quickly. In the next meeting, our teacher asks many things about history of mathematics. History can shows from two aspects, artifact and idea. In history, we study the fact of the past but there are any problems such as the sources especially documents was very old so we need internet to up date the documents.

There is some manner to study mathematics:

• Empiric: observation, draw a conclusion with induction

Example: Pythagoras develops a theory, then we calls theorem of Pythagoras.

• Deduction: this manner develop by Euclid’s, he created book calls “the elements” consist of 13 books containing what referred as definition, postulate or axiom. Euclid also called as father of mathematics axiom.

Then Aristotle discovers infinite regress: the turning meaning which never ends.

There are two worlds in mathematics:

• Believe that mathematics have a reason
• Disbelieve that mathematics have a reason

A person said that mathematics must have dynamic foundation he is Immanuel Kant. He said that mathematics has foundation calls epistemology but in fact, epistemology is knowledge has not any foundation.

B. Activity outside class

In the second meeting, we get a duty, created the erudite masterpiece. Therefore, we search the sources to answers the questions. There are some questions, examples the different in mathematics between the periods of the Ancient Egypt and Greek, Pythagoras service and role to mathematics growth, Euclid’s finding, etc. Then, I got book entitle “the history of mathematics”, that book I refer to doing the duty. From the book, I get much information that I have never find previously. In there, I know that Pythagoras never find a theorem in right triangle that hypotenuse square is amount of other square two sides, Pythagoras only gives best verification systematically. Babylonian people have recognized that theorem since Hamurabi periods. Therefore, after I read the book I get the fact from the Pythagoras theorem. Besides that, I also read about mathematics in Babylonia and Egypt periods. Babylonian people used burned clay tablet as equipment to write while Egypt people used papyrus. Papyrus is ancient material to write as a paper made from water grass called papu. There are some papyruses in there, likes Moscow Papyrus, Rhind Papyrus, Rollin Papyrus, and Harris Papyrus.

Besides Pythagoras, that book also discuses the finding from many intellectual, likes Thales, Euclid, Eudexus, Plato, etc. Eudexus service in mathematics is proportion theorem that finished “logic scandal” about irrational number. Euclid’s service is created a book calls “The Elements” consist of 13 books discuses geometry, number theorem and elementary or geometry algebra. From the book, we can find intellectual like Paul Tannery, T.L. Heath, H.G. Zeuthan, A. Rome, J.L. Heiberg and E. Franle in tracing again history of mathematics in Ancient Greek. They only used sources from report in Arab and Nasrani report. They were reorganizing original report like Euclid, Apollonius, Archimedes, etc.