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Präsentation zum Thema: "?."—  Präsentation transkript:

1 ?

2 Horus was the son Isis and Osiris, who was treacherously slain by by his brother Seth. In revenge, Horus sought out his uncle and slew him, but Seth teared his eye out and broke it in six parts.

3 ? But another god, Thot, the eye doctor, spit on the parts
and the parts came together again.”

4 This is why the Eye of Horus became the heraldic flag of ophthalmology
But is this all about? Thot was also the god of the moon, the creator of the calender and the master over time for gods and humans!

5 The Horus Eye a glimpse on Egyptian writing of numbers and dealing with fractions
Balder P. Gloor

6 Egyptian writing 2900 – 100 ac Hieroglyphic ≈ typwritten or print Hyeratic ≈ handwriting  difficult to read Demotic = Ptolemies, Romans Text from right to the left, numbers variabel In our time: Usually (!) transposed: from left to right (transliteration), then translated in Indo-Arabic Indo-Arabic (we) from left to right We and Egyptians from right to left! In German In English 13 – 19 also r  l But addition and subtraktion: 4 7 3 1 8 9 2 6

7 Egyptian numerical writing
handle rope rolled up Lotos flower Raised finger tadpole god Egyptian numerical writing decimal system no zero ( 0 )! additive To read in the direction where a head of a digit is looking

8 Egyptian = additive writing of numbers
20 against 6 digits !

9 Example of big numbers prisoners 100 000 20 000 120 000
cows goats prisoners

10 Addition

11 Major difficulties with fractions Egyptians calculated with unit fractions (1/ n)
the scribes had tables of important fractions, like 1/3, 2/3, of the most commun numbers, e.g. 2/3 of 27 (the month)  18 2/3 of 365 (the year)  243 the least common multiple ¾ was written ½ + ¼ 6/7 was written ½ + ¼ + 1/14 + 1/28 14/ / / /28 = 24/28 = 6/7

12 I 1 1/2 1/4 1/8 1/16 1/32 1/64 The whole eye = hekat
The six parts of the Horus Eye are used as hieroglyphs of fractions for measurement of volumes of grain (Hekat)

13 Hekat = dry measure for grain
The whole eye = 1 hekat 1 hekat ≈ 1 gallon ≈ 4,5 l ½ hekat ≈ ,25 l ¼ hekat ≈ 1 quart ≈ 1,125 l 1/8 ≈ 1 pint 1/64 hekat = 5 ro 1 ro = 1/325 Hekat ≈ 1 spoon

14 Summary: The egyptian scribes had, with the parts of the eye of Horus, simple hieroglyphes at hand, to write, add and handle fractions for the most important thing in daily life: FOOD (GRAIN); the story behind - a tale or myth to provide an explanation!

15 Where my wisdom comes from:
Richard J. Gillings, Mathematics in the time of the Pharaohs, Dover publications, New York 1972, 1981 Geniève Guitel, Histoire comparée des numérations écrites, Nouvelle Bibliothèque Scientifique, Flammarion, Paris 1975 André Pichot, Die Geburt der Wissenschaft, Campus, Frankfurt, 1991, 1995

16 Thank you for your attention
Osiris underneath the eye of Horus Thank you for your attention

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18 A glimpse on Egyptian writing of numbers and handling of fractions
Balder P. Gloor

19 ? But another god, Thot, the eye doctor, spit on the the parts
and the parts came together again.”

20 Osiris underneath the eyes of Horus
Fractions of the measures of grain Hekat = ca 4,5 l ≈1 gallon ro = 1/325 Hekat = 1 spoon

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23 Addition Rind Mathematical Papyrus

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30 Boisseau = scheffel = bushel

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32 Ägyptische Schrift 2900 – 100 ac
Hieroglyphen = „Maschinen- oder Druckschrift“ Hieratisch = Handschrift, verbunden  wird + unleserlich Demotisch = Ptolemäer, Römer Geschrieben von rechts nach links, Zahlen Zahlen lesen: Beginn dort wo ein Kopf hinschaut zum besseren Verständnis umgeschrieben  li nach rechts (Transliteration), dann noch in indo-arabisch transponiert („übersetzt“) indo-arabisch (wir) von links nach rechts! Aber Addition Subtraktion: auch wir von rechts nach links Ägypter von rechts nach links 4 7 3 1 8 9 2 6

33 ¾ wurde geschrieben ½ + ¼
Big problems with fractions Egyptians calculated with unit fractions (1/ n) For 2/3 the scribes had tables of the most commun z. B. 27  9 365  /3 ¾ wurde geschrieben ½ + ¼ 6/7 wurde geschrieben ½ + ¼ + 1/14 + 1/28

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41 Osiris war von seinem Bruder Seth getötet worden, und als Horus, der Sohn des Osiris und der Isis, seinen Vater zu rächen versuchte, riss ihm Seth ein Auge aus und zerriss es in sechs Teile. Doch ein anderer Gott, Thot, der “Augenarzt”, spuckte darauf und stellte es so wieder her” A. Pichot, Die Geburt der Wissenschaft, Campus Verlag 1995, S.164

42 Wappentier der Ophthalmologie Und was noch?
Das Auge des Horus Wappentier der Ophthalmologie Und was noch?