?. Horus was the son Isis and Osiris, who was treacherously slain by by his brother Seth. In...

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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.

But another god, Thot, the eye doctor, spit on the parts

and the parts came together again.”

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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!

The Horus Eyea glimpse on Egyptian writing

of numbers and dealing with fractions

Balder P. Gloor

Egyptian writing 2900 – 100 acHieroglyphic ≈ typwritten or print

Hyeratic ≈ handwriting difficult to readDemotic = 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 13 - 99 In English 13 – 19 also r l

But addition and subtraktion: We and Egyptians from right to left!

4 7 3 1

3 8 9 2

1 1

8 6 2 3

Egyptian numerical writing

decimal system

no zero ( 0 )!

additive

To read in the direction where a head of a digit is looking

handle

rope rolled up

Lotos flower

Raised finger

tadpole

god

Egyptian = additive writing of numbers

7 50 100 20 000 400 000 3000

7 5 1 3 2 4

4 2 3 1 5 7

20 against 6 digits !

cows goats prisoners

400 000 1 422 000 120 000

prisoners

100 000

20 000

120 000

Example of big numbers

Addition

Major difficulties with fractions Egyptians

calculated with unit fractions (1/ n)

¾ was written ½ + ¼

6/7 was written ½ + ¼ + 1/14 + 1/28 14/28 + 7/28 + 2/28 + 1 /28 = 24/28 = 6/7

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

1

1/2

1/4

1/8

1/16

1/32

1/64

I

The six parts of the Horus Eye are used as hieroglyphs of fractions for measurement of volumes of grain (Hekat)

The whole eye = hekat

Hekat = dry measure for grain

The whole eye = 1 hekat

1 hekat ≈ 1 gallon ≈ 4,5 l

½ hekat ≈ 2,25 l

¼ hekat ≈ 1 quart ≈ 1,125 l

1/8 ≈ 1 pint

1/64 hekat = 5 ro

1 ro = 1/325 Hekat

≈ 1 spoon

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!

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

Thank youfor your

attention

Osiris underneath the eye of Horus

A glimpse on Egyptian writing of numbers and

handling of fractions

Balder P. Gloor

But another god, Thot, the eye doctor, spit on the the parts

and the parts came together again.”

?

Osiris underneath the eyes of Horus

Fractions of the measures of grain 1 Hekat = ca 4,5 l ≈1 gallon 1 ro = 1/325 Hekat = 1 spoon

Addition

Rind Mathematical Papyrus

Boisseau = scheffel = bushel

Ägyptische Schrift 2900 – 100 acHieroglyphen = „Maschinen- oder Druckschrift“

Hieratisch = Handschrift, verbunden wird + unleserlichDemotisch = 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

3 8 9 2

1 1

8 6 2 3

Big problems with fractions Egyptians calculated with unit fractions (1/ n)

¾ wurde geschrieben ½ + ¼

6/7 wurde geschrieben ½ + ¼ + 1/14 + 1/28

For 2/3 the scribes had tables of the most commun z. B.

27 9

365 243 1/3

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

Das Auge des HorusWappentier der Ophthalmologie

Und was noch?