Egyptian Mathematics

1 Egyptian MathematicsOurfirst knowledge of mankind s use of Mathematics beyond merecounting comes from the Egyptians and Babylonians. Both civi-lizations developed Mathematics that was similar in some ways butdifferent in others. The Mathematics of egypt , at least what isknown from the papyri, can essentially be called applied was practical information communicated via example on how tosolve at GizaThis point, that Mathematics was communicated by example, ratherthan by principle, is significant and is different than today s mathe-matics that is communicated essentially by principle with examplesto illustrate principles.

2 The reasons for this are unknown but couldbe due partly to the fact that symbolism, the medium of principles,did not exist in these early times. Indeed, much of Mathematics formany centuries was communicated in this way. It may be much eas-ier to explain to a young student an algorithm to solve a problemand for them to learn to solve like problems, than to explain theabstract conceptfirst and basing examples upon this facts about ancient hieroglyphics are in great abundance throughout were essentially indecipherable until 1799 when in Alexandriathe trilingualRosetta Stonewas discovered.

3 The Rosetta stone,an irregularly shaped tablet of black basalt measuring about 3 feetEgypt29 inches by 2 feet 4 inches, was found near the town of Rosetta(Rashid) just a few miles northwest of Alexandria. Written in thetwo languages (Greek and Egyptian but three writing systems (hi-eroglyphics, its cursive form demotic script, and Greek, it providedthe key toward the deciphering of hieroglyphic writing. The inscrip-tions on it were the benefactions conferred by Ptolemy V Epiphanes(205 - 180 BCE) were written by the priests of Memphis. The trans-lation was primarily due to Thomas Young1(1773 - 1829) andTemple at Al KarnakJean Francois Champollion (1790-1832)2(1790-1832), who, veryearly in his life was inspired to Egyptology by the French math-ematician Jean Baptiste Joseph Fourier (1768 - 1830).))

4 Champollioncompleted the work begun by Youngand correctly deciphered thecomplete stone. An Egyptologist of thefirst rank, he was thefirst torecognize the signs could be alphabetic, syllabic, or determinative( standing for complete ideas)He also established the originallanguage of the Rosetta stone was Greek, and that the hieroglyphictext was a translation from the Greek. An unusual aspect of hiero-glyphics is that they can be1 English physician and physicist established the principle of interference of light and thusresurrected the century-old wave theory of historian and linguist who founded scientific Egyptology.

5 Academically prodigious,he had already mastered six ancient Oriental languages by the age of 16. At 19, he wasappointed professor of history at the lyc e of Grenoble, where he was to remain for eight hieroglyphics became his constant preoccupationEgypt3read from left to right, orright to left, or vertically(top to bottom). It is theorientation of the glyphs thatgives the clue; the directionof people and animals facetoward the beginning of the Egyptianswriting was an estheticexperience, and they viewedtheir writing signs as God swords.

6 This could explainthe unnecessary complexity,in face of the fact thatobviously simplificationswould certainly haveoccurred if writing weredesigned for all StoneThe demotic script was for more general use, the hieroglyphics con-tinued to be used for priestly and formal Egyptians established an annual calendar of 12 months of30 days each plusfive feast days. Religion was a central feature ofEgyptian society. There was a preoccupation with death. Manyof egypt s greatest monuments were tombs constructed at greatexpense, and which required detailed logistical calculations and atleast basic projects on a massive scale were routinely carriedout.

7 The logistics of construction require all sorts of will see several mensuration (measurement) problems, simplealgebra problems, and the methods for sources of Egyptian Mathematics are scarce. Indeed, much ofour knowledge of ancient Egyptian Mathematics comes not from thehieroglyphics3(carved sacred letters or sacred letters) inscribed onthe hundreds of temples but from two papyri containing collections3 The words hieroglyph or hieroglyphic are derived from the Greek wordsgrammatahieraorgrammata mathematical problems with their solutions.

8 TheRhind Mathematical (1833-1863) who purchased it at Luxor in 1858. Origin: 1650 BCEbut it was written very much earlier. It is 18 feet long and13 inches wide. It is also called theAhmes Papyrusafter thescribe that last copied it. TheMoscow Mathematical Papyruspurchased by V. S. Golen-ishchev (d. 1947). Origin: 1700 BC. It is 15 ft long and 3 incheswide. Two sections of this chapter offer highlights from , the writing material of ancient times, takes its name fromthe plant from which it is made. Long-cultivated in the Nile deltaregion in egypt , theCyperuspapyruswasgrownfor its stalk, whose innerpith was cut into thin stripsand laid at right angles and pressedtogether, the result wassmooth, thin, cream-coloredpapery sheets, normallyaboutfive to six incheswide.

9 To write on itbrushes or styli, reeds withcrushed tips, were dippedinto ink or colored the Duke Papyrus Archive*A remarkable number of papyri, some dating from 2,500 BCE,have been found, protected from decomposition by the dry heatof the region though they often lay unprotected in desert sands orburial tombs.* See the URL: and Arithmetic basicsThe Egyptian counting system wasdecimal. Though non positional,it could deal with numbers of great scale. Yet, there is no apparentway to construct numbers arbitrarily large. (Compare that withmodern systems, which is positional, which by its nature allows andeconomy for expressing huge numbers.)

10 The number system was decimal with special symbols for 1, 10,100, 1,000, 10,000, 100,000, and 1,000,000. Addition was accom-plished by grouping and regrouping. Multiplication and divisionwere essentially based on binary multiples. Fractions were ubiqui-tous but only unit fractions, with two exceptions, were allowed. Allother fractions were required to be written as a sum of unit was limited to areas, volumes, and similarity. Curiously,though, volume measures for the fractional portions of thehekata volume measuring about liters, were symbolically expresseddifferently from algebraic equations were solvable, even systems of equa-tions in two dimensions could be notation for vertical stroke10= heal bone100= a snare1,000= lotusflower10,000= a bentfinger100,000= a burbotfish1,000.