## The history of mathematics

Did you know the history of mathematics? Did you read any text about that history?

In this essay I want to show this history and what the importance of math?

Mathematics is a part of science which care about (the structure, order, and relation) that has evolved from elemental practices of counting, measuring, and describing the shapes of objects. It deals with logical reasoning and quantitative calculation, and its development has involved an increasing degree of idealization and abstraction of its subject matter.

There are many civilizations that used mathematics such as (Babylonia, Sumerian, ancient Egyptians, Greece and the mathematics of Islam) they were use mathematics in architectural building and design a lot of spectacular views.

The first one is ancient Egyptian era Writing began in Egypt at about this time, and much of the earliest writing concerned accounting, primarily of various types of goods. There were several different systems of measuring, depending on the particular goods being measured. From the beginning of Egyptian writing, there were two styles, the hieroglyphic writing for monumental inscriptions and the hieratic, or cursive, writing, done with a brush and ink on papyrus.

Much of our knowledge of ancient Egyptian mathematics comes not from the hieroglyphics inscribed on the hundreds of temples but from two papyri containing collections of mathematical problems with their solutions.

- The
*Rhind Mathematical Papyrus (RMP)*, named for the Scotsman A. H. Rhind (1833–1863) who purchased it at Luxor in 1858. The British Museum acquired it in 1865. - The
*Moscow Mathematical Papyrus (MMP)*, purchased in 1893 by V. S. Golenishchev (1947) who later sold it to the Moscow Museum of Fine Arts.

These two mathematical texts (RMP&MMP) inform us first of all about the types of problems that needed to be solved. The majority of problems were concerned with topics involving the administration of the state. That scribes were occupied with such tasks is shown by illustrations found on the walls of private tombs .Very often ,in tombs of high officials, scribes are depicted working together, probably in accounting for cattle or produce and these two papyrus help us to know how ancient Egyptian solve a lot of math problems.

References

The contents of these slides are taken from the following texts:

A History of Mathematics, an Introduction by Victor J. Katz , Addison-Wesley,3^{rd} edition ,2009.

The second era is Greece era

Greek merchants and accountants, for example, needed fractions as well .Generally, in this early period; the Greeks used the Egyptian system of “parts.” There was a special symbol, which represented a half (ሖ), (?) represented two-thirds. For the rest, the system was standard (?) represented one-third, (?) one-fourth, and soon. More complicated fractions than simple parts are expressed as the sum of an integer and different simple parts

The most complete reference to the earliest Greek mathematics is in the commentary to Book I of Euclid’s *Elements *written in the fifth century CE by Proclus ,some 800 to 1000 years after the fact. This account of the early history of Greek mathematics is generally thought to be a summary of a formal history written by Eudemus of Rhodes in about 320 BCE ,the original of which is lost. In any case, the earliest Greek mathematician mentioned is Thales (624–547BCE), There are many stories recorded about him, most written down several hundred years after his death. These include his prediction of a solar eclipse in 585BCE and his application of the angle-side-angle criterion of triangle congruence to the problem of measuring the distance to a ship at sea. He is said to have impressed Egyptian officials by determining the height of a pyramid by comparing the length of its shadow to that of the length of the shadow of a stick of known height, Thales is also credited with discovering the theorems that the base angles of an isosceles triangle are equal and that vertical angles are equal and with proving that the diameter of a circle divides the circle into two equal parts. Although exactly how Thales “proved” any of these results is not known, it does seem clear that he advanced some logical arguments.

References

The contents of these slides are taken from the following texts:

A History of Mathematics, an Introduction by Victor J. Katz, Addison-Wesley, 3rd edition 2009.

The final era is Mesopotamian Mathematics

Writing began in Mesopotamia ,quite possibly in the southern city of Uruk , at about the same time as in Egypt ,namely, at the end of the fourth millennium BCE .In fact , writing began there also with the needs of accountancy, of the necessity of recording and managing labor and the flow of goods. The temple ,the home of the city’s patron god or goddess, came to own large tracts of farming land and vast herds of sheep and goats.

The scribes of the temple managed these assets to provide for the well-being of the god (dess) and his or her followers. Thus, in the temple of goddess Inana in Uruk, the scribes represented numbers on small clay slabs, using various pictograms to represent the objects that were being counted or measured.

Using geometry for solving quadratic equations

Example: We present a problem given on tablet BM 13901.

The translation shows the geometric flavor of the problem:

“I summed the area and two-thirds of my square-side and it

Was 0; 35. You put down 1, the projection. Two-thirds of 1,

The projection, is 0; 40. You combined its half, 0; 20 and

0; 20. You add 0; 06, 40 to 0; 35 and 0; 41, 40 squares 0; 50.

You take away 0; 20 that you combined from the middle of 0,50

Square side is half

And in the modern mathematics

In modern terms, the equation to be solved is

*X^2*+ (2*/*3)* X *= 7*/*12.

For the solution, the scribe took half of 2/3 and squared it

(“combine its half, 0; 20 and 0; 20”), then took the result 1/9

(Or 0; 06, 40) and added it to 7/12 (0; 35) to get 25/36

(0; 41, 40). The scribe then noted that 5/6 (0; 50) is the

Square root of 25/36 (“0; 41, 40 squares 0; 50”). He then

Subtracted the 1/3 from 5/6 to get the result 1/2.

References

The contents of these slides are taken from the following texts:

A History of Mathematics, an Introduction by Victor J. Katz, Addison-Wesley, 3rd edition 2009.

As we see there are a lot of calculations that they do and no one know how they do it like ( The pyramids, Petra, Hanging Gardens Of Babylon and Al-hamraa palace)

It’s really architectural masterpiece, when you watch them, you will be amazed at the extent of the understanding mathematics it’s weird but it’s true.