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1. Premise You surely know that But maybe you don’t know that “censo et cose egual a numero”

2. FRACTIONS

3. We have got used to thinking and to reading Maths like it’s written today. But Maths was used by humans from the Paleolithic Age, and it has been written in really different ways (engraved on caverns, on tablets, written by strange symbols named “runes” on papyrus, explained with poems and so on) from that Era to today. They started to write Maths as we do today only about 1600/1700. We are going to show you how Maths was written “YESTERDAY” and how it is “TODAY”

4. Comenius Project 2011 Parts of Algebra First of all,Algebracan be divided into: - RHETORICAL = expressed by words and lines generally in latin or in the current language (from the start of Maths* to 1550 ca) - SYNCOPATED = composed by abbrevations to express unknowns and mathematical operations(from 1550 to 1650 ca) - SYMBOLIC = uses letters and symbols to express unknowns and mathematical operations (from 1650 to today) * We can define “intuitive algebra” as the one used by pre-egyptian people to describe Nature.

5. Maths in the world

6. “INTUITIVE” ALGEBRA RHETORICAL ALGEBRA BULGARIAN AGE CHINESE AGE PRE - EGYPTIAN AGE PALEOLITHIC AGE EGYPTIAN AGE RHETORICAL ALGEBRA SYNCOPATED A. SYMBOLIC A. ROMANS AND GREEKS 1300 – 1550 1550 - 1650 1650 - 2011

7. Babylonian maths SeeBabylon numbers on the twinspace by GiuliaCelano andValentina Benedictis

8. TheancıentEgyptıan Math PAPYRUS PYRAMIDS WHAT? WHERE? WHO? FRACTIONS WHEN?

9. There are three known egypt mathematicians: Ahmes Joseph Robins

10. MAYAS: THE ANCIENT PROPHETS ONE CULTURE, ONE HISTORY

11. 2nd session:THE TWENTY SYSTEM • The dot and the dash were the only symbols. • The dot represented the number 1 and the dash the number 5. Therefore, the “ ._” meant 6 for the tribe of Mayas. • The number 0 is another symbol of the Mayan calendar. • The Mayas were the first tribe to use zero.

12. 3RD SESSION:THE MAYAN CALENDAR • What’s the Mayan Calendar? • the most acurrate calendar, that has ever been invented by any culture, including our own. • It’s based on 3 circles: • A) the Great Circle(26000 years) • B)the Tzolkin Circle, or “Sacredcircle”, which included260 days • C) the Haab Circle, the only calendar with 365 days(approximately)

13. A) THE HAAB CIRCLE: • part of the Mayan calendar • determines the solar year • consists of 18 months, and each of themof 20 days, plus an additional period of 5 days at the end of the year • foundation of the rural calendar

14. B) the Tzolkin circleOR the "SACRED CIRCLE»: • corresponds to the cycle of human gestation (biologically) and the time between planting and harvesting corn at a certain elevation in mountainous regions (agriculturally). • (astronomically) is used to follow thephases of the moon. • Two circlesare equal to 260 days and 3 eclipses. • the Mayas predicted eclipses using the Tzolkin . • A complete circle Tzolkin-Haab iscompleted once every 52 years.

15. c)the great circle: • The Mayas also created a Large Circle (26,000 years), consisting of 5 cycles of 5,125 years. • Each of these circles is cosindered to be a world creation. • This long circle (3113 BC-2012 AD) is called the "age of the 5th Sun. • Every great circle( according to the Mayas)closeswith a major disaster.

16. Chinese math

17. The Nine Chapters on the Mathematical Art,

18. UTILISATION

19. Rectangular Fields • into two parts: We have a/b and c/d one about the So (a/b)+(c/d) formulas for = (a/d + b/c)/ bd calculating the area of fields, the other rules for the operations on fractions.

20. I would like to know the area of my field … • So I multiply the length by the width

21. Indian Mathematicians

22. Introduction • Indians’ texts with clear mathematical content that were written during the pre-Christian times, have not been found so far. • Works with clear mathematical content appeared after 500 A.C. • The most remarkable Indian mathematicians are Aryabhata, Brahmagupta and Bhaskara.

23. ARYABHATA • Aryabhatiya in 499 • Astronomy and mathematics • a/b=c/x then x=bc/a

25. BHASKARA • in 1114. • Lilavati • x²=1+py² • Pythagorean theorem

26. Arabian math

27. Project Comenius Numbers and Symbols ArabianMathematicians A little bitofHistory…

28. Al-Khwarizmi

29. ArabicNumbers InIndian 1 2 3 4 5 6 7 8 9 Makessense, doesn’tit?! InArabic InArabic (nowadays) InArabic (nowadays)

30. Comenius Project 2011 1300 - 1400 - 1500 a.C. As we said before mathematicians in this period used the rhetorical algebra. “Quando che il cubo con le cose appresso se agguaglia a qualche numero discreto trovan due altri defferenti in esso. Da poi terrai questo per consueto che il lor prodotto sempre sia eguale al terzo cubo delle cose neto. El residuo poi suo generale dalli loro lati cubi sottratti verra la tuacosaprincipale.” Here there is an example of this kind of algebra. In this short poem Tartaglia (Italian mathematician who lived in 1500) explains the way to solve this cubic equation: x3 +px = q. Causa/res/cosa were the words to indicate the unknown. Census was the one used to indicate unknown’s powers of two.

31. Then, around 1550/1600 they started to use the “syncopated algebra” in which they use both words and symbols. For example Luca Pacioli to say 3x2 - 5 + 6 = 0, wrote: 3 census p. 6 de 5 rebus ac 0 One century later, meaning the same thing, François Viète wrote: 3 in A quad – 5 in A plano + 6 aequatur 0. From this we can clearly see the evolution of mathematical language.

32. Comenius Project 2011 Considerations The passage from “intuitive” Maths and “rethoric” Maths to “symbolic” Maths is surely an advantage. Mathematics becomes easier to write and to understand. But, above all, it becomes INTERNATIONAL. That is why we can be here today and understand each other: because Maths changes through History.

33. The end Presentation done by : • Nikolaou Eirini, Bakogianni Christina, Koumaditi Kleopatra, Belet Auriane : Indian Mathematicians • Maria-Christina Fouka, Foteini-Maria Karkaletsou : Mayas • Pauline Blanc : Chinese Maths • Sofia Rodrigues, Mariana Santiago, Berivan Yavuz : Egyptian Numbers • Maria Joao Santos, Joana Bigodinho : Arabian mathematicians All the complete files are on the twinspace, in Math History Presentations, Numbers History section.